scholarly journals A Macroeconomic SIR Model for COVID-19

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1901
Author(s):  
Erhan Bayraktar ◽  
Asaf Cohen ◽  
April Nellis
Keyword(s):  
High Risk ◽  
Transmission Rate ◽  
Adult Population ◽  
Exit Time ◽  
Herd Immunity ◽  
Virus Transmission ◽  
Total Mortality ◽  
Sir Model ◽  
Social Planner ◽  
Macroeconomic Factors

The COVID-19 pandemic and subsequent lockdowns highlight the close and delicate relationship between a country’s public health and economic health. Models that combine macroeconomic factors with traditional epidemic dynamics to calculate the impacts of a disease outbreak are therefore extremely useful for policymakers seeking to evaluate the best course of action in such a crisis. We developed a macroeconomic SIR model that considers herd immunity, behavior-dependent transmission rates, remote workers, and the indirect externalities of lockdowns. It is formulated as an exit time control problem where a social planner is able to prescribe separate levels of the lockdown low-risk and high-risk portions of the adult population. The model predicts that by considering the possibility of reaching herd immunity, high-risk individuals are able to leave lockdown sooner than in models where herd immunity is not considered. Additionally, a behavior-dependent transmission rate (which represents increased personal caution in response to increased infection levels) can lower both output loss and total mortality. Overall, the model-determined optimal lockdown strategy, combined with individual actions to slow virus transmission, is able to reduce total mortality to one-third of the model-predicted no-lockdown level of mortality.

scholarly journals A Macroeconomic SIR Model for COVID-19

2020 ◽  
Author(s):  
Erhan Bayraktar ◽  
Asaf Cohen ◽  
April Nellis
Keyword(s):  
High Risk ◽  
Transmission Rate ◽  
Adult Population ◽  
Exit Time ◽  
Herd Immunity ◽  
Virus Transmission ◽  
Total Mortality ◽  
Sir Model ◽  
Social Planner ◽  
Time Control

AbstractThe current COVID-19 pandemic and subsequent lockdowns have highlighted the close and delicate relationship between a country’s public health and economic health. Macroeconomic models which use preexisting epidemic models to calculate the impacts of a disease outbreak are therefore extremely useful for policymakers seeking to evaluate the best course of action in such a crisis. We develop an SIR model of the COVID-19 pandemic which explicitly considers herd immunity, behavior-dependent transmission rates, remote workers, and indirect externalities of lockdown. This model is presented as an exit time control problem where the lockdown ends when the population achieves herd immunity, either naturally or via a vaccine. A social planner prescribes separate levels of lockdown for two separate sections of the adult population - those who are low-risk (ages 20-64) and those who are high-risk (ages 65 and over). These levels are determined via optimization of an objective function which assigns a macroeconomic cost to the level of lockdown and the number of deaths. We find that, by ending lockdowns once herd immunity is reached, high-risk individuals are able to leave lockdown significantly before the arrival of a vaccine without causing large increases in mortality. Additionally, if we incorporate a behavior-dependent transmission rate which represents increased personal caution in response to increased infection levels, both output loss and total mortality are lowered. Lockdown efficacy is further increased when there is less interaction between low- and high-risk individuals, and increased remote work decreases output losses. Overall, our model predicts that a lockdown which ends at the arrival of herd immunity, combined with individual actions to slow virus transmission, can reduce total mortality to one-third of the no-lockdown level, while allowing high-risk individuals to leave lockdown well before vaccine arrival.

scholarly journals Modelling infectious diseases with herd immunity in a randomly mixed population

2021 ◽  
Author(s):  
Kian Boon Law ◽  
Kalaiarasu M. Peariasamy ◽  
Hishamshah Mohd. Ibrahim ◽  
Noor Hisham Abdullah
Keyword(s):  
Infectious Disease ◽  
Infectious Diseases ◽  
Transmission Rate ◽  
Herd Immunity ◽  
Sir Model ◽  
Mixed Population ◽  
Transmission Dynamics ◽  
Transmission Model ◽  
Infection Model ◽  
Vaccination Rates

