## 1. A SIR Model: Baseline

## Source details

**Canonical URL:** [1. A SIR Model: Baseline](https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020114-print-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2020/english/wpiea2020114-print-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2020/english/wpiea2020114-print-pdf.pdf.json)

---

### I. INTRODUCTION — pandemic context and core proposal
- COVID-19 first reported in Wuhan, China; resulted in "millions of cases and hundreds of thousands of deceased (Johns Hopkins University, 2020)".
- Global solution necessary to avoid re-importation ("whack-a-mole").
- Core proposal: universal testing and isolation at a rate of about "5–10 percent of the population per day" would:
  - lead to a rapid reopening of the economy;
  - prevent a second wave of the epidemic.
- Without smart testing strategies required daily testing rises to "20–30 percent of the population".
- Combining symptom-based "tests" (e.g., fever measurement) with other tests could reduce daily testing needs "substantially, below 5 percent of the population a day", at the cost of isolating many false positives.
- Recommended smart testing methods:
  - group testing (pooling individual samples);
  - periodic testing (e.g., blocks of population on a geographic grid) rather than purely random testing.
- Policy shift recommended: epidemiological rather than clinical testing—sacrifice some sensitivity/specificity for scalability, speed, and convenience.
- Candidate scalable tests: rapid serological tests for antibodies (IgM), antigen tests, point-of-care rapid molecular tests.
- TIP (True Industrial Policy) recommended to overcome market failures and rapidly scale test production.

### II. A RETURN TO NORMALCY — limits of waiting and costs of lockdowns
- Vaccine timelines uncertain; mutation evidence "adds even more uncertainty and increases the possibility of reinfections (Korber and others, 2020)".
- Lockdowns temporary and economically costly; only "37 percent of jobs can be done at home" in the U.S. (Dingel and Neiman, 2020); in Mexico and Turkey about "25 percent" of jobs can be done from home.
- June IMF estimate for global growth in 2020: "-4.9 percent", down from "3.3 percent" (January 2020) — loss in output in 2020 about "$10 trillion (in 2011 PPP dollars)".
- IMF (2020) estimated "$8 trillion (current dollars)" of fiscal stimulus injected into world economy.
- U.S. projections: IMF June WEO projects U.S. growth of about "-8 percent in 2020", compared to January projection of "2 percent" → potential output loss about "$2.1 trillion, or about $175 billion a month".
- Historical evidence: 1918 flu produced deadly second waves when restrictions lifted; cities that reintroduced restrictions reduced peak mortality (Bootsma and Ferguson, 2007; Hatchett, Mecher, and Lipsitch, 2007).

### III. TESTING AND ISOLATION POLICY — epidemiological framework and core mechanisms
- Epidemiological framework: SIR model with population N = S + I + R and dynamics:
  - Ṡ = -β SI/N
  - İ = β SI/N - γ I
  - Ṙ = γ I
  - Basic reproduction number R0 = β/γ.
- Baseline example: R0 ≈ 3 (infections double every five days); other estimates up to 5.7 (doubling every 3 days).
- Universal testing model parameters and effective testing rate:
  - At each period a proportion t* of the population is randomly tested (n = t* N).
  - False negative probability = z; quarantine leakage proportion = e.
  - Effective testing/isolation rate:
    - t = (1 - e)(1 - z) t* = (1 - q) t*                                                        (2)
  - Leakage q assumed to be 25 percent in simulations.
- Quarantine dynamics with Q quarantined: proportion infected becomes I/(N-Q); expected number quarantined equals t N I/(N-Q).

### IV. MODELING RESULTS AND SCENARIOS — quantitative simulation outcomes
- Initial conditions used in simulations: 5 percent infected, 10 percent recovered, no one quarantined.
- Baseline R0 = 3 scenarios:
  - Testing rate 20 percent of population a day:
    - Threshold of one infected in a thousand reached in about two months.
    - Susceptible population share falls from 85 percent to about 60 percent.
  - Testing rate 30 percent:
    - Takes a little over a month to reach one in a thousand infected.
    - Susceptible share about 73 percent.
- With R0 = 0.75 (lockdown/squash curve) comparable targets reached about two months faster than R0 = 3 with 20–30 percent testing.
- Combining social distancing (R0 = 1.5) with testing:
  - 30 percent testing rate: a little over two weeks to reach one in a thousand infected; susceptible share 83 percent.
  - 20 percent testing rate: about a month to reach one in a thousand; susceptible share 80 percent.
- Tests needed for a large country example (initial I = 5 percent, effective identifying rate 15 percent): initial tests/day needed ≈ 66 million (20 percent of population) to squash the epidemic relatively fast.
- Phase-two with mobility (after lifting lockdown) simulations:
  - Phase-two initial I' = one in a thousand, recovered = 15 percent, R0 reverting to 3.
  - Mortality-relative metric ρ:
    - Testing and isolation: ρ = 8.2.
    - Standard SIR: ρ = 77.
    - SIR with full mobility: ρ = 81.7.
  - Travel restriction scenarios:
    - Reducing movement across grids by 25 percent (off-diagonal α = 0.75) → ρ = 4.4.
    - Focusing restrictions on the hub → ρ = 1.02 (approximate seasonal influenza mortality target μ = 0.2 percent in U.S. example).

