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Background: As one of the strategies to mitigate the COVID-19 pandemic, social distancing (SD) measures are recommended to control disease spread and reduce the attack rate. Therefore, this study aims to estimate the costs and effects of SD measures through school closures, workforce, and community contact reductions for mitigating the COVID-19 pandemic in Indonesia., Methods: Two mitigation scenarios of SD for 1 month and continuous SD were compared with the baseline (no intervention). A modified Susceptible-Exposed-Infected-Recovered (SEIR) compartmental model accounting for disease spread during the latent period was applied by considering a 1-year time horizon. The costs of healthcare, school closures, and productivity loss due to disease as well as intervention were considered to estimate the total pandemic cost among all scenarios., Results: In a comparison with the baseline, the result showed that total savings in scenarios of SD for 1 month and continuous SD was approximately $415 billion and $699 billion, respectively, while the averted deaths were 4.6 million and 8.5 million, respectively. Sensitivity analysis showed that basic reproduction number, infectious period, daily wage, incubation period, daily ICU admission cost, and case fatality rate were the most influential parameters affecting the savings and the number of averted deaths., Conclusions: SD measures through school closures, workforce, and community contact reductions were concluded to be cost-saving. Increasing the duration of social distancing tends to increase both the savings and the number of averted deaths., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

We investigate the impact of the delay in compulsory mask wearing on the spread of COVID-19 in the community, set in the Singapore context. By using modified SEIR-based compartmental models, we focus on macroscopic population-level analysis of the relationships between the delay in compulsory mask wearing and the maximum infection, through a series of scenario-based analysis. Our analysis suggests that collective masking can meaningfully reduce the transmission of COVID-19 in the community, but only if implemented within a critical time window of approximately before 80-100 days delay after the first infection is detected, coupled with strict enforcement to ensure compliance throughout the duration. We also identify a delay threshold of about 100 days that results in masking enforcement having little significant impact on the Maximum Infected Values. The results therefore highlight the necessity for rapid implementation of compulsory mask wearing to curb the spread of the pandemic.

Objectives: While highly effective in preventing SARS-CoV-2 spread, national lockdowns come with an enormous economic price. Few countries have adopted an alternative "testing, tracing, and isolation" approach to selectively isolate people at high exposure risk, thereby minimizing the economic impact. To assist policy makers, we performed a cost-effectiveness analysis of these 2 strategies., Methods: A modified Susceptible, Exposed, Infectious, Recovered, and Deceased (SEIRD) model was employed to assess the situation in Israel, a small country with ∼9 million people. The incremental cost-effectiveness ratio (ICER) of these strategies as well as the expected number of infected individuals and deaths were calculated., Results: A nationwide lockdown is expected to save, on average, 274 (median 124, interquartile range: 71-221) lives compared to the "testing, tracing, and isolation" approach. However, the ICER will be, on average, $45 104 156 (median $49.6 million, interquartile range: 22.7-220.1) to prevent 1 case of death., Conclusion: A national lockdown has a moderate advantage in saving lives with tremendous costs and possible overwhelming economic effects. These findings should assist decision makers dealing with additional waves of this pandemic., (Copyright © 2020 ISPOR–The Professional Society for Health Economics and Outcomes Research. Published by Elsevier Inc. All rights reserved.)

The spreading of infectious diseases including COVID-19 depends on human interactions. In an environment where behavioral patterns and physical contacts are constantly evolving according to new governmental regulations, measuring these interactions is a major challenge. Mobility has emerged as an indicator for human activity and, implicitly, for human interactions. Here, we study the coupling between mobility and COVID-19 dynamics and show that variations in global air traffic and local driving mobility can be used to stratify different disease phases. For ten European countries, our study shows a maximal correlation between driving mobility and disease dynamics with a time lag of [Formula: see text] days. Our findings suggest that trends in local mobility allow us to forecast the outbreak dynamics of COVID-19 for a window of two weeks and adjust local control strategies in real time.