Abstract Background The conventional susceptible-infectious-recovered (SIR) model tends to overestimate the transmission dynamics of infectious diseases and ends up with total infections and total immunized population exceeding the threshold required for control and eradication of infectious diseases. The study aims to overcome the limitation by allowing the transmission rate of infectious disease to decline along with the reducing risk of contact infection. Methods Two new SIR models were developed to mimic the declining transmission rate of infectious diseases at different stages of transmission. Model A mimicked the declining transmission rate along with the reducing risk of transmission following infection, while Model B mimicked the declining transmission rate following recovery. Then, the conventional SIR model, Model A and Model B were used to simulate an infectious disease with a basic reproduction number (r0) of 3.0 and a herd immunity threshold (HIT) of 0.667 with and without vaccination. The infectious disease was expected to be controlled or eradicated when the total immunized population either through infection or vaccination reached the level predicted by the HIT. Outcomes of simulations were assessed at the time when the total immunized population reached the level predicted by the HIT, and at the end of simulations. Findings All three models performed likewise at the beginning of the transmission when sizes of infectious and recovered were relatively small as compared with the population size. The infectious disease modelled using the conventional SIR model appeared completely out of control even when the HIT was achieved in all scenarios with and without vaccination. The infectious disease modelled using Model A appeared to be controlled at the level predicted by the HIT in all scenarios with and without vaccination. Model B projected the infectious disease to be controlled at the level predicted by the HIT only at high vaccination rates. At lower vaccination rates or without vaccination, the level at which the infectious disease was controlled cannot be accurately predicted by the HIT. Conclusion Transmission dynamics of infectious diseases with herd immunity can accurately be modelled by allowing the transmission rate of infectious disease to decline along with the combined risk of contact infection. Model B provides a more credible framework for modelling infectious diseases with herd immunity in a randomly mixed population.

scholarly journals Modelling infectious diseases with herd immunity in a randomly mixed population

2021 ◽  
Author(s):  
Kian Boon Law ◽  
Kalaiarasu M Peariasamy ◽  
Hishamshah Ibrahim ◽  
Noor Hisham Abdullah
Keyword(s):  
Infectious Disease ◽  
Infectious Diseases ◽  
Transmission Rate ◽  
Herd Immunity ◽  
Sir Model ◽  
Mixed Population ◽  
Transmission Dynamics ◽  
Transmission Model ◽  
Infection Model ◽  
Vaccination Rates

Abstract Background The conventional susceptible-infectious-recovered (SIR) model tends to overestimate transmission dynamics of infectious diseases and ends up with total infections exceeding the threshold required for control and eradication of infectious diseases. The study aims to overcome the limitation by allowing the transmission rate of infectious disease to decline along with the reducing risk of contact infection. MethodsTwo new SIR models were developed to mimic the declining transmission rate of infectious diseases at different stages of transmission. Model A mimicked the declining transmission rate along with the reducing risk of transmission following infection, while Model B mimicked the declining transmission rate following recovery. Then, the conventional SIR model, Model A and Model B were used to simulate an infectious disease with a basic reproduction number (r0) of 3.0 and a herd immunity threshold (HIT) of 0.667 with and without vaccination. The infectious disease was expected to be controlled or eradicated when the total immunized population either through infection or vaccination reached the level predicted by the HIT. Outcomes of simulations were assessed at the time when the total immunized population reached the level predicted by the HIT, and at the end of simulations.Findings All three models performed likewise at the beginning of transmission when sizes of infectious and recovered were relatively small as compared with the population size. The infectious disease modelled using the conventional SIR model appeared completely out of control even when the HIT was achieved in all scenarios with and without vaccination. The infectious disease modelled using Model A appeared to be controlled at the level predicted by the HIT in all scenarios with and without vaccination. Model B projected the infectious disease to be controlled at the level predicted by the HIT only at high vaccination rates. At lower vaccination rates or without vaccination, the level at which the infectious disease was controlled cannot be accurately predicted by the HIT. ConclusionTransmission dynamics of infectious diseases with herd immunity can accurately be modelled by allowing the transmission rate of infectious disease to decline along with the combined risk of contact infection. Model B provides a more realistic framework for modelling infectious diseases with herd immunity in a randomly mixed population.