### V. SMART TESTING STRATEGIES — periodic, group, staggered, and hubs
- Periodic versus random testing:
  - With 20 percent random testing, about a quarter chance same individual tested more than once within a 5-day window.
  - Cleevely and others (2020): efficiency gain 37 percent with periodic vs random testing.
  - In SIR model: 20 percent random ≈ slightly less than 10 percent periodic; efficiency gains over 50 percent claimed.
- Group testing (pooling) examples:
  - Example: 5000 people, groups of 10, infected prevalence 1 percent → group negative prob ≈ 0.904 → ~10 percent groups positive → retest 50 groups → additional 500 tests → total 1000 tests → ~fivefold gain (~80 percent reduction).
  - Shental and others (2020) observed an eightfold gain using 384 samples and 48 pools.
- Combined gains:
  - Periodic + group testing could reduce required tests from 20–30 percent daily to the order of 2–3 percent daily given sufficient test accuracy.
- Staggered and targeted testing:
  - Prioritize metropolitan centers/hubs then sweep grids.
  - Example: with 5 percent initial infected, R0 = 3, 10 percent population-per-day testing rate, and 50 percent of tested negatives staying at home → epidemic squashed within 20 days instead of three months.
- Complementary measures to reduce tests needed:
  - Light NPIs: distancing, masks, temperature checks.
  - Stronger NPIs if feasible: staggered work/school times, quarantining infected outside homes.
  - Testing at points of departure (airports) with reimbursement/clause mechanisms.

### VI. EPIDEMIOLOGICAL TESTING TRADEOFFS — accuracy, false negatives/positives, and numeric examples
- Effective testing relation reiterated:
  - t = (1 - e)(1 - z) t*                                                            (9)
  - t* = share of people tested per day; e = noncompliance with isolation; z = false negative rate.
- Numerical tradeoff example:
  - If t* = 40 percent, e = 20 percent, test could have false negatives up to 37.5 percent and still reach effective t > 20 percent.
- False positives and economic cost formula:
  - Expected share of susceptible incorrectly quarantined f = (1 - e) s t* S / N                                                            (10)
  - Example: false positive rate s = 10 percent, susceptible share = 80 percent, t* = 40 percent → f ≈ 2.5 percent of population quarantined.
- Candidate epidemiological tests and costs:
  - Serological rapid tests cost about $2–$5 (de Walque and others, 2020) with 15-minute results; a $1 test under development (Bradley, 2020).
  - Administering cost per test ≈ $5:
    - Global population ≈ 7.7 billion → 23 billion tests a month (equivalent to 10 percent periodic testing of population daily) → cost ≈ 115 billion dollars a month (less than one week of global output loss).
  - Diagnostic group testing (periodic + group testing ≈ 5 percent daily) with cost ≈ $20 per test (including related costs) → about a quarter of a trillion dollars a month (still below two weeks of global output loss).
  - $1 per test possibility would make strategy a fraction of monthly global output loss.

### VII. LIMITATIONS OF CONTACT TRACING AND NEED FOR TESTING IN DENSE SETTINGS
- High prevalence and presymptomatic/asymptomatic transmission reduce effectiveness of contact tracing:
  - Presymptomatic/asymptomatic infections constitute "more than half of all infections (Ferretti and others, 2020)".
  - Kucharski and others (2020): over 25 contacts may need tracing per new infected.
  - With R ≈ 1.5, more than 50 percent of contacts need tracing/quarantining; with R0 = 2, 75–90 percent of contacts required.
- Conclusion: universal testing and isolation is essential in dense urban settings and developing-country contexts where tracing alone is infeasible.

### VIII. MARKET FAILURES, INDUSTRIAL POLICY (TIP), AND PRODUCTION STRATEGY
- Market failures identified: uncertainty, capacity constraints, coordination failures, externalities, market power.
- TIP principles and implementation elements:
  - Clear numerical targets (e.g., scalable epidemiological test for 20–30 percent of population per day, or 5–10 percent with periodic/group testing).
  - Organize and coordinate public and private resources across whole value chain (reagents, swabs, machinery, logistics).
  - Share knowledge; state assumes risk; redesign/build manufacturing facilities quickly; pool resources for economies of scale.
  - Institutions: high-level taskforce reporting to top council involving science, treasury, central bank, development bank, and private sector.
  - Incentives and accountability: taskforce authority to change incentives, enforce quality/quantity commitments, and provide financing.
- Policy tools suggested: patent pooling, compulsory licensing, mandated reorientation of existing firms, GOCO plants, guaranteed procurement/demand, development bank financing, tax breaks, loan guarantees, prizes.
- Rationale for local production in developing countries: faster access to tests, lower dependence on imports, preparation for vaccine production, potential manufacturing renaissance.