Background: The effect of the COVID-19 outbreak has led policymakers around the world to attempt transmission control. However, lockdown and shutdown interventions have caused new social problems and designating policy resumption for infection control when reopening society remains a crucial issue. We investigated the effects of different resumption strategies on COVID-19 transmission using a modeling study setting., Methods: We employed a susceptible-exposed-infectious-removed model to simulate COVID-19 outbreaks under five reopening strategies based on China's business resumption progress. The effect of each strategy was evaluated using the peak values of the epidemic curves vis-à-vis confirmed active cases and cumulative cases. Two-sample t-test was performed in order to affirm that the pick values in different scenarios are different., Results: We found that a hierarchy-based reopen strategy performed best when current epidemic prevention measures were maintained save for lockdown, reducing the peak number of active cases and cumulative cases by 50 and 44%, respectively. However, the modeled effect of each strategy decreased when the current intervention was lifted somewhat. Additional attention should be given to regions with significant numbers of migrants, as the potential risk of COVID-19 outbreaks amid society reopening is intrinsically high., Conclusions: Business resumption strategies have the potential to eliminate COVID-19 outbreaks amid society reopening without special control measures. The proposed resumption strategies focused mainly on decreasing the number of imported exposure cases, guaranteeing medical support for epidemic control, or decreasing active cases.

Background and Objective: The currently active COVID-19 pandemic has increased, among others, public interest in the computational techniques enabling the study of disease-spreading processes. Thus far, numerous approaches have been used to study the development of epidemics, with special attention paid to the identification of crucial elements that can strengthen or weaken the dynamics of the process. The main thread of this research is associated with the use of the ordinary differential equations method. There also exist several approaches based on the analysis of flows in the Cellular Automata (CA) approach., Methods: In this paper, we propose a new approach to disease-spread modeling. We start by creating a network that reproduces contacts between individuals in a community. This assumption makes the presented model significantly different from the ones currently dominant in the field. It also changes the approach to the act of infection. Usually, some parameters that describe the rate of new infections by taking into account those infected in the previous time slot are considered. With our model, we can individualize this process, considering each contact individually., Results: The typical output from calculations of a similar type are epidemic curves. In our model, except of presenting the average curves, we show the deviations or ranges for particular results obtained in different simulation runs, which usually lead to significantly different results. This observation is the effect of the probabilistic character of the infection process, which can impact, in different runs, individuals with different significance to the community. We can also easily present the effects of different types of intervention. The effects are studied for different methods used to create the graph representing a community, which can correspond to different social bonds., Conclusions: We see the potential usefulness of the proposition in the detailed study of epidemic development for specific environments and communities. The ease of entering new parameters enables the analysis of several specific scenarios for different contagious diseases., (Copyright © 2020 Elsevier B.V. All rights reserved.)

We introduce a deterministic SEIR model and fit it to epidemiological data for the COVID-19 outbreak in Ireland. We couple the model to economic considerations - we formulate an optimal control problem in which the cost to the economy of the various non-pharmaceutical interventions is minimized, subject to hospital admissions never exceeding a threshold value corresponding to health-service capacity. Within the framework of the model, the optimal strategy of disease control is revealed to be one of disease suppression, rather than disease mitigation., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 The Author(s). Published by Elsevier Inc. All rights reserved.)

The coronavirus disease 2019 (COVID-19) has become a life-threatening pandemic. The epidemic trends in different countries vary considerably due to different policy-making and resources mobilization. We calculated basic reproduction number (R 0 ) and the time-varying estimate of the effective reproductive number (R t ) of COVID-19 by using the maximum likelihood method and the sequential Bayesian method, respectively. European and North American countries possessed higher R 0 and unsteady R t fluctuations, whereas some heavily affected Asian countries showed relatively low R 0 and declining R t now. The numbers of patients in Africa and Latin America are still low, but the potential risk of huge outbreaks cannot be ignored. Three scenarios were then simulated, generating distinct outcomes by using SEIR (susceptible, exposed, infectious, and removed) model. First, evidence-based prompt responses yield lower transmission rate followed by decreasing R t . Second, implementation of effective control policies at a relatively late stage, in spite of huge casualties at early phase, can still achieve containment and mitigation. Third, wisely taking advantage of the time-window for developing countries in Africa and Latin America to adopt adequate measures can save more people's life. Our mathematical modeling provides evidence for international communities to develop sound design of containment and mitigation policies for COVID-19.

