## Section 3 — Main results across mitigation policy scenarios

## Source details

**Canonical URL:** [Section 3 — Main results across mitigation policy scenarios](https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020233-print-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2020/english/wpiea2020233-print-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2020/english/wpiea2020233-print-pdf.pdf.json)

---

### Overview of model and purpose
- Integrated epidemiological-macroeconomic model extending SIR to SEIRQD with daily frequency and distinction between diagnosed and undiagnosed infected individuals.
- Purpose: simulate specific mitigation policies to quantify health versus economic tradeoffs from COVID-19.
- Noted limitations: abstraction from capital services; no explicit household tradeoff between consumption and savings or between consumption and labor; no external sector considerations; absence of detailed monetary and fiscal policy transmission.

### Epidemiological block: states, flows, and key parameters
- Health states: susceptible (S); undiagnosed infected latent (UIL); undiagnosed infected infectious (UII); undiagnosed infected non-infectious (UINI); diagnosed infected quarantined/isolated (Q); recovered (R); dead (D).
- Population identity:
  - T(t) = S(t) + UIL(t) + UII(t) + UINI(t) + Q(t) + R(t) + D(t)     (1)
- Infection process:
  - Three infection sources j ∈ {L, C, RM} (labor, consumption, random meetings).
  - New susceptible change:
    - ∆S(t) = −β(t) γ(t) ∑_j ω_j α_j(t)_j · [1 − κ · τ(t)]     (2)
  - Definitions: β = probability of infection given a contact; γ = contact frequency; ω_j = relative shares of infections’ originations; α_j = modality of contact by activity; τ(t) = (UIL(t) + UII(t) + UINI(t) + Q(t)) / T(t); κ = sensitivity parameter governing voluntary social distancing.
- Discrete-time flows:
  - ∆UIL(t) = β(t) γ(t) ∑_j ω_j α_j(t)_j · [1 − κ · τ(t)] − UIL(t)/χ − φ(t) UIL(t)/δ     (3)
  - ∆UII(t) = UIL(t)/χ + M(t) − φ(t) UII(t)/δ − UII(t)/σ − ρ UII(t)     (4)
  - ∆UINI(t) = UII(t)/σ − φ(t) UINI(t)/δ − ψ UINI(t)     (5)
  - ∆Q(t) = φ(t) (UIL(t) + UII(t) + UINI(t))/δ − ρ Q(t) − ψ Q(t)     (6)
  - ∆R(t) = ψ UINI(t) + ψ Q(t)     (7)
  - ∆D(t) = ρ UII(t) + ρ Q(t)     (8)
- Key modeling assumptions:
  - Only UII transmit the virus.
  - Diagnosed infectious (Q) are fully compliant with isolation and do not create new infections.
  - Voluntary behavioral response captured via κ and τ(t).

### Macroeconomic block: production, labor, and lockdown
- Output by labor under log-linear production function; abstraction from capital and intertemporal household decisions:
  - Y(t) = Z(t) L(t)
- Labor input L aggregates contributions from each health group i with working-age shares and voluntary distancing:
  - Y(t) = Z(t) ∑_i (t)_i · washare_i(t) · emplrate_i(t) · sharework_i(t)_i · [1 − κ · τ(t)]
- Z(t) used to simulate investment in digital equipment for teleworking; sharework_i used to simulate targeted labor market restrictions (“smart containment”).
- Lockdown formulation (alternative to voluntary distancing κ=0):
  - Lockdown(t) = [1 − θ(t) · P(t)]     (10)
  - P = share of population subject to stay-at-home policy; θ = efficiency factor of lockdown.