### IX. POLICY RECOMMENDATIONS — operational exit strategy components
- Implement universal testing and isolation strategy complemented by:
  - Prioritize development and deployment of scalable epidemiological tests (trade scale for accuracy when appropriate).
  - Combine testing with targeted travel restrictions (especially to hubs), light social distancing, and quarantining infected (preferably outside homes when feasible).
  - Use smart testing: periodic testing, group testing, staggered testing starting with metropolitan hubs and grids.
  - Establish a high-level TIP-style taskforce to coordinate production, remove bottlenecks, finance scale-up, manage IP, and enforce accountability.
  - Design early warning systems: continuous lower-scale testing, sewage surveillance, and tracing at low prevalence to avoid repeated mass-testing rounds.
  - Consider compulsory and free testing to correct coordination failures and externalities, with enforcement mechanisms (proof-of-testing for job/building access).
- Numerical objectives and tradeoffs emphasized:
  - Simulations suggest testing 20–30 percent of population daily would suffice to squash the epidemic and reopen the economy.
  - Periodic testing could reduce required daily testing to around 10 percent.
  - Combining group and periodic testing could reduce required rates to approximately 2–3 percent daily given sufficiently accurate tests.

### X. CONCLUSION — feasibility and imperative
- Large-scale testing and isolation presented as the only viable strategy to indefinitely “squash the curve” while allowing major economic activity to resume.
- Less than a billion tests per day globally required in principle; economies of scale make production costs small relative to repeated lockdown costs or uncontrolled spread.
- A shift to epidemiological testing, TIP-style state coordination, and smart testing strategies can make universal testing feasible and affordable, especially benefiting developing countries and strengthening long-term preparedness.

*Source: wpiea2020114-print-pdf - 1. A SIR Model: Baseline (IMF PDF).*

### 1. A SIR Model: Baseline ...............................................................................................

### 1. A SIR Model: Baseline

### Contained headings and related sections
- 1. A SIR Model: Baseline ..........................................................................................................9
- 2. Intervention: Social Distancing (10-day Lag and Immediate) .............................................10
- 3. The Second Wave of the Epidemic ......................................................................................11
- 4. U.S. Real GDP and Pre-2007 Trend (2010 $) .....................................................................13
- 5. SIR Model with a Quarantine: Initial R0=3 .........................................................................16
- 6. Phase Two with Mobility: Number of Infected (Initial R0=3) ............................................19
- 7. Travel Restrictions: Number of Infected (Initial R0=3) ......................................................20

*Source: wpiea2020114-print-pdf - 1. A SIR Model: Baseline (IMF PDF).*

### References .............................................................................................................

### I.   INTRODUCTION

### Pandemic context and problem statement
- COVID-19 first reported in Wuhan, China, spread rapidly in early months of 2020; resulted in "millions of cases and hundreds of thousands of deceased (Johns Hopkins University, 2020)".
- Pandemic requires a global solution because a "whack-a-mole" strategy risks re-importing the virus.
- Current measures (national lockdowns, social distancing) have produced extraordinary strains on health care and unprecedented economic fallouts.

### Core proposal: universal testing and isolation
- Universal testing and isolation at a rate of about "5–10 percent of the population per day" would:
  - lead to a rapid reopening of the economy;
  - prevent a second wave of the epidemic.
- In densely populated areas, testing policy should account for movement patterns, especially commuting; measures discouraging mobility to hubs or urban centers increase testing efficiency while largely preserving economic activity.
- "Smart" testing strategies recommended:
  - group testing (pooling individual samples);
  - periodic testing (e.g., blocks of population on a geographic grid) rather than purely random testing.
- Without smart testing strategies the required daily testing rate would increase to "20–30 percent of the population".
- Combining symptom-based "tests" (e.g., fever measurement) with other tests could reduce daily testing needs "substantially, below 5 percent of the population a day", at the cost of isolating many false positives but still much cheaper than lockdowns.

### Testing technology and epidemiological vs clinical approach
- Policymakers should adopt:
  - an epidemiological rather than clinical approach to testing, sacrificing accuracy (sensitivity and specificity) for scalability, convenience, and speed;
  - an industrial policy to tackle market failures and ramp up production quickly.
- Candidate tests for scalability: rapid serological tests for antibodies (IgM), antigen tests similar to pregnancy tests, point-of-care rapid molecular tests.
- Epidemiological aim: regularly identify and isolate enough infected individuals rather than provide a precise clinical diagnosis.

### Complementary and transitional measures
- While ramping up test-kit supply, optimize by:
  - prioritizing potential infection clusters or hubs (hospitals, senior housing, prisons, grocery stores, schools, public gatherings, etc.);
  - light non-pharmaceutical interventions (NPI) such as distancing in public and mask wearing.
- Evidence: about "20 percent of the infected generates about 80 percent of the transmission due to superspreader events (Adam and Cowling, 2020)".

### Industrial policy (True Industrial Policy, TIP) to scale production
- Market failures (uncertainty, capacity constraints, coordination failures, externalities, market power) prevent private-sector-only rapid scale-up.
- Proposed intervention: a "True Industrial Policy (TIP) (Cherif and Hasanov, 2019)" to solve market failures effectively and fast.
- Key TIP principles: create capabilities in sophisticated products with competition (domestic and international) and accountability for support received.
- Implementation elements:
  - organize and coordinate public and private resources across whole value chain for medical products for testing;
  - share knowledge and have the state assume risk;
  - redesign or build manufacturing facilities quickly;
  - pool resources to achieve economies of scale.
- International institutions could help developing countries pool resources and capabilities.