Background: Proactive interventions have halted the pandemic of coronavirus infected disease in some regions. However, without reaching herd immunity, the return of epidemic is possible. We investigate the impact of population structure, case importation, asymptomatic cases, and the number of contacts on a possible second wave of epidemic through mathematical modeling., Methods: we built a modified Susceptible-exposed-Infectious-Removed (SEIR) model with parameters mirroring those of the COVID-19 pandemic and reported simulated characteristics of epidemics for incidence, hospitalizations and deaths under different scenarios., Results: A larger percent of elderly people leads to higher number of hospitalizations, while a large percent of prior infection will effectively curb the epidemic. The number of imported cases and the speed of importation have small impact on the epidemic progression. However, a higher percent of asymptomatic cases slows the epidemic down and reduces the number of hospitalizations and deaths at the epidemic peak. Finally, reducing the number of contacts among young people alone has moderate effects on themselves, but little effects on the elderly population. However, reducing the number of contacts among elderly people alone can mitigate the epidemic significantly in both age groups, even though young people remain active within themselves., Conclusion: Reducing the number of contacts among high risk populations alone can mitigate the burden of epidemic in the whole society. Interventions targeting high risk groups may be more effective in containing or mitigating the epidemic., (Copyright © 2020 Elsevier Ltd. All rights reserved.)

For the first time in history, on March 17, 2020, the European Union closed all its external borders in an attempt to contain the spreading of the coronavirus 2019, COVID-19. Throughout two past months, governments around the world have implemented massive travel restrictions and border control to mitigate the outbreak of this global pandemic. However, the precise effects of travel restrictions on the outbreak dynamics of COVID-19 remain unknown. Here we combine a global network mobility model with a local epidemiology model to simulate and predict the outbreak dynamics and outbreak control of COVID-19 across Europe. We correlate our mobility model to passenger air travel statistics and calibrate our epidemiology model using the number of reported COVID-19 cases for each country. Our simulations show that mobility networks of air travel can predict the emerging global diffusion pattern of a pandemic at the early stages of the outbreak. Our results suggest that an unconstrained mobility would have significantly accelerated the spreading of COVID-19, especially in Central Europe, Spain, and France. Ultimately, our network epidemiology model can inform political decision making and help identify exit strategies from current travel restrictions and total lockdown.

Objective: Coronavirus disease 2019 (COVID-19) is a pandemic respiratory illness spreading from person-to-person caused by a novel coronavirus and poses a serious public health risk. The goal of this study was to apply a modified susceptible-exposed-infectious-recovered (SEIR) compartmental mathematical model for prediction of COVID-19 epidemic dynamics incorporating pathogen in the environment and interventions. The next generation matrix approach was used to determine the basic reproduction number [Formula: see text]. The model equations are solved numerically using fourth and fifth order Runge-Kutta methods., Results: We found an [Formula: see text] of 2.03, implying that the pandemic will persist in the human population in the absence of strong control measures. Results after simulating various scenarios indicate that disregarding social distancing and hygiene measures can have devastating effects on the human population. The model shows that quarantine of contacts and isolation of cases can help halt the spread on novel coronavirus.

The coronavirus COVID-19 has recently started to spread rapidly in Malaysia. The number of total infected cases has increased to 3662 on 05 April 2020, leading to the country being placed under lockdown. As the main public concern is whether the current situation will continue for the next few months, this study aims to predict the epidemic peak using the Susceptible-Exposed-Infectious-Recovered (SEIR) model, with incorporation of the mortality cases. The infection rate was estimated using the Genetic Algorithm (GA), while the Adaptive Neuro-Fuzzy Inference System (ANFIS) model was used to provide short-time forecasting of the number of infected cases. The results show that the estimated infection rate is 0.228 ± 0.013, while the basic reproductive number is 2.28 ± 0.13. The epidemic peak of COVID-19 in Malaysia could be reached on 26 July 2020, with an uncertain period of 30 days (12 July-11 August). Possible interventions by the government to reduce the infection rate by 25% over two or three months would delay the epidemic peak by 30 and 46 days, respectively. The forecasting results using the ANFIS model show a low Normalized Root Mean Square Error (NRMSE) of 0.041; a low Mean Absolute Percentage Error (MAPE) of 2.45%; and a high coefficient of determination (R 2 ) of 0.9964. The results also show that an intervention has a great effect on delaying the epidemic peak and a longer intervention period would reduce the epidemic size at the peak. The study provides important information for public health providers and the government to control the COVID-19 epidemic.