### Calibration: representative country and epidemiological parameters
- Representative EMDE: Malaysia (population 32.4 million in 2018; nominal GDP US$364 billion in 2019; GDP per capita around US$11 thousand in 2019).
- Export shares in 2018: electrics and electronics 38 percent; petroleum 23 percent.
- Epidemiological parameter choices:
  - χ = 4 (days) latency period.
  - σ = 10 (days) duration of infectiousness.
  - Transition period from non-infectious to recovery = 21 (days); ψ = 1/21.
  - ρ = 0.0025 mortality rate.
  - β = 0.15 probability of infection given contact.
  - γ(t):
    - γ(t | t < 58) = 5
    - γ(t | t ≥ 58) = 2
    - Emergency state in Malaysia occurs at day 58.
  - δ = 5 (days) isolation delay.
  - φ0 = 0.05; φ1 = 10 for quarantine fraction φ(t) = φ0 · [1 − φ1 · τ(t)].
  - Infection shares by activity: ω_C = 0.17; ω_L = 0.33; ω_RM = 0.5.
- Macroeconomic calibration notes:
  - washare_i = 0.696 (69.6 percent).
  - emplrate_i = 0.668 (66.8 percent).
  - Baseline sharework_i: susceptible, UIL, and R work; UII and UINI: 50 percent work; Q restricted from labor market.
- Time-to-return-to-work implication:
  - 4 days latency + 10 days infectiousness + 21 days until full recovery ⇒ 35 days between contracting virus and returning to labor market.

### Calibration and behavioral parameter sensitivity
- Baseline sensitivity: κ = 1; baseline assumes no active lockdown policy: θ = 0 when κ = 1.
- Alternative calibration: κ = 0 and θ = 0.75 (lockdown efficiency compared with 0.5 and 0.9 benchmarks).
- Matching Malaysia (late-January to early-July 2020) parameter changes:
  - recovery duration = 18 days
  - isolation delay = 10 days
  - constant fraction quarantined = 60 percent
  - estimated contact frequency = 4.5069 persons
  - estimated probability of infection given contact = 0.1678
- κ and θ can be anchored to the Oxford COVID-19 Government Response Tracker “stringency index” and mobility data.

### Reference, baseline, and lockdown scenarios — core quantitative results
- Reference epidemiological model (κ=θ=0) — by end of one year:
  - about 1/3 of the population is infected
  - deaths represent about 0.8 percent of the population
  - economic costs: average annual GDP loss of about 2.2 percent
- Baseline model (behavioral response κ=1; θ=0):
  - voluntary social distancing reduces infections and deaths relative to reference but increases output loss
  - annual average GDP loss = 4.8 percent
  - sharpest output drop in the third and fourth months after the first case
  - infections peak at around 15 weeks
- Lockdown policy (exogenous P(t) rising to about 20 percent):
  - with θ = 0.75:
    - infection prevalence reduced to 23 percent
    - death rate reduced to 0.6 percent
    - output declines by 9 percent during the year
  - lower compliance (low θ) flattens recession trough by about 5 percentage points but yields higher disease prevalence and mortality
- Endogenizing θ:
  - θ(t) = θ · [1 + μ · ∆%Y(t)], where ∆%Y(t) = Y(t)/Y(0) ·100 − 100
  - Example: μ = 3 vs μ = 1 — average output loss during first year about 1 percentage point lower for μ = 3, while population share of deaths is 0.03 percentage points higher
  - In endogenous θ simulations voluntary distancing turned off (κ = 0) to minimize disease incidence

### Mitigation policies — effects and comparisons
- Enhanced social distancing (reduce effective contact frequency by 15 percent: from 2 to 1.7 persons per day for t ≥ 58):
  - total infection rate reduces to 10 percent of the population
  - death rate = 0.25 percent of the population
  - GDP declines by an annual average of less than 2 percent
- Targeted labor market restrictions (sharework changes):
  - UIL working share from 1 to 0.5; UII and UINI from 0.5 to 0.25
  - results: significant gains in both output and health outcomes, similar to improved social distancing
- Improved quarantine/isolation (double φ0 to 0.1 or halve δ to 2.5 days):
  - flattens both infection and recession curves relative to baseline
- Increasing telework capacity (increase Z by 2.5 percent over four months from emergency declaration):
  - contact frequency decreases proportionally to TFP change
  - results: less steep output decline, quicker recovery, slightly better infection prevalence and death rates

### Pandemic possibility frontier and tradeoffs
- Tradeoff shaped by κ; simulation grid κ ∈ [0,5] with step 0.5 for baseline and increased quarantine capacity scenarios.
- Entities with low death-risk tolerance: large contact curtailment → fewer deaths but larger output drop (north-west on frontier).
- Risk-taking entities: higher death rate but milder output drop (south-east on frontier).
- Increased quarantine capacity shifts frontier outward, improving both health and economic outcomes.