### Development opportunity and broader benefits
- Production mobilization for testing is an opportunity for developing countries to:
  - jumpstart or expand manufacturing capabilities;
  - prepare for future vaccine production.
- Benefits: mitigates short-term economic fallout (lockdowns, decline in tourism and commodity revenues) and paves way for long-term growth via manufacturing capability creation.

---

### II.   A RETURN TO NORMALCY

### Limits of waiting for vaccine or cure
- Vaccine and cure timelines are uncertain despite rapid global scientific collaboration; clinical trials for vaccines and drugs started in mid-March 2020 after the genetic sequence was published on January 11, 2020.
- Virus mutation evidence "adds even more uncertainty and increases the possibility of reinfections (Korber and others, 2020)".
- For developing countries lacking production capabilities, discovery is only first step; securing quantities needed can be a long, difficult process (Okonjo-Iweala, 2020).

### Lockdowns: temporary measure with high cost
- Most countries resorted to lockdowns to "flatten the curve"; such measures are temporary and cannot prevent resurgence.
- Perfect eradication via lockdown is nearly impossible because essential workers continue operations.
- In the U.S., "only 37 percent of jobs can be done at home", with much lower shares in developing countries (Dingel and Neiman, 2020).
- Lockdowns produce exorbitant economic fallout and cannot last beyond a few months without dramatic consequences.

### Policy objective reframing
- Debate should be about expanding how much economic activity can continue while keeping epidemic in check (Budish, 2020).
- Goal: a "return to normalcy" — keeping minimal restrictions on most economic activities.
- Policies solely relying on NPIs (lockdowns, distancing, contact tracing) are unlikely to fully reopen economies safely, especially in developing countries or advanced epidemic stages.

### Empirical examples where large-scale testing helped
- Korea: widespread testing slowed epidemic spread.
- Veneto (Italy) vs Lombardy: Veneto's large-scale testing including asymptomatic people slowed progression.
- Vo’ Euganeo (Veneto): virus wiped out within a fortnight after two rounds of universal testing and isolation (Zingales, 2020).
- Germany: some companies periodically test employees (e.g., weekly) to allow normal operations while keeping employees safe (Storbeck, 2020).
- Wuhan: tested whole population of 7 million in 12 days to prevent a second wave (Fearnow, 2020).

### Asymptomatic/presymptomatic transmission supports universal testing
- Large proportion of presymptomatic and asymptomatic infections — "more than half of all infections (Ferretti and others, 2020)" — reduces effectiveness of symptomatic isolation and contact tracing.
- Epidemiological approach calls for testing all but symptomatic individuals; symptomatic screening (e.g., thermic cameras) can be used as interim epidemiological "tests".
- Contact tracing is ineffective unless done very early at low prevalence with extremely efficient tracing and fast quarantine (Peak and others, 2020; Hellewell and others, 2020).

### Current testing rates and feasibility debate
- By late June 2020, maximum daily (7-day rolling average) population testing rates: Luxembourg "0.9 percent", Bahrain and Iceland "0.5 percent", Denmark and Lithuania "0.25 percent" (Roser et. al., 2020).
- Many experts call for increased daily testing (Romer 2020a, 2020b; Siddarth and Weyl 2020; others), but no consensus on exact quantities; this work calls for higher random testing rates than Romer (2020b) and Siddarth and Weyl (2020) but fewer periodic tests than Romer (2020b).
- Perception of infeasibility stems from a clinical testing perspective and laissez-faire production; market failures block rapid scale-up.

### Comparison to wartime mobilization and relative cost
- Feasibility of rapid scale up likened to WWII war mobilization (building ammunition factories in 3 months).
- Monthly ramp up cost amounts on average to about "one to two weeks of global economic losses projected over 2020" — described as minuscule compared to wartime efforts.
- Number of test kits needed is only a fraction of soft drink cans consumed globally (about a trillion per year).
- With sufficient firm coordination and public funding, most countries could meet demand for tests in a matter of a few months.

---

### III.   TESTING AND ISOLATION POLICY

### Epidemiological modeling framework (SIR)
- Uses Susceptible, Infected, Recovered (SIR) compartmental model; population N = S + I + R (Hill and others, 2020).
- Simple SIR differential equations presented in the text (infection rate β, recovery rate γ):
  - Ṡ = -β SI/N
  - İ = β SI/N - γ I
  - Ṙ = γ I
- Basic reproduction number R0 = β/γ; if R0 > 1 outbreak grows, if R0 < 1 outbreak wanes.

### Baseline modeling assumptions and parameter examples
- Baseline example uses R0 ≈ 3, implying infections double every five days (consistent with Wuhan January 2020 data, Verity and others, 2020).
- Recent work suggests R0 in Wuhan could have been as high as 5.7, with infections doubling every 3 days (Sanche and others, 2020).

### Effects of social distancing vs lockdowns in SIR simulations
- Social distancing illustrated as 50 percent reduction in transmission, reducing R0 from 3 to 1.5; if R0 remains above one, epidemic not eradicated and will infect large share of population over time.
- Lockdown/squashing the curve illustrated as a 75 percent reduction in transmission, reducing R0 to 0.75; infection numbers dwindle rapidly but can take "a little over three months" to bring infected to about "one in a thousand".
- Timing matters: interventions closer to the peak have smaller effects; early interventions are more effective.