News reporting has the potential to modify a community's knowledge of emerging infectious diseases and affect peoples' attitudes and behavior. Here we developed a quantitative approach to evaluate the effects of media on such behavior. Statistically significant correlations between the number of new hospital notifications, during the 2009 A/H1N1 influenza epidemic in the Shaanxi province of China, and the number of daily news items added to eight major websites were found from Pearson correlation and cross-correlation analyses. We also proposed a novel model to examine the implication for transmission dynamics of these correlations. The model incorporated the media impact function into the intensity of infection, and enhanced the traditional epidemic SEIR model with the addition of media dynamics. We used a nonlinear least squares estimation to identify the best-fit parameter values in the model from the observed data. We also carried out the uncertainty and sensitivity analyses to determine key parameters during early phase of the disease outbreak for the final outcome of the outbreak with media impact. The findings confirm the importance of responses by individuals to the media reports, with behavior changes having important consequence for the emerging infectious disease control. Therefore, for mitigating emerging infectious diseases, media reports should be focused on how to guide people's behavioral changes, which are critical for limiting the spread of disease., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

In order to understand the evolution of the 2009 influenza A (H1N1) pandemic within local regions of Japan, we studied the significance of regional migration between these regions. For this purpose, we have employed an extended SEIR model to describe the immigration of infected people and the stochastic variation of the infectious efficiency. We then applied a data assimilation technique in order to study how the agreement of the simulation results with the observed data depends on the presence/absence of immigration and the degree of variation of the infectious efficiency. Reproducibility is evaluated by log-likelihood values. The log-likelihood does not indicate the significance of immigration. Although there are multiple waves in the time course of the number of reported infected individuals, these waves could be explained by the stochastic nature of infectious events., (Copyright © 2013 Elsevier Inc. All rights reserved.)

Basic Susceptible-Exposed-Infectious-Removed (SEIR) models of COVID-19 dynamics tend to be excessively pessimistic due to high basic reproduction values, which result in overestimations of cases of infection and death. We propose an extended SEIR model and daily data of COVID-19 cases in the U.S. and the seven largest European countries to forecast possible pandemic dynamics by investigating the effects of infection vulnerability stratification and measures on preventing the spread of infection. We assume that (i) the number of cases would be underestimated at the beginning of a new virus pandemic due to the lack of effective diagnostic methods and (ii) people more susceptible to infection are more likely to become infected; whereas during the later stages, the chances of infection among others will be reduced, thereby potentially leading to pandemic cessation. Based on infection vulnerability stratification, we demonstrate effects brought by the fraction of infected persons in the population at the start of pandemic deceleration on the cumulative fraction of the infected population. We interestingly show that moderate and long-lasting preventive measures are more effective than more rigid measures, which tend to be eventually loosened or abandoned due to economic losses, delay the peak of infection and fail to reduce the total number of cases. Our calculations relate the pandemic's second wave to high seasonal fluctuations and a low vulnerability stratification coefficient. Our characterisation of basic reproduction dynamics indicates that second wave of the pandemic is likely to first occur in Germany, Spain, France, and Italy, and a second wave is also possible in the U.K. and the U.S. Our findings show that even if the total elimination of the virus is impossible, the total number of infected people can be reduced during the deceleration stage. [ABSTRACT FROM AUTHOR]