### Second infection wave, medical solutions, and temporary immunity
- Second-wave simulation: contact frequency increased to 2.5 starting day 200; horizon extended to 600 days.
  - resurgence leads to prevalence > 60 percent
  - fatality rate = 1.5 percent of the total population
  - generates a double dip recession; average output loss = 8 percent over the first year
- Policies deployed after day 230 (one month after second wave emerges); no formal cost-benefit ranking of policies provided.
- Finding: "the more the measures flatten the second infection curve, the more these measures are efficient at reducing the severity of the economic contraction."
- Medical solutions assumed to arrive at day 300:
  - Treatment: mortality reduced to zero; infected fully recover — mortality eliminated but infection curve and economic outcomes remain similar because transmission persists; model caveat that behavioral relaxation would raise infections but reduce economic damage under effective treatment.
  - Vaccine: no new infections; epidemic disappears once infected recover or die; output quickly rebounds once vaccine administered population-wide.
- Temporary immunity (finite λ) extension:
  - Introduce loss-of-immunity flow R(t)/λ back to susceptibles and amend equation (2) accordingly.
  - Example: λ = 90 days vs λ = ∞ — with λ = 90 days susceptible pool continually replenished; disease prevalence much higher and persistent; output loss very persistent.
  - Conclusion: temporary immunity increases importance of mitigation and medical research.

### Multisector extension: heterogeneity and substitutability
- N-sector framework with sector-specific κ_n and ω_n; sectoral behavioral sensitivity [1 − κ_n · τ(t)] in production.
- CES aggregator for final good with elasticity η.
- Two-sector illustrative calibrations:
  - Equal shares ω1 = ω2 = 0.5; contagion κ1 = 5, κ2 = 2.5 (sector 1 twice as contagious).
    - When η = 0.5 (complements), total output declines more.
    - When η = 3 (substitutes), total output declines less due to substitution toward less-affected sector.
    - Tradeoff: lower output loss implies more widespread infection and higher fatalities absent mitigation.
  - Concentrated activity ω1 = 0.75, ω2 = 0.25: substitutability provides limited buffer; total output decrease larger than equal-weights case.
- Policy implication: sector-specific policies (targeted lockdowns) are especially relevant when sectors are substitutable and more infectious activities can be restricted.

### Conclusion and policy messages
- Framework links epidemiological dynamics and macroeconomic outcomes, calibrated to EMDE features: limited healthcare/financial resources, reduced telework capacity, limited precautionary savings, high informality.
- Model features: multiple health states; government-mandated lockdowns with endogenous compliance; voluntary behavior changes; medical solutions; multisector reallocation.
- Main takeaways:
  - Simulations assess policy options to alleviate the tradeoff between saving lives and preserving economic outcomes.
  - Efficient containment policies can minimize adverse health outcomes while improving economic activity, particularly important with repeated infection waves or limited immunity.

*Source: wpiea2020233-print-pdf — Section 3 presents the main results across various mitigation policy scenarios. In Section 4 we present additional*

### Section 3 presents the main results across various mitigation policy scenarios. In Section 4 we present additional

### wpiea2020233-print-pdf - Section 3 presents the main results across various mitigation policy scenarios. In Section 4 we present additional

### Overview
- Presents an integrated epidemiological-macroeconomic model extending SIR to SEIRQD structure with daily frequency and differentiation between diagnosed and undiagnosed infected individuals.
- Model purpose: simulate specific mitigation policies to quantify health versus economic tradeoffs from COVID-19.
- Limitations noted: abstraction from capital services as a production factor; no explicit household tradeoff between consumption and savings or between consumption and labor; no external sector (open economy) considerations; absence of detailed monetary and fiscal policy transmission.