### Second wave risk and historical evidence
- Lifting NPIs while a large susceptible population remains can lead to a second wave (SIR simulation example: lifting lockdown after 40 days when infected ~ "one out of a hundred" leads to resurgence when R0 returns to 1.5 or 3).
- 1918 Flu Pandemic evidence: many U.S. cities experienced deadly second waves when restrictions were relaxed; cities that reintroduced restrictions when transmission rose reduced peak mortality rates (Strochlic and Champine, 2020; Bootsma and Ferguson, 2007; Hatchett, Mecher, and Lipsitch, 2007).
- Moore and others (2020): COVID-19 may persist for "the next couple of years" until vaccine arrives or "herd immunity of about 60 percent to 70 percent of population is achieved"; pandemic may manifest as waves and valleys or a slow burn.

### Economic cost of pandemic vs lockdowns
- June IMF estimate for global growth in 2020: "-4.9 percent", down from "3.3 percent" projected in January 2020 — loss in output in 2020 about "$10 trillion (in 2011 PPP dollars)".
- IMF (2020) estimated about "$8 trillion (current dollars)" of fiscal stimulus injected into world economy, mostly in advanced countries.
- U.S. example:
  - 2009 U.S. real output drop compared to pre-2007 trend: about "12 percent (about $1.7 trillion)".
  - By 2019, output had not recovered pre-2007 trend, resulting in losses of about "$2.8 trillion per year since 2008".
  - IMF June World Economic Outlook projects U.S. growth of about "-8 percent in 2020", compared to January projection of "2 percent", resulting in potential output loss of about "$2.1 trillion, or about $175 billion a month".
- Lockdowns may still be economically justified in the absence of alternatives (Eichenbaum, Rebelo, and Trabandt, 2020b); historical evidence (Correia, Luck, and Verner, 2020) suggests cities implementing early and aggressive restrictions experienced higher manufacturing growth after the 1918 pandemic.
- Economic and human costs of pandemic and lockdowns would be even greater in developing countries due to:
  - weaker health systems;
  - large informal sectors and smaller shares of jobs that can be done from home (e.g., about "25 percent in Mexico and Turkey" can work from home, Dingel and Neiman, 2020);
  - larger median family sizes living in small, crowded spaces with limited access to water/soap;
  - potential for civil strife if governments cannot rapidly deploy support.

*Source: Excerpt from IMF working paper content unit wpiea2020114-print-pdf*

### 2.1 percent of the global population. In many low-income countries, the devastation was

### wpiea2020114-print-pdf - 2.1 percent of the global population. In many low-income countries, the devastation was

### Historical impact and context
- 2.1 percent of the global population.  
- Killed more than 5 percent of the population in Kenya and India, and more than 3 percent in South Africa, Guatemala, and Indonesia (Barro, Ursua, and Weng, 2020).  
- More than 20 million orphaned children in sub-Saharan Africa estimated after the 1918 pandemic.

### Testing and isolation policy: core proposition
- Continuous universal testing and isolation is presented as a cost-effective strategy to “squash the curve” while lifting lockdowns quickly.  
- Prolonged lockdowns are described as infeasible and very costly; social distancing alone may not bring R0 below one.  
- Romer (2020a, 2020b) proposal cited: universal testing of the U.S. population on the order of about 7-7.5 percent per day (25 million people/day, or each person every two weeks), quarantining those with positive tests.  
  - Romer contends the cost should be less than 1 percent of GDP per year, about $100 billion in current dollars.  
  - Cost comparison: one month of lockdown estimated at $350–400 billion.  
- Other studies cited: about 20 percent a day may be needed for universal random testing to bring R0 below one (Cleevely and others, 2020; Siddarth and Weyl, 2020).

### SIR model with random testing and quarantine: assumptions and formulas
- At each period a proportion t* of the population is randomly tested (n = t* N).  
- Infected proportion p; probability of false negative = z. Expected successfully drawn infected in a draw without replacement: np(1-z).  
- Quarantine leakage: a proportion e escape quarantine. Effective testing/isolation rate t is:
  - t = (1 - e)(1 - z) t* = (1 - q) t*                                                        (2)
- Leakage q assumed to be 25 percent in simulations.
- With Q individuals quarantined, proportion of infected becomes I/(N-Q) and expected number quarantined equals t N I/(N-Q) (Equation 3).

### Simulation scenarios and key quantitative outcomes
- Initial conditions for simulations: 5 percent infected, 10 percent recovered, no one quarantined.
- Scenario (i): systematic isolation and testing policy without social distancing. Scenario (ii): combination of social distancing and testing/isolation.
- Results with initial R0 = 3:
  - Testing rate of 20 percent of the population a day:
    - Threshold of one infected in a thousand is reached in about two months.
    - Susceptible population share falls from 85 percent to about 60 percent (many became infected).
  - Testing rate of 30 percent:
    - Takes a little over a month to reach one in a thousand infected.
    - Susceptible share higher at about 73 percent; overall fewer infected.
  - Comparable scenario with R0 = 0.75 reaches one in a thousand about two months faster than R0 = 3 with 20–30 percent testing rates.
- Combining social distancing (R0 = 1.5) with testing:
  - With 30 percent testing rate: a little over two weeks to reach one in a thousand infected; susceptible share at 83 percent.
  - With 20 percent testing rate: about a month to reach one in a thousand; susceptible share falls to 80 percent.
- Tests needed for a large country (e.g., U.S.) to squash the epidemic within a month:
  - With initial infected share 5 percent and a 15 percent effective rate of identifying infected, initial number of tests a day needed is 66 million (20 percent of population) to squash the epidemic relatively fast.