When humanity faces a potentially contagious disease, most processes of society are affected, the workforce capable of performing tasks decreases, and healthcare systems become overwhelmed by sudden disease outbreaks. In 2020, the world fell victim to Covid-19. Its spread had devastating consequences in many countries, changing the lives of all individuals. The poor management of the pandemic on a global scale highlighted the lack of preparedness for this type of catastrophe, leading to efforts and research being conducted to facilitate the management of this disease. One of the most important endeavors undertaken to control the spread of the infectious virus was to attempt to predict its behavior and take measures to mitigate the damage caused. Pandemic control models, such as the SEIR model, were employed to create predictions, but the results proved to be imprecise due to the lack of infection data. Furthermore, a highly contagious virus that is transmitted by people behaves in a very erratic manner, making it more challenging to develop rigid prediction methods. It was determined that geographic and demographic characteristics greatly influenced the virus's behavior. Agent-Based Simulation was used to model processes and environments with unique characteristics while allowing for individual interaction. In this work, Agent-Based Simulation is employed to model the spread of a virus that affects individuals in a city in Cuba. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has highlighted the necessity for policymakers to design interventions that allow to promptly resume economic activities while taking control of the healthcare emergency. We analyze the response of differentiated policy measures by exploiting a meta-population SEIR model based on transaction data that map human mobility through daily physical transactions performed by cardholders of a major Italian bank. We calibrate multiple counterfactual scenarios and study the impact of alternative combinations of tailored mobility restrictions with different intensity across sectors. Although the Retail sector accounts for the largest portion of mobility and drive results in terms of infections and consumption dynamics, other economic activities, such as those related to Restaurants, have a relevant role in the design of the optimal policy. Finally, we show how the proposed approach can be used by policymakers to evaluate the trade-off between economic and healthcare impacts by identifying the alternative policy restrictions that minimize either the economic impact given a certain level of infections or the spread of contagion for a target value of economic impact. [ABSTRACT FROM AUTHOR]

Ever since the World Health Organization gave the name COVID-19 to the coronavirus pneumonia disease, much of the world has been severely impact by the pandemic socially and economically. In this paper, the mathematical modeling and stability analyses in terms of the susceptible–exposed–infected–removed (SEIR) model with a nonlinear incidence rate, along with media interaction effects, are presented. The sliding mode control methodology is used to design a robust closed loop control of the epidemiological system, where the property of symmetry in the Lyapunov function plays a vital role in achieving the global asymptotic stability in the output. Two policies are considered: the first considers only the governmental interaction, the second considers only the vaccination policy. Numerical simulations of the control algorithms are then evaluated. [ABSTRACT FROM AUTHOR]

Like other European countries, Germany has experienced the 2nd wave of the COVID-19 amid obligations of social distancing and wearing of face masks in public spaces. Although Germany successfully contained the virus during the 1st wave, it has faced difficulties in controlling the COVID-19 during the 2nd wave. This study develops a computer model representing the COVID-19 flow in Germany by comparing the effects of the measures taken during the 1st and the 2nd waves. The computer model is based on the SEIR concept and the system dynamics (SD) approach in which some unknown parameters are estimated through the calibration process. Moreover, the SEIR computer model is developed by considering different cases in older and young people and the SEIR model successfully reproduces similar patterns of infected, recovered, and death cases in the 1st and the 2nd waves in Germany. The SEIR model also shows that the measures taken in the 1st wave have different efficacies than those in the 2nd wave, leading to higher infected cases during the 2nd wave. Since the SEIR model can successfully reproduce similar patterns, the SEIR model can be a basis for further studies in estimating other resource needs such as health workers, and bed capacities. [ABSTRACT FROM AUTHOR]

The World Health Organization (WHO) reported the covid-19 epidemic a global health emergency on January 30 and confirmed its transformation into a pandemic on March 11. China has been the hardest hit since the virus's outbreak, which may date back to late November. Saudi Arabia realized the danger of the Coronavirus in March 2020, took the initiative to take a set of pre-emptive decisions that preceded many countries of the world, and worked to harness all capabilities to confront the outbreak of the epidemic. Several researchers are currently using various mathematical and machine learning-based prediction models to estimate this pandemic's future trend. In this work, the SEIR model was applied to predict the epidemic situation in Saudi Arabia and evaluate the effectiveness of some epidemic control measures, and finally, providing some advice on preventive measures. [ABSTRACT FROM AUTHOR]