### Epidemiological block: health states and transitions
- Health states: susceptible (S); undiagnosed infected latent (UIL); undiagnosed infected infectious (UII); undiagnosed infected non-infectious (UINI); diagnosed infected quarantined/isolated (Q); recovered (R); dead (D).
- Total population:
  - T(t) = S(t) + UIL(t) + UII(t) + UINI(t) + Q(t) + R(t) + D(t)     (1)
- Infection process:
  - Three infection sources j ∈ {L, C, RM} (labor, consumption, random meetings).
  - New susceptible change:
    - ∆S(t) = −β(t) γ(t) ∑_j ω_j α_j(t)_j · [1 − κ · τ(t)]     (2)
  - Definitions:
    - β: probability of infection given a contact.
    - γ: contact frequency (time-varying).
    - ω_j: calibrate relative shares of infections’ originations.
    - α_j: modality of contact by activity (workplace, consumption, random meetings).
    - τ(t) = (UIL(t) + UII(t) + UINI(t) + Q(t)) / T(t): current fraction of infected population.
    - κ: sensitivity parameter governing voluntary social distancing; term [1 − κ · τ(t)] captures voluntary reduction in transmission.
- Latent, infectious, non-infectious, quarantined, recovered, dead dynamics (discrete time flows):
  - ∆UIL(t) = β(t) γ(t) ∑_j ω_j α_j(t)_j · [1 − κ · τ(t)] − UIL(t)/χ − φ(t) UIL(t)/δ     (3)
    - χ: latency period.
    - δ: isolation delay (average period to identify an infected person).
    - φ(t) = φ0 · [1 − φ1 · τ(t)]: time-varying quarantine fraction.
  - ∆UII(t) = UIL(t)/χ + M(t) − φ(t) UII(t)/δ − UII(t)/σ − ρ UII(t)     (4)
    - M(t): imported cases.
    - σ: period of infectiousness.
    - ρ: mortality rate.
  - ∆UINI(t) = UII(t)/σ − φ(t) UINI(t)/δ − ψ UINI(t)     (5)
    - ψ: recovery rate (inverse of transition period from non-infectious to recovered).
  - ∆Q(t) = φ(t) (UIL(t) + UII(t) + UINI(t))/δ − ρ Q(t) − ψ Q(t)     (6)
  - ∆R(t) = ψ UINI(t) + ψ Q(t)     (7)
  - ∆D(t) = ρ UII(t) + ρ Q(t)     (8)
- Key modeling assumptions:
  - Only undiagnosed infected infectious (UII) transmit the virus.
  - Diagnosed infectious individuals (Q) are fully compliant with isolation and do not create new infections.
  - Voluntary behavioral response incorporated via κ and τ(t), consistent with empirical findings linking mobility decline to reported cases.

### Macroeconomic block: production and labor
- Output determined by labor input under log-linear production function; abstraction from capital services and intertemporal household decisions.
- Total labor input L is sum of labor supplied by each health group i ∈ {S, UIL, UII, UINI, Q, R, D}, adjusted by working age population share, employment rate, share of persons in group i supplying labor services, and voluntary social distancing:
  - Y(t) = Z(t) L(t)
  - L(t) = ∑_i (t)_i · WAP_i(t) · L_i(t)/WAP_i(t) · sharework_i(t) · [1 − κ · τ(t)]_i
  - Equivalent specification used in text:
    - Y(t) = Z(t) ∑_i (t)_i · washare_i(t) · emplrate_i(t) · sharework_i(t)_i · [1 − κ · τ(t)]
  - Z(t): total factor productivity, used to simulate investment in digital equipment to facilitate teleworking.
  - sharework_i used to simulate targeted labor market restrictions (“smart containment”).
- Lockdown formulation (alternative to voluntary distancing κ=0):
  - Lockdown(t) = [1 − θ(t) · P(t)]     (10)
    - P: share of population subject to stay-at-home policy.
    - θ: efficiency factor of lockdown (time-varying to capture compliance changes).