### Mobility, grids, hubs, and second-wave risk
- Model extended to K+1 grids with Origin-Destination matrix C and movement restriction matrix α (elements in [0,1], diagonal = 1).  
- Mobility increases implicit transmission; critical role of hubs in densely populated areas emphasized.
- Stylized four-grid OD matrix used for simulations:
  - C = [ [8 5 5 5 5], [4 5 4 5 5 5], [5 5 5 3 5 5], [5 5 1 0 1 0 2 5] ]  (as in source; OD matrix presented in text)
- Phase-two simulations (after lockdown lifted) with initial I' = one in a thousand, recovered = 15 percent, R0 reverting to 3:
  - Comparison: standard SIR (no mobility), SIR with full mobility (α = 1), and SIR with full mobility plus testing & isolation.
  - Mortality relative metric ρ:
    - Testing and isolation: ρ = 8.2.
    - Standard SIR: ρ = 77.
    - SIR with full mobility: ρ = 81.7.
- Travel restriction scenarios and mortality:
  - Reducing movement across grids by 25 percent (off-diagonal α = 0.75) → ρ = 4.4.
  - Focusing restrictions on the hub (restricting movement to the hub) → ρ = 1.02 (approximates seasonal influenza mortality target, μ = 0.2 percent in U.S. example).
- Key policy insight: combining massive testing and targeted travel restrictions (especially to hubs) can achieve much lower mortality while imposing lighter economic burdens than blanket social distancing.

### Smart testing strategies and efficiency gains
- Periodic testing (vs random):
  - With a 20 percent random testing rate, about a quarter chance the same individual tested more than once within a 5-day window.
  - Cleevely and others (2020): efficiency gain of 37 percent with periodic vs random testing.
  - In SIR model: 20 percent random ≈ slightly less than 10 percent periodic testing; efficiency gains over 50 percent.
- Group testing:
  - Example: 5000 people, groups of 10 → 500 groups; infected prevalence 1 percent ⇒ group negative probability ≈ 0.904 (0.99^10); ~10 percent groups positive → retest 50 groups → additional 500 tests → total 1000 tests → ~fivefold gain (~80 percent reduction).
  - Shental and others (2020) observed an eightfold gain using 384 samples and 48 pools.
  - Formula structure provided for tests per group and gains (sensitivity of group testing to test specificity and false positives noted).
- Combined gains:
  - Periodic + group testing could reduce tests from 20–30 percent of population daily to the order of 2–3 percent, provided test accuracy is sufficient.
- Staggered testing:
  - Prioritize metropolitan centers and then sweep grids; example: with 5 percent initial infected, R0 = 3, 10 percent population-per-day testing rate, and 50 percent of tested negatives staying at home, epidemic squashed within 20 days instead of three months.
- Other complements to reduce required tests:
  - Light interventions: distancing, masks, temperature checks.
  - Stronger interventions: staggered work/school times, quarantining infected outside homes.
  - Testing at points of departure (airports) with reimbursement/clause mechanisms suggested.

### Epidemiological (probabilistic) testing approach: tradeoffs and numeric examples
- Shift from clinical-standard tests (very low error margins) toward epidemiological tests that trade accuracy for scale, speed, convenience, and cost.
- Effective testing rate relation reiterated:
  - t = (1 - e)(1 - z) t*                                                            (9)
  - t* = share of people tested per day; e = noncompliance with isolation; z = false negative rate.
- Numerical tradeoff example:
  - If t* = 40 percent, e = 20 percent, test could have false negatives up to 37.5 percent and still reach effective t > 20 percent.
- False positives and economic costs:
  - Expected share of susceptible incorrectly quarantined f = (1 - e) s t* S / N                                                            (10)
  - Example: false positive rate s = 10 percent, susceptible share = 80 percent, t* = 40 percent → f ≈ 2.5 percent of population quarantined.
- Candidate epidemiological tests:
  - Serological IgM tests (detect earlier antibodies), rapid antigen tests, point-of-care rapid molecular tests; examples of cost and characteristics provided:
    - Serological rapid tests cost about $2–$5 (de Walque and others, 2020) and can yield results within 15 minutes; a $1 test is being developed (Bradley, 2020).
  - Using multiple rapid tests on same individual could improve accuracy.
- Cost estimates for large-scale testing:
  - Administering cost per test ≈ $5 (de Walque and others, 2020):
    - Global population ≈ 7.7 billion → 23 billion tests a month (equivalent to 10 percent periodic testing of population daily) → cost ≈ 115 billion dollars a month (less than one week of global output loss).
  - Diagnostic group testing (periodic + group testing ≈ 5 percent of population daily) with cost ≈ $20 per test (including related costs) → about a quarter of a trillion dollars a month (still below two weeks of global output loss).
  - $1 per test possibility would make the testing strategy a fraction of monthly global output loss.