scholarly journals Emergence of N antigen SARS-CoV-2 genetic variants escaping detection of antigenic tests

2021 ◽  
Author(s):  
Claudia Del Vecchio ◽  
Giuseppina Brancaccio ◽  
Alessandra Rosalba Brazzale ◽  
Enrico Lavezzo ◽  
Francesco Onelia ◽  
...  
Keyword(s):  
Genetic Variants ◽  
Vaccine Development ◽  
Transmission Rate ◽  
Herd Immunity ◽  
Virus Transmission ◽  
Host Cells ◽  
N Gene ◽  
Sequencing Analysis ◽  
Antigen Test ◽  
Rt Pcr

SARS-CoV-2 genetic variants are emerging as a major threat to vaccination efforts worldwide as they may increase virus transmission rate and/or confer the ability to escape vaccine induced immunity with knock on effects on the level of herd immunity and vaccine efficacy respectively. These variants concern the Spike protein, which is encoded by the S gene, involved in virus entry into host cells and the major target of vaccine development. We report here that genetic variants of the N gene can impair our ability to utilize antigenic tests for both diagnosis and mass testing efforts aimed at controlling virus transmission. While conducting a large validation study on the Abbott Panbio COVID-19 Ag test, we noticed that some swab samples failed to generate a positive result in spite of a high viral load in Rt-PCR assays. Sequencing analysis of viruses showing discordant results in the Rt-PCR and antigen assays revealed the presence of multiple disruptive amino-acid substitutions in the N antigen (the viral protein detected in the antigen test) clustered from position 229 to 374 a region known to contain an immunodominant epitope. A relevant fraction of the variants, undetected by the antigen test, contained the mutations A376T coupled to M241I. Intriguingly we found that virus sequences with this mutation were over-represented in the antigen-test-negative and PCR-positive samples and progressively increased in frequency over time in Veneto, a region of Italy that has aggressively scaled up the utilization of antigen tests, which reached nearly 68% of all the SARS-CoV-2 swab assays performed there. We speculate that mass utilization of antigen assays could create a selection pressure on the target that may favor the spread of undetectable virus variants.

scholarly journals Modelling infectious diseases with herd immunity in a randomly mixed population

2021 ◽  
Author(s):  
Kian Boon Law ◽  
Kalaiarasu M. Peariasamy ◽  
Hishamshah Mohd. Ibrahim ◽  
Noor Hisham Abdullah
Keyword(s):  
Infectious Disease ◽  
Infectious Diseases ◽  
Transmission Rate ◽  
Herd Immunity ◽  
Sir Model ◽  
Mixed Population ◽  
Transmission Dynamics ◽  
Transmission Model ◽  
Infection Model ◽  
Vaccination Rates

Abstract Background The conventional susceptible-infectious-recovered (SIR) model tends to overestimate the transmission dynamics of infectious diseases and ends up with total infections and total immunized population exceeding the threshold required for control and eradication of infectious diseases. The study aims to overcome the limitation by allowing the transmission rate of infectious disease to decline along with the reducing risk of contact infection. Methods Two new SIR models were developed to mimic the declining transmission rate of infectious diseases at different stages of transmission. Model A mimicked the declining transmission rate along with the reducing risk of transmission following infection, while Model B mimicked the declining transmission rate following recovery. Then, the conventional SIR model, Model A and Model B were used to simulate an infectious disease with a basic reproduction number (r0) of 3.0 and a herd immunity threshold (HIT) of 0.667 with and without vaccination. The infectious disease was expected to be controlled or eradicated when the total immunized population either through infection or vaccination reached the level predicted by the HIT. Outcomes of simulations were assessed at the time when the total immunized population reached the level predicted by the HIT, and at the end of simulations.Findings All three models performed likewise at the beginning of the transmission when sizes of infectious and recovered were relatively small as compared with the population size. The infectious disease modelled using the conventional SIR model appeared completely out of control even when the HIT was achieved in all scenarios with and without vaccination. The infectious disease modelled using Model A appeared to be controlled at the level predicted by the HIT in all scenarios with and without vaccination. Model B projected the infectious disease to be controlled at the level predicted by the HIT only at high vaccination rates. At lower vaccination rates or without vaccination, the level at which the infectious disease was controlled cannot be accurately predicted by the HIT. Conclusion Transmission dynamics of infectious diseases with herd immunity can accurately be modelled by allowing the transmission rate of infectious disease to decline along with the combined risk of contact infection. Model B provides a more credible framework for modelling infectious diseases with herd immunity in a randomly mixed population.