### Model calibration: approach and representative country
- Malaysia chosen as representative EMDE for parameter calibration because relevant structural indicators numerically close to group averages.
  - Population: 32.4 million in 2018.
  - Nominal GDP: US$364 billion in 2019.
  - GDP per capita: around US$11 thousand in 2019.
  - Export shares in 2018: electrics and electronics 38 percent of total exports; petroleum 23 percent of total exports.
- Epidemiological parameter choices follow literature evidence and country-specific data where applicable (Table 1 in source).
  - Latency period χ = 4 (days).
  - Duration of infectiousness σ = 10 (days).
  - Transition period from non-infectious to recovery (inverse of ψ) calibrated at 21 (days).
  - Recovery rate ψ = 1/21.
  - Mortality rate ρ = 0.0025.
  - Probability of infection given contact β = 0.15.
  - Contact frequency γ(t):
    - γ(t | t < 58) = 5 (contact frequency before emergency state declared)
    - γ(t | t ≥ 58) = 2 (contact frequency after emergency state declared)
    - Emergency state in Malaysia occurs at day 58 in the calibration narrative.
  - Isolation delay δ = 5 (days).
  - Quarantine parameters:
    - φ0 = 0.05 (quarantine fraction under no infection)
    - φ1 = 10 (quarantine fraction sensitivity to infection rate)
  - Shares of new infections by activity:
    - ω_C = 0.17 (consumption)
    - ω_L = 0.33 (labor)
    - ω_RM = 0.5 (random meetings)
  - Rationale: for EMDEs, workplace-related infection share doubled relative to some AE calibrations to reflect labor informality and limited teleworking.
- Macroeconomic block calibration notes (Table 2 in source excerpts):
  - Working age share washare_i = 0.696 (69.6 percent).
  - Employment rate emplrate_i = 0.668 (66.8 percent).
  - Baseline assumptions on sharework_i:
    - Susceptible, unidentified latent, and recovered: work (assumed not sick or asymptomatic and able to work).
    - Undiagnosed infectious and non-infectious: 50 percent work (reflects undetected cases and asymptomatic workers).
    - Quarantined: restricted from labor market.
- Time-to-return-to-work implication:
  - 4 days latency + 10 days infectiousness + 21 days until full recovery ⇒ average 35 days between contracting the virus and returning to the labor market (as noted in source footnote).

*Source: wpiea2020233-print-pdf - Section 3 presents the main results across various mitigation policy scenarios. In Section 4 we present additional*

### 0.668 Employment rate

### 0.668 Employment rate

### Calibration and behavioral parameters
- Sensitivity of contact frequency to infection risk, 휅, set to 1 in baseline calibration; sensitivity analysis performed for other values.
- Baseline assumes no active lockdown policy: 휃 = 0 when 휅 = 1.
- Alternative calibration: 휅 = 0 (no voluntary behavioral change) and lockdown efficiency parameter 휃 = 0.75.
- Lockdown efficiency 휃 = 0.75 is compared to values 0.5 (Alvarez et al. (2020)) and 0.9 (Oxford COVID-19 Government Response Tracker for Malaysia Stringency Index).
- Matching epidemiological data for Malaysia (late-January to early-July 2020): parameter changes with respect to baseline calibration in Table 1 are:
  - recovery duration of 18 days
  - isolation delay of 10 days
  - constant fraction quarantined of 60 percent
  - (estimated) contact frequency of 4.5069 persons
  - (estimated) probability of infection given contact of 0.1678
- Both sensitivity parameter 휅 and lockdown efficiency 휃 can be anchored to (i) the Oxford COVID-19 Government Response Tracker “stringency index” and (ii) population mobility data.

### Matching exercise: Malaysia
- Model matches COVID-19 cases well during the initial period (first three months); cumulative measures worsen around days 120-130 (late-May to early-June) due to one-day spikes.
- Matching could be improved by allowing parameter break points or time variation in parameter values.

### Reference epidemiological model (휅=휃=0)
- By the end of one year:
  - about 1/3 of the population is infected
  - deaths represent about 0.8 percent of the population
- Economic costs: average annual GDP loss of about 2.2 percent.

### Baseline model (behavioral response, 휅=1; 휃=0)
- Voluntary social distancing reduces infections and deaths relative to reference model but increases output loss.
- For benchmark calibration (휅=1):
  - annual average GDP loss amounts to 4.8 percent
  - sharpest output drop in the third and fourth months after the first COVID-19 case
  - infections peak at around 15 weeks before slowly returning to equilibrium

### Lockdown policy (exogenous path of restricted interactions P(t))
- Policy specification: abrupt increase to about 20 percent of the population, followed by a slow return by the end of the simulation interval.
- Simulation with lockdown efficiency parameter 휃 = 0.75:
  - infection prevalence reduced to 23 percent
  - death rate reduced to 0.6 percent
  - output declines by 9 percent during the year
- Lower compliance (low 휃) produces a recession curve flatter by about 5 percentage points at the trough but with higher disease prevalence and mortality.
- Endogenizing lockdown efficiency:
  - 휃(t) = 휃 · [1 + μ · ∆%Y(t)], where ∆%Y(t) = Y(t)/Y(0) ·100 − 100
  - Higher μ implies stronger decline in compliance with larger output contractions.
  - Example: μ = 3 vs μ = 1 — average output loss during the first year is about 1 percentage point lower for μ = 3, while population share of deaths is 0.03 percentage points higher.
  - In simulations with endogenous 휃, voluntary social distancing channel is turned off (휅 = 0), which minimizes disease incidence.

