A simple model for COVID-19

Novel multi-cluster workflow system to support real-time HPC-enabled epidemic science: Investigating the impact of vaccine acceptance on COVID-19 spread

We present MacKenzie, a HPC-driven multi-cluster workflow system that was used repeatedly to configure and execute fine-grained US national-scale epidemic simulation models during the COVID-19 pandemic. Mackenzie supported federal and Virginia policymakers, in real-time, for a large number of "what-if" scenarios during the COVID-19 pandemic, and continues to be used to answer related questions as COVID-19 transitions to the endemic stage of the disease. MacKenzie is a novel HPC meta-scheduler that can execute US-scale simulation models and associated workflows that typically present significant big data challenges. The meta-scheduler optimizes the total execution time of simulations in the workflow, and helps improve overall human productivity. As an exemplar of the kind of studies that can be conducted using Mackenzie, we present a modeling study to understand the impact of vaccine-acceptance in controlling the spread of COVID-19 in the US. We use a 288 million node synthetic social contact network (digital twin) spanning all 50 US states plus Washington DC, comprised of 3300 counties, with 12 billion daily interactions. The highly-resolved agent-based model used for the epidemic simulations uses realistic information about disease progression, vaccine uptake, production schedules, acceptance trends, prevalence, and social distancing guidelines. Computational experiments show that, for the simulation workload discussed above, MacKenzie is able to scale up well to 10K CPU cores. Our modeling results show that, when compared to faster and accelerating vaccinations, slower vaccination rates due to vaccine hesitancy cause averted infections to drop from 6.7M to 4.5M, and averted total deaths to drop from 39.4K to 28.2K across the US. This occurs despite the fact that the final vaccine coverage is the same in both scenarios. We also find that if vaccine acceptance could be increased by 10% in all states, averted infections could be increased from 4.5M to 4.7M (a 4.4% improvement) and total averted deaths could be increased from 28.2K to 29.9K (a 6% improvement) nationwide.

Susceptible-Infected-Susceptible type COVID-19 spread with collective effects

Many models developed to forecast and attempt to understand the COVID-19 pandemic are highly complex, and few take collective behavior into account. As the pandemic progressed individual recurrent infection was observed and simpler susceptible-infected type models were introduced. However, these do not include mechanisms to model collective behavior. Here, we introduce an extension of the SIS model that accounts for collective behavior and show that it has four equilibria. Two of the equilibria are the standard SIS model equilibria, a third is always unstable, and a fourth where collective behavior and infection prevalence interact to produce either node-like or oscillatory dynamics. We then parameterized the model using estimates of the transmission and recovery rates for COVID-19 and present phase diagrams for fixed recovery rate and free transmission rate, and both rates fixed. We observe that regions of oscillatory dynamics exist in both cases and that the collective behavior parameter regulates their extent. Finally, we show that the system exhibits hysteresis when the collective behavior parameter varies over time. This model provides a minimal framework for explaining oscillatory phenomena such as recurring waves of infection and hysteresis effects observed in COVID-19, and other SIS-type epidemics, in terms of collective behavior.

Delay-differential SEIR modeling for improved modelling of infection dynamics

SEIR (Susceptible-Exposed-Infected-Recovered) approach is a classic modeling method that is frequently used to study infectious diseases. However, in the vast majority of such models transitions from one population group to another are described using the mass-action law. That causes inability to reproduce observable dynamics of an infection such as the incubation period or progression of the disease's symptoms. In this paper, we propose a new approach to simulate the epidemic dynamics based on a system of differential equations with time delays and instant transitions to approximate durations of transition processes more correctly and make model parameters more clear. The suggested approach can be applied not only to Covid-19 but also to the study of other infectious diseases. We utilized it in the development of the delay-based model of the COVID-19 pandemic in Germany and France. The model takes into account testing of different population groups, symptoms progression from mild to critical, vaccination, duration of protective immunity and new virus strains. The stringency index was used as a generalized characteristic of the non-pharmaceutical government interventions in corresponding countries to contain the virus spread. The parameter identifiability analysis demonstrated that the presented modeling approach enables to significantly reduce the number of parameters and make them more identifiable. Both models are publicly available.