This investigation is based on the application of Susceptible-Exposed-Infectious-Recovered (SEIR) model to simulate the number of diseases spread in a region, along with a historical approach of epidemic outbreak cases. Dengue fever pandemic outbreak is used to apply the proposed model for drug demand uncertainty in a pandemic. The aim of this research is to predict the number of drugs needed in a hospital for the treatment of dengue fever cases during the epidemic outbreak. The SEIR model is used to simulate the number of dengue fever patients in a hospital atGresik district, East Java in Indonesia. This analysis was carried out in a comparative way with the other forecasting methods. The result showed that the simulation’s result is different from other forecasting methods, depending on the context in which it is used, such as the disease type and the area of epidemic under study. In the future research, the proposed model is could applied in Malaria, COVID-19 pandemic, and another in order to ensuring the applicability of proposed model. This investigation is based on the application of Susceptible-Exposed-Infectious-Recovered (SEIR) model to simulate the number of diseases spread in a region, along with a historical approach of epidemic outbreak cases. Dengue fever pandemic outbreak is used to apply the proposed model for drug demand uncertainty in a pandemic. The aim of this research is to predict the number of drugs needed in a hospital for the treatment of dengue fever cases during the epidemic outbreak. The SEIR model is used to simulate the number of dengue fever patients in a hospital atGresik district, East Java in Indonesia. This analysis was carried out in a comparative way with the other forecasting methods. The result showed that the simulation’s result is different from other forecasting methods, depending on the context in which it is used, such as the disease type and the area of epidemic under study. In the future research, the proposed model is could applied in Malaria, COVID-19 pandemic, and another in order to ensuring the applicability of proposed model. [ABSTRACT FROM AUTHOR]

The COVID-19 outbreak is of great concern due to the high rates of infection and the large number of deaths worldwide. In this paper, we considered a Bayesian inference and failure mode and effects analysis of the modified susceptible-exposed-infectious-removed model for the transmission dynamics of COVID-19 with an exponentially distributed infectious period. We estimated the effective reproduction number based on laboratory-confirmed cases and death data using Bayesian inference and analyse the impact of the community spread of COVID-19 across the United Kingdom. We used the failure mode and effects analysis tool to evaluate the effectiveness of the action measures taken to manage the COVID-19 pandemic. We focused on COVID-19 infections and therefore the failure mode is taken as positive cases. The model is applied to COVID-19 data showing the effectiveness of interventions adopted to control the epidemic by reducing the reproduction number of COVID-19. Results have shown that the combination of Bayesian inference, compartmental modelling and failure mode and effects analysis is effective in modelling and studying the risks of COVID-19 transmissions, leading to the quantitative evaluation of the action measures and the identification of the lessons learned from the governmental measures and actions taken in response to COVID-19 in the United Kingdom. Analytical and numerical methods are used to highlight the practical implications of our findings. The proposed methodology will find applications in current and future COVID-19 like pandemics and wide quality engineering. [ABSTRACT FROM AUTHOR]

The COVID-19 outbreak is of great concern due to the high rates of infection and the large number of deaths worldwide. In this paper, we considered a Bayesian inference and failure mode and effects analysis of the modified susceptible-exposed-infectious-removed model for the transmission dynamics of COVID-19 with an exponentially distributed infectious period. We estimated the effective reproduction number based on laboratory-confirmed cases and death data using Bayesian inference and analyse the impact of the community spread of COVID-19 across the United Kingdom. We used the failure mode and effects analysis tool to evaluate the effectiveness of the action measures taken to manage the COVID-19 pandemic. We focused on COVID-19 infections and therefore the failure mode is taken as positive cases. The model is applied to COVID-19 data showing the effectiveness of interventions adopted to control the epidemic by reducing the reproduction number of COVID-19. Results have shown that the combination of Bayesian inference, compartmental modelling and failure mode and effects analysis is effective in modelling and studying the risks of COVID-19 transmissions, leading to the quantitative evaluation of the action measures and the identification of the lessons learned from the governmental measures and actions taken in response to COVID-19 in the United Kingdom. Analytical and numerical methods are used to highlight the practical implications of our findings. The proposed methodology will find applications in current and future COVID-19 like pandemics and wide quality engineering. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behavior of a SEIR epidemic system that takes into account governmental action and individual reaction is investigated. The transmission rate takes into account the impact of governmental action modeled as a step function while the decreasing contacts among individuals responding to the severity of the pandemic is modeled as a decreasing exponential function. We show that the proposed model is capable of predicting Hopf bifurcation points for a wide range of physically realistic parameters for the COVID-19 disease. In this regard, the model predicts periodic behavior that emanates from one Hopf point. The model also predicts stable oscillations connecting two Hopf points. The effect of the different model parameters on the existence of such periodic behavior is numerically investigated. Useful diagrams are constructed that delineate the range of periodic behavior predicted by the model. [ABSTRACT FROM AUTHOR]