### Mitigation policies: results and key statistics
- Enhanced social distancing (reduce effective contact frequency by 15 percent: from 2 to 1.7 persons per day for t ≥ 58):
  - total infection rate reduces to 10 percent of the population
  - death rate accounts for 0.25 percent of the population
  - GDP declines by an annual average of less than 2 percent
- Targeted labor market restrictions (change working shares):
  - undiagnosed latent (UIL) working share from 1 to 0.5
  - undiagnosed infectious (UII) and non-infectious (UINI) from 0.5 to 0.25
  - Results: significant gains in both output and health outcomes; improvements resemble those under better social distancing.
- Improved quarantine and isolation (double baseline quarantine fraction to 휙0 = 0.1; equivalent to halving isolation delay to 훿 = 2.5 days):
  - flattens both infection and recession curves relative to baseline.
- Increasing telework capacity (impose increase in TFP term Z of 2.5 percent over four months starting from declaration of emergency):
  - contact frequency decreased proportionally to change in TFP
  - results: less steep output decline, quicker recovery, slightly better infection prevalence and death rates.

### Capturing tradeoffs (pandemic possibility frontier)
- Tradeoff between health and economic outcomes shaped by sensitivity parameter 휅.
- Simulation grid: 휅 between 0 and 5 with step change of 0.5 for baseline calibration and increased quarantine capacity scenario.
- Entities with low death risk tolerance: curtail contacts a lot → preserve more lives but suffer larger output drop (north-west of frontier).
- Risk-taking entities: higher death rate but milder output drop (south-east of frontier).
- Increased quarantine capacity shifts pandemic possibility frontier outward, improving both health and economic outcomes.

### Second infection wave, medical solutions, and temporary immunity
- Second infection wave simulation: increase contact frequency to 2.5 (from 2) persons starting day 200; simulation horizon extended from 365 days to 600 days.
  - resurgence leads to prevalence of COVID-19 of more than 60 percent
  - fatality rate amounts to 1.5 percent of the total population
  - epidemic generates a double dip recession, with average output loss of 8 percent over the first year
- In the second-wave context, mitigation policies retain their comparative designs; for better social distancing the 15 percent reduction in effective contact frequency implies a decrease from 2.5 to [text truncated in source].

*Source: wpiea2020233-print-pdf - 0.668 Employment rate*

### 2.125 persons. Each policy is deployed after day 230, i.e. one month after the second infection wave emerges.

### wpiea2020233-print-pdf - 2.125 persons. Each policy is deployed after day 230, i.e. one month after the second infection wave emerges.

### Mitigation policies and second infection wave
- Policies in the scenarios are deployed after day 230, i.e. one month after the second infection wave emerges.
- Scenarios do not include a proper cost-benefit assessment; therefore a ranking of mitigation policies based on the simulations is not applicable.
- Finding: "the more the measures flatten the second infection curve, the more these measures are efficient at reducing the severity of the economic contraction," reflecting containment benefits.
- Interpretation: accumulated learning across the population makes the second infection wave likely different from the first; simulations present a “Baseline + 2nd wave” and alternative simulations that include mitigation policies (Figure 13 and Figure 14 referenced).