### Limitations of contact tracing and role of testing in dense settings
- Contact tracing effective only at very low prevalence and requires extreme efficiency:
  - Kucharski and others (2020): over 25 contacts may need tracing per new infected.
  - With presymptomatic/asymptomatic cases accounting for half or more of infections, tracing becomes daunting.
  - Peak contagion often occurs before symptom onset (Ferretti and others, 2020).
  - With R ≈ 1.5, more than 50 percent of contacts need tracing and quarantining to reduce reproductive number close to 1; with R0 = 2, this increases to 75–90 percent of contacts.
  - Delays of 2–3 days in tracing make little difference; mobile apps help but require early and large-scale deployment.
- Conclusion: universal testing and isolation is essential especially in densely populated and developing-country urban contexts where tracing alone is insufficient.

### Market failures, capacity, and the need for state coordination
- Market alone may fail to deliver required test volumes due to capacity constraints, uncertainty, coordination failures, and short-term profit incentives. Key observations:
  - Firms face uncertainty and risk of overinvestment; historical precedent: post-2009 H1N1 excess vaccine capacity led to losses.
  - Ramping up production requires coordinating entire value chain (reagents, swabs, machinery, logistics), expedited regulatory action, and resolving IP/knowledge barriers.
  - Policy tools suggested:
    - Patent pooling, compulsory licensing if needed, mandated reorientation of existing firms, use of GOCO (government-owned, contractor-operated) plants, guaranteed procurement/demand, financing via development banks, tax breaks, loan guarantees, prizes.
  - Compulsory free testing for all recommended to resolve coordination failure and positive externality; enforcement via proof-of-testing for jobs/building entry suggested.
- “True Industrial Policy” (TIP) principles proposed:
  - Objective: clear numerical targets (e.g., select scalable epidemiological test for 20–30 percent of population per day, produce tests on the order of 5–10 percent of population a day), deadlines, endgame (e.g., virus free within two weeks then early warning system).  
  - Institutions: high-level taskforce reporting to top council, involving science, treasury, central bank, development bank, and private sector.  
  - Incentives and accountability: taskforce authority to change incentives and enforce quality/quantity commitments; access to financing; information-sharing across firms and levels.  
- Historical parallel and lessons from WWII mobilization cited to argue feasibility of large production ramp-up and state coordination.

### Why developing countries should pursue local production
- Developing countries risk being left out of global testing supply if they do not build local capacity. Benefits highlighted:
  - Faster access to tests, lower dependence on imports, capacity for vaccine production in future, potential manufacturing renaissance reversing premature deindustrialization.
  - Emerging economies have higher likelihood of success than low-income countries but regional coordination and international assistance could help smaller countries.
  - Example innovations from developing countries: a test by Senegalese National Institute for Health and a British biotech possibly costing as little as $1.

### Policy recommendations and practical exit strategy components
- Implement a universal testing and isolation strategy with supportive measures:
  - Prioritize development and deployment of scalable epidemiological tests (trade scale for accuracy when appropriate).  
  - Combine testing with targeted travel restrictions (to hubs), light social distancing, and quarantine of infected (preferably outside homes when feasible).  
  - Use smart testing: periodic testing, group testing, staggered testing starting with metropolitan hubs and grids.  
  - Establish high-level taskforce and TIP-style industrial policy to coordinate production, remove bottlenecks, ensure financing, manage IP, and enforce accountability.  
  - Design early warning systems (continuous lower-scale testing, sewage surveillance, tracing at low prevalence) to avoid repeated mass-testing rounds.  
  - Consider compulsory and free testing to correct coordination failures and externalities, with enforcement mechanisms (proof of testing for job/building access).  
- Numerical targets and tradeoffs emphasized:
  - Simulations suggest testing 20–30 percent of population daily would suffice to squash the epidemic and reopen the economy; periodic testing could reduce required daily testing to around 10 percent; with group and periodic testing combined, achievable rates could be around 2–3 percent daily given sufficiently accurate tests.

### Conclusion: feasibility and imperative
- Large-scale testing and isolation is presented as the only viable strategy to indefinitely “squash the curve” while allowing major economic activity to resume.  
- Less than a billion tests per day globally are required in principle; economies of scale make production costs small relative to costs of repeated lockdowns or uncontrolled spread.  
- A shift toward an epidemiological testing approach, TIP-style state coordination, and smart testing strategies can make universal testing feasible and affordable, particularly benefiting developing countries and contributing to long-term epidemic preparedness.

*Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020114-print-pdf.pdf*

### REFERENCES

### REFERENCES

### Major topics covered
- Infectious-disease modeling and epidemiology
  - “A Multi-SIR Model with Optimally Targeted Lockdown.” NBER Working Paper 27102.
  - “An SEIR Infectious Disease Model with Testing and Conditional Quarantine.” Manuscript, Duke University, March.
  - “The Macroeconomics of Epidemics.” NBER Working Paper 26882, April.
  - “Quantifying SARS-CoV-2 transmission suggests epidemic control with digital contact tracing.” Science 368 (6491), May 8.
  - “Feasibility of Controlling COVID-19 Outbreaks by Isolation of Cases and Contacts.” The Lancet Global Health 8(4), April: E488-E496.
  - “Estimates of the Severity of COVID-19 Disease.” medRxiv, March.