Modeling and multi-objective optimal control of reaction-diffusion COVID-19 system due to vaccination and patient isolation

In this paper, a reaction-diffusion COVID-19 model is proposed to explore how vaccination-isolation strategies affect the development of the epidemic. First, the basic dynamical properties of the system are explored. Then, the system's asymptotic distributions of endemic equilibrium under different conditions are studied. Further, the global sensitivity analysis of R 0 is implemented with the aim of determining the sensitivity for these parameters. In addition, the optimal vaccination-isolation strategy based on the optimal path is proposed. Meantime, social cost C ( m , σ ) , social benefit B ( m , σ ) , threshold R 0 ( m , σ ) three objective optimization problem based on vaccination-isolation strategy is explored, and the maximum social cost ( M S C ) and maximum social benefit ( M S B ) are obtained. Finally, the instance prediction of the Lhasa epidemic in China on August 7, 2022, is made by using the piecewise infection rates β 1 ( t ) , β 2 ( t ) , and some key indicators are obtained as follows: (1) The basic reproduction numbers of each stage in Lhasa, China are R 0 ( 1 : 8 ) = 0.4678 , R 0 ( 9 : 20 ) = 2.7655 , R 0 ( 21 : 30 ) = 0.3810 and R 0 ( 31 : 100 ) = 0.7819 ; (2) The daily new cases of this epidemic will peak at 43 on the 20th day (August 26, 2022); (3) The cumulative cases in Lhasa, China will reach about 640 and be cleared about the 80th day (October 28, 2022). Our research will contribute to winning the war on epidemic prevention and control.

Mathematical analysis of the impact of the media coverage in mitigating the outbreak of COVID-19

In this paper, a mathematical model with a standard incidence rate is proposed to assess the role of media such as facebook, television, radio and tweeter in the mitigation of the outbreak of COVID-19. The basic reproduction numberR 0 which is the threshold dynamics parameter between the disappearance and the persistence of the disease has been calculated. And, it is obvious to see that it varies directly to the number of hospitalized people, asymptomatic, symptomatic carriers and the impact of media coverage. The local and the global stabilities of the model have also been investigated by using the Routh-Hurwitz criterion and the Lyapunov's functional technique, respectively. Furthermore, we have performed a local sensitivity analysis to assess the impact of any variation in each one of the model parameter on the thresholdR 0 and the course of the disease accordingly. We have also computed the approximative rate at which herd immunity will occur when any control measure is implemented. To finish, we have presented some numerical simulation results by using some available data from the literature to corroborate our theoretical findings.

Application of Quantifier Elimination in Epidemiology

Background

An application of a novel method of a quantifier elimination in epidemiology was presented in this paper.

Objective

We investigated the existence of the endemic equilibrium for the SEIRS model by QE method and gave a short review of the epidemic prediction models for covid-19.

Methods

A new method for quantifier elimination for the theory of real closed fields.

Results

Obtained value of a reproduction number and endemic equilibrium for the SEIRS model by QEAnalysis of the SEIR model with the concrete values through the example of Severe Acute Respiratory Syndrome (SARS) (a critical value of a transmission rate is evaluated in the example).

Conclusion

The main result of this paper is the obtained value of the endemic equilibrium for the SEIRS model (similar result is obtained for the SEIR model). Also, we have analysed the SEIR model through the examle of SARS and we reviewed several epidemic prediction models for covid-19.

Analysis of optimal lockdown in integral economic-epidemic model

We analyze the optimal lockdown in an economic-epidemic model with realistic infectiveness distribution. The model is described by Volterra integral equations and accurately depicts the COVID-19 infectivity pattern from clinical data. A maximum principle is derived, and a qualitative dynamic analysis of the optimal lockdown problem is provided over finite and infinite horizons. We analytically prove and economically justify the possibility of an endemic scenario when the infection rate begins to climb after the lockdown ends.

Dynamics and strategies evaluations of a novel reaction-diffusion COVID-19 model with direct and aerosol transmission

The COVID-19 epidemic has infected millions of people and cast a shadow over the global economic recovery. To explore the epidemic's transmission law and provide theoretical guidance for epidemic prevention and control. In this paper, we investigate a novel SEIR-A reaction-diffusion COVID-19 system with direct and aerosol transmission. First, the solution's positivity and boundedness for the system are discussed. Then, the system's the basic reproduction number is defined. Further, the uniform persistence of disease when R 0 > 1 is explored. In addition, the system equilibrium's global stability based on R 0 is demonstrated. Next, the system's NSFD scheme is investigated and the discrete system's positivity, boundedness, and global properties are studied. Meantime, global sensitivity analysis on threshold R 0 is investigated. Interestingly, the effects of three strategies, including vaccination, receiving treatment, and wearing a mask, are evaluated numerically. The results suggest that the above three strategies can effectively control the peak and final scale of infection and shorten the duration of the epidemic. Finally, theoretical simulations and instance predictions are used to give several key indicators of the epidemic, including threshold R 0 , peak, time to peak, time to clear cases, and final size. The instance prediction results are as follows: (1) The basic reproduction numbers of Yangzhou and Putian in China are R 0 = 2.5107 and R 0 = 1.8846 , respectively. (2) This epidemic round in Yangzhou will peak at 56 new daily confirmed cases on the 9th day (August 5), and Putian will peat at 37 new daily confirmed cases on the 6th day (September 15). (3) The final scale of infections in Yangzhou and Putian reached 570 and 205 cases, respectively. (4) The Yangzhou epidemic is expected to be completely cleared on the 25th day (August 21). In addition, the Putian epidemic will continue for 15 days and be cleared on September 24. The analysis results mean that we should improve our immunity by actively vaccinating, reducing the possibility of aerosol transmission by wearing masks. In particular, people should maintain proper social distance, and the government should strengthen medical investment and COVID-19 project research.