### Medical solutions: treatment and vaccine (arrival at day 300)
- Assumptions:
  - Treatment and vaccine are both assumed to arrive at day 300 (late-autumn 2020 in the paper's timeline).
  - Treatment: mortality rate is reduced to zero; infected individuals fully recover.
  - Vaccine: no more new infections; epidemic disappears once already infected individuals recover or die.
- Simulation outcomes:
  - Effective treatment eliminates mortality risk completely, but because virus transmission remains, infection curve and economic outcomes remain very similar to the initial scenario.
  - Model caveat: treatment scenario likely understates infection rates and overstates economic downturn severity because in practice:
    - People would change behavior toward more interactions (equivalent to lower 휅).
    - Labor market access across health groups would be relaxed (equivalent to higher 푠ℎ푎푟푒푤표푟푘
푖
).
    - These behavioral and access changes would produce more infections but less economic damage under efficient treatment.
  - Vaccine discovery eliminates infection risk; once administered across the population and virus eradicated, output quickly rebounds to the pre-pandemic level.
- Policy implication: countries should collaborate and prepare efficient protocols to speed-up production and delivery of a vaccine worldwide once available; simulation results are optimistic because administration to all the population will likely take time.

### Temporary immunity consideration (finite immunity λ)
- Baseline model assumes permanent immunity (recovery is an absorbing state).
- Alternative scenario introduces finite duration of immunity with parameter 휆:
  - Recovered equation amended to include a loss-of-immunity flow: R(t)/휆 (equation (11) in the text).
  - Equation (2) is amended with the same flow of individuals losing immunity transitioning back to the susceptible pool, R(t)/휆.
- Simulation specifics and results:
  - Figure 16 compares 휆 = 90 days alongside baseline 휆 = ∞.
  - With 휆 = 90 days, the susceptible pool is constantly supplemented by recovered persons who lose immunity.
  - In the absence of mitigation policies or medical solutions, disease prevalence is significantly higher and continues in the long run.
  - Output loss under temporary immunity is very persistent.
- Conclusion: temporary immunity underscores the importance of efficient mitigation policies and medical research to avoid permanent losses in lives and livelihoods.

### Multisector extension: sectoral heterogeneity and substitutability
- Framework extends to N sectors (n = 1,2,...,N) with sector-specific infection intensity 휅
푛
 and sector share 휔
푛
.
- Sectoral production function (equation (12) in the text) includes a behavioral response sensitivity term [1 − 휅
푛
∙휏(푡)] and sector share 휔
푛
.
- Aggregate final good uses a CES aggregator with elasticity of substitution 휂 (equation (13) in the text).
- Illustrative two-sector calibration:
  - N = 2; equal shares: 휔1 = 휔2 = 0.5.
  - Contagiousness: 휅1 = 5, 휅2 = 2.5 (sector 1 twice as contagious as sector 2).
  - Result: aggregate outcomes depend on substitutability 휂.
    - When 휂 = 0.5 (goods are complements), total output declines more.
    - When 휂 = 3 (goods are substitutes), total output declines less because activity in less-affected sector can partly compensate for losses in the more-affected sector.
  - Tradeoff: absent mitigation policies, lower output loss implies more widespread infection and higher fatality rates (consistent with Section III outcomes).
- Concentration example:
  - Calibration with concentrated activity: 휔1 = 0.75, 휔2 = 0.25 (more affected sector more important).
  - Result: substitutability provides limited buffer; total output decreases by more than in the equal-weights case, with small relative gains in lower infections and deaths.
- Policy implication: relevance of sector-specific policies, e.g. lockdown restrictions targeted toward more infectious activities/occupations, especially when there is substitutability across sectors.
- Extension possibilities noted: more than two sectors (primary, secondary, tertiary), differentiation in production technologies, and adjusting labor-access shares for "essential sectors".

### Conclusion and policy messages
- The paper develops a flexible analytical framework linking epidemiological dynamics of COVID-19 and macroeconomic outcomes, calibrated to EMDEs with limited healthcare and financial resources, reduced telework capacity, limited precautionary savings, and high informality.
- Model features:
  - Multiple health states (latent, infectious, non-infectious).
  - Government-mandated lockdowns with endogenous compliance linked to current economic conditions.
  - Voluntary behavior changes where individuals internalize infection risk.
  - Medical solutions (treatment or vaccine) and multisector reallocation effects.
- Main takeaways:
  - Simulations provide broad assessment of policy options to alleviate the tradeoff between saving lives and preserving economic outcomes.
  - Results underscore benefits in minimizing adverse health-related outcomes while improving economic activity.
  - Efficient deployment and propagation of containment policies are especially important in the case of repeated infection waves or limited immunity for recovered patients.

*Source: wpiea2020233-print-pdf*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020233-print-pdf.pdf_