scholarly journals Modelling infectious diseases with herd immunity in a randomly mixed population

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Kian Boon Law ◽  
Kalaiarasu M. Peariasamy ◽  
Hishamshah Mohd Ibrahim ◽  
Noor Hisham Abdullah
Keyword(s):  
Infectious Disease ◽  
Infectious Diseases ◽  
Transmission Rate ◽  
Herd Immunity ◽  
The United States ◽  
Sir Model ◽  
Mixed Population ◽  
Transmission Dynamics ◽  
Vaccination Rates ◽  
Reduced Risk

AbstractThe conventional susceptible-infectious-recovered (SIR) model tends to magnify the transmission dynamics of infectious diseases, and thus the estimated total infections and immunized population may be higher than the threshold required for infection control and eradication. The study developed a new SIR framework that allows the transmission rate of infectious diseases to decline along with the reduced risk of contact infection to overcome the limitations of the conventional SIR model. Two new SIR models were formulated to mimic the declining transmission rate of infectious diseases at different stages of transmission. Model A utilized the declining transmission rate along with the reduced risk of contact infection following infection, while Model B incorporated the declining transmission rate following recovery. Both new models and the conventional SIR model were then used to simulate an infectious disease with a basic reproduction number (r0) of 3.0 and a herd immunity threshold (HIT) of 0.667 with and without vaccination. Outcomes of simulations were assessed at the time when the total immunized population reached the level predicted by the HIT, and at the end of simulations. Further, all three models were used to simulate the transmission dynamics of seasonal influenza in the United States and disease burdens were projected and compared with estimates from the Centers for Disease Control and Prevention. For the simulated infectious disease, in the initial phase of the outbreak, all three models performed expectedly when the sizes of infectious and recovered populations were relatively small. As the infectious population increased, the conventional SIR model appeared to overestimate the infections even when the HIT was achieved in all scenarios with and without vaccination. For the same scenario, Model A appeared to attain the level predicted by the HIT and in comparison, Model B projected the infectious disease to be controlled at the level predicted by the HIT only at high vaccination rates. For infectious diseases with high r0, and at low vaccination rates, the level at which the infectious disease was controlled cannot be accurately predicted by the current theorem. Transmission dynamics of infectious diseases with herd immunity can be accurately modelled by allowing the transmission rate of infectious diseases to decline along with the reduction of contact infection risk after recovery or vaccination. Model B provides a credible framework for modelling infectious diseases with herd immunity in a randomly mixed population.

scholarly journals Dynamics of the COVID-19 epidemic in Ireland under mitigation

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Bernard Cazelles ◽  
Benjamin Nguyen-Van-Yen ◽  
Clara Champagne ◽  
Catherine Comiskey
Keyword(s):  
Transmission Rate ◽  
Vaccination Campaign ◽  
Virus Transmission ◽  
Reporting Rate ◽  
Mitigation Measures ◽  
Third Wave ◽  
The European Union ◽  
Hospital Data ◽  
Prevalence Survey ◽  
Epidemic Curve