- Testing, tracing, and screening strategies
  - “COVID-19 Testing for Testing Times: Fostering Economic Recovery and Preparing for the Second Wave.” VoxEU. March 26.
  - “A workable strategy for Covid-19 testing: Stratified periodic testing rather than universal random testing.” COVID Economics, Vetted and Real-Time Papers 8, CEPR, April 22.
  - “Group Testing Against Covid-19.” COVID Economics, Vetted and Real-Time Papers 2, CEPR, April 8.
  - “Why We Must Test Millions a Day.” Edmond J. Safra Center for Ethics, Harvard University, April 8.
  - “How Two Tests Can Help Contain COVID-19 and Revive the Economy.” Research and Policy Briefs. The World Bank. April 8.

- Non-pharmaceutical interventions and historical pandemic evidence
  - “Public Health Interventions and Epidemic Intensity During the 1918 Influenza Pandemic.” PNAS, May 1, 104 (18): 7582-7587.
  - “The Effect of Public Health Measures on the 1918 Influenza Pandemic in U.S. Cities.” PNAS, May 1, 104 (18): 7588-7593.
  - “Pandemics Depress the Economy, Public Health Interventions Do Not: Evidence from the 1918 Flu.” March. Working paper.
  - “How Some Cities ‘Flattened the Curve’ During the 1918 Flu Pandemic.” National Geographic. March 27.

- Economic policy responses, mobilization, and industrial policy
  - “The Public Role in Economic Transformation: Lessons from World War II.” Roosevelt Institute working paper, March.
  - “The Quintessential Mobilization Economy.” (series of pieces cited by author, 2018).
  - “The Return of the Policy That Shall Not Be Named: Principles of Industrial Policy,” IMF Working Paper 19/074.
  - Fiscal Monitor. April. International Monetary Fund (IMF). 2020.

- Vaccine, therapeutics, and supply-chain capacity
  - “Drugmakers Race to Scale Up Vaccine Capacity.” Financial Times. April 27.
  - “The Quest for a Vaccine Could Restore Faith in Big Pharma.” The Economist. June 6.
  - “Patents vs. the Pandemic.” Project Syndicate. April 23.
  - “Diagnostic Detection of 2019-nCoV by Real-Time RT-PCR.” January 17. World Health Organization.
  - “The Global Use of Medicine in 2019 and Outlook to 2023: Forecasts and Areas to Watch.” The IQVIA Institute. 2019.

### Policy-relevant findings and recommendations (as reflected in cited works)
- Testing and tracing are central to containment and economic reopening strategies:
  - Stratified periodic testing and group testing are proposed alternatives to universal random testing.
  - Combining multiple test modalities (“How Two Tests Can Help Contain COVID-19 and Revive the Economy”) can support containment while enabling economic activity.
  - Digital contact tracing can contribute to epidemic control (Science 368 (6491), May 8).

- Targeted non-pharmaceutical interventions informed by modeling can reduce transmission while limiting economic costs:
  - Isolation, testing, contact tracing, and physical distancing reduce transmission in different settings (MedRxiv; The Lancet Infectious Diseases).
  - Age-specific and targeted lockdown policies are examined (NBER Working Paper 27102; working papers on age-specific policies).

- Historical mobilization and industrial policy lessons can inform supply-side responses:
  - World War II mobilization and production lessons are cited as analogies for rapid scaling of production capacity for medical supplies and vaccines.
  - Industrial policy principles and public role in economic transformation are referenced for accelerating production and innovation.

### Methodologies, data sources, and empirical approaches represented
- Compartmental epidemic models: SIR, SEIR, multi-SIR extensions, and agent-based models.
- Empirical historical analyses using 1918 influenza pandemic data (PNAS studies).
- Working papers and rapid preprints: NBER, CEPR COVID Economics series, medRxiv, BioRxiv.
- Real-world data sources and dashboards: “Coronavirus Resource Center.” The Center for Systems Science and Engineering, Johns Hopkins University.
- Policy briefs and opinion pieces complementing academic analyses (Project Syndicate, Vox, The New York Times, The Economist, Financial Times).

### Representative numeric and bibliographic identifiers preserved exactly
- NBER Working Paper 27102.
- NBER Working Paper 26882.
- CEPR Working Paper 14688, May.
- COVID Economics, Vetted and Real-Time Papers 11, CEPR, April 29.
- COVID Economics, Vetted and Real-Time Papers 8, CEPR, April 22.
- COVID Economics, Vetted and Real-Time Papers 2, CEPR, April 8.
- PNAS, May 1, 104 (18): 7588-7593.
- PNAS, May 1, 104 (18): 7582-7587.
- The Lancet Global Health 8(4), April: E488-E496.
- Science 368 (6491), May 8.
- “Systematic Review of the Impact of Point-of-care Testing for Influenza on the Outcomes of Patients with Acute Respiratory Tract Infection.” 2018. Reviews in Medical Virology 28(5).
- “Historical Reference of Seasonal Influenza Vaccine Doses Distributed.” CDC. 2019.
- “The Global Use of Medicine in 2019 and Outlook to 2023: Forecasts and Areas to Watch.” The IQVIA Institute. 2019.

*References list extracted from the source PDF: wpiea2020114-print-pdf - REFERENCES*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020114-print-pdf.pdf_