We consider the control of the COVID-19 pandemic through a standard SIR compartmental model. This control is induced by the aggregation of individuals' decisions to limit their social interactions: when the epidemic is ongoing, an individual can diminish his/her contact rate in order to avoid getting infected, but this effort comes at a social cost. If each individual lowers his/her contact rate, the epidemic vanishes faster, but the effort cost may be high. A Mean Field Nash equilibrium at the population level is formed, resulting in a lower effective transmission rate of the virus. We prove theoretically that equilibrium exists and compute it numerically. However, this equilibrium selects a sub-optimal solution in comparison to the societal optimum (a centralized decision respected fully by all individuals), meaning that the cost of anarchy is strictly positive. We provide numerical examples and a sensitivity analysis, as well as an extension to a SEIR compartmental model to account for the relatively long latent phase of the COVID-19 disease. In all the scenario considered, the divergence between the individual and societal strategies happens both before the peak of the epidemic, due to individuals' fears, and after, when a significant propagation is still underway. [ABSTRACT FROM AUTHOR]

In modeling disease transmission, contacts are assumed to have different infection rates. Aproper simulation must model the heterogeneity in the transmission rates. In this article, we present a computationally efficient algorithm that can be applied to a populationwith heterogeneous transmission rates. We conducted a simulation study to show that the algorithm is more efficient than other algorithms for sampling the disease transmission in a subset of the heterogeneous population. We use a valid stochastic model of pandemic influenza to illustrate the algorithm and to estimate the overall infection attack rates of influenza A (H1N1) in a Canadian city. [ABSTRACT FROM AUTHOR]

Pandemics have the potential to cause immense disruption and damage to communities and societies. In this paper, we model the influenza pandemic of 2009. We propose a hybrid model to determine how the pandemic spreads through the world. The model considers both SEIR-based model for local areas and the network model for global connection between countries referring to data on international travelers. Our interest is to reproduce the situation using the data of the early stage of the pandemic and to predict the future transition by extending the simulation cycle. Our simulation result predicts the second peak of the pandemic in the real world by considering the factors of tendency of seasonal influenza and people’s reaction against the infection. Without considering these factors, the simulation does not predict the second peak of the pandemic in the real world. We conclude that the seasonal tendency and people’s reaction are important factors for the spreading of the pandemic. [ABSTRACT FROM PUBLISHER]

The emergence of novel SARS-CoV-2 variants of concern (VOC), in late 2020, with selective transmission advantage and partial immunity escape potential, has been driving further evolution in the pandemic. The timing of mutational evolution and its limits are thus of paramount importance in preparedness planning. Here, we present a model predicting the pattern of epidemic growth including the emergence of variants through mutation. It is based on the SEIR (Susceptible, Exposed, Infected, Removed) model, but its equations are modified according to the transmission parameters of novel variants. Since more transmissible strains will drive a further increase in the number of cases, they will also lead to further novel mutations. As one cannot predict whether there is a viral mutational evolutionary limit, we model a cascade that could lead to hyper-exponential growth (HEG) involving the emergence of even more transmissible mutants that could overwhelm any systematic response. Our results are consistent with the timing, since the beginning of the pandemic, of the concurrent and independent emergence of the VOCs. The current dominance of the Delta variant and the need for additional public health measures indicates some of the risks of a possible HEG. We examine conditions that favor the expected appearance of similar variants, thus enabling better preparedness and more targeted research. • Modified SEIR model with mutation predicts emergence of many variants of SARS-CoV-2 • This model predicts the observed pattern of increasing infectiousness of variants • The results are consistent with the timing of the emergence of VOCs • Hyper-exponential growth possible, but dominance by only a few variants is more likely [ABSTRACT FROM AUTHOR]

We consider a scenario where the pandemic infection rate is inversely proportional to the power of the distance between the infected region and the non-infected region. In our study, we analyze the case where the exponent of the distance is 2, which is in accordance with Reilly's law of retail gravitation. One can test for infection but such tests are costly so one seeks to determine the region of infection while performing few tests. Our goal is to find a boundary region of minimal size that contains all infected areas. We discuss efficient algorithms and provide the asymptotic bound of the testing cost and simulation results for this problem. [ABSTRACT FROM AUTHOR]