Abstract Background In Ireland and across the European Union the COVID-19 epidemic waves, driven mainly by the emergence of new variants of the SARS-CoV-2 have continued their course, despite various interventions from governments. Public health interventions continue in their attempts to control the spread as they wait for the planned significant effect of vaccination. Methods To tackle this challenge and the observed non-stationary aspect of the epidemic we used a modified SEIR stochastic model with time-varying parameters, following Brownian process. This enabled us to reconstruct the temporal evolution of the transmission rate of COVID-19 with the non-specific hypothesis that it follows a basic stochastic process constrained by the available data. This model is coupled with Bayesian inference (particle Markov Chain Monte Carlo method) for parameter estimation and utilized mainly well-documented Irish hospital data. Results In Ireland, mitigation measures provided a 78–86% reduction in transmission during the first wave between March and May 2020. For the second wave in October 2020, our reduction estimation was around 20% while it was 70% for the third wave in January 2021. This third wave was partly due to the UK variant appearing in Ireland. In June 2020 we estimated that sero-prevalence was 2.0% (95% CI: 1.2–3.5%) in complete accordance with a sero-prevalence survey. By the end of April 2021, the sero-prevalence was greater than 17% due in part to the vaccination campaign. Finally we demonstrate that the available observed confirmed cases are not reliable for analysis owing to the fact that their reporting rate has as expected greatly evolved. Conclusion We provide the first estimations of the dynamics of the COVID-19 epidemic in Ireland and its key parameters. We also quantify the effects of mitigation measures on the virus transmission during and after mitigation for the three waves. Our results demonstrate that Ireland has significantly reduced transmission by employing mitigation measures, physical distancing and lockdown. This has to date avoided the saturation of healthcare infrastructures, flattened the epidemic curve and likely reduced mortality. However, as we await for a full roll out of a vaccination programme and as new variants potentially more transmissible and/or more infectious could continue to emerge and mitigation measures change silent transmission, challenges remain.

scholarly journals Estimating asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan: a mathematical modeling study

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Xi Huo ◽  
Jing Chen ◽  
Shigui Ruan
Keyword(s):  
Disease Transmission ◽  
Large Scale ◽  
Transmission Rate ◽  
Control Strategies ◽  
Herd Immunity ◽  
Antibody Prevalence ◽  
Screening Process ◽  
Vaccination Programs ◽  
Prevalence Level ◽  
The Impact

Abstract Background The COVID-19 outbreak in Wuhan started in December 2019 and was under control by the end of March 2020 with a total of 50,006 confirmed cases by the implementation of a series of nonpharmaceutical interventions (NPIs) including unprecedented lockdown of the city. This study analyzes the complete outbreak data from Wuhan, assesses the impact of these public health interventions, and estimates the asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan. Methods By taking different stages of the outbreak into account, we developed a time-dependent compartmental model to describe the dynamics of disease transmission and case detection and reporting. Model coefficients were parameterized by using the reported cases and following key events and escalated control strategies. Then the model was used to calibrate the complete outbreak data by using the Monte Carlo Markov Chain (MCMC) method. Finally we used the model to estimate asymptomatic and undetected cases and approximate the overall antibody prevalence level. Results We found that the transmission rate between Jan 24 and Feb 1, 2020, was twice as large as that before the lockdown on Jan 23 and 67.6% (95% CI [0.584,0.759]) of detectable infections occurred during this period. Based on the reported estimates that around 20% of infections were asymptomatic and their transmission ability was about 70% of symptomatic ones, we estimated that there were about 14,448 asymptomatic and undetected cases (95% CI [12,364,23,254]), which yields an estimate of a total of 64,454 infected cases (95% CI [62,370,73,260]), and the overall antibody prevalence level in the population of Wuhan was 0.745% (95% CI [0.693%,0.814%]) by March 31, 2020. Conclusions We conclude that the control of the COVID-19 outbreak in Wuhan was achieved via the enforcement of a combination of multiple NPIs: the lockdown on Jan 23, the stay-at-home order on Feb 2, the massive isolation of all symptomatic individuals via newly constructed special shelter hospitals on Feb 6, and the large scale screening process on Feb 18. Our results indicate that the population in Wuhan is far away from establishing herd immunity and provide insights for other affected countries and regions in designing control strategies and planing vaccination programs.

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