An Epidemic Model with Time Delay Determined by the Disease Duration

Immuno-epidemiological models with distributed recovery and death rates can describe the epidemic progression more precisely than conventional compartmental models. However, the required immunological data to estimate the distributed recovery and death rates are not easily available. An epidemic model with time delay is derived from the previously developed model with distributed recovery and death rates, which does not require precise immunological data. The resulting generic model describes epidemic progression using two parameters, disease transmission rate and disease duration. The disease duration is incorporated as a delay parameter. Various epidemic characteristics of the delay model, namely the basic reproduction number, the maximal number of infected, and the final size of the epidemic are derived. The estimation of disease duration is studied with the help of real data for COVID-19. The delay model gives a good approximation of the COVID-19 data and of the more detailed model with distributed parameters.

Incorporating mass vaccination into compartment models for infectious diseases

The standard way of incorporating mass vaccination into a compartment model for an infectious disease is as a spontaneous transition process that applies to the entire susceptible class. The large degree of COVID-19 vaccine refusal, hesitancy, and ineligibility, and initial limitations of supply and distribution require reconsideration of this standard treatment. In this paper, we address these issues for models on endemic and epidemic time scales. On an endemic time scale, we partition the susceptible class into prevaccinated and unprotected subclasses and show that vaccine refusal/hesitancy/ineligibility has a significant impact on endemic behavior, particularly for diseases where immunity is short-lived. On an epidemic time scale, we develop a supply-limited Holling type 3 vaccination model and show that it is an excellent fit to vaccination data. We then extend the Holling model to a COVID-19 scenario in which the population is divided into two risk classes, with the high-risk class being prioritized for vaccination. In both cases, with and without risk stratification, we see significant differences in epidemiological outcomes between the Holling vaccination model and naive models. Finally, we use the new model to explore implications for public health policies in future pandemics.

Bistability in deterministic and stochastic SLIAR-type models with imperfect and waning vaccine protection

Various vaccines have been approved for use to combat COVID-19 that offer imperfect immunity and could furthermore wane over time. We analyze the effect of vaccination in an SLIARS model with demography by adding a compartment for vaccinated individuals and considering disease-induced death, imperfect and waning vaccination protection as well as waning infections-acquired immunity. When analyzed as systems of ordinary differential equations, the model is proven to admit a backward bifurcation. A continuous time Markov chain (CTMC) version of the model is simulated numerically and compared to the results of branching process approximations. While the CTMC model detects the presence of the backward bifurcation, the branching process approximation does not. The special case of an SVIRS model is shown to have the same properties.

An efficient nonstandard computer method to solve a compartmental epidemiological model for COVID-19 with vaccination and population migration

BACKGROUND AND OBJECTIVE

In this manuscript, we consider a compartmental model to describe the dynamics of propagation of an infectious disease in a human population. The population considers the presence of susceptible, exposed, asymptomatic and symptomatic infected, quarantined, recovered and vaccinated individuals. In turn, the mathematical model considers various mechanisms of interaction between the sub-populations in addition to population migration.

METHODS

The steady-state solutions for the disease-free and endemic scenarios are calculated, and the local stability of the equilibium solutions is determined using linear analysis, Descartes' rule of signs and the Routh-Hurwitz criterion. We demonstrate rigorously the existence and uniqueness of non-negative solutions for the mathematical model, and we prove that the system has no periodic solutions using Dulac's criterion. To solve this system, a nonstandard finite-difference method is proposed.

RESULTS

As the main results, we show that the computer method presented in this work is uniquely solvable, and that it preserves the non-negativity of initial approximations. Moreover, the steady-state solutions of the continuous model are also constant solutions of the numerical scheme, and the stability properties of those solutions are likewise preserved in the discrete scenario. Furthermore, we establish the consistency of the scheme and, using a discrete form of Gronwall's inequality, we prove theoretically the stability and the convergence properties of the scheme. For convenience, a Matlab program of our method is provided in the appendix.

CONCLUSIONS

The computer method presented in this work is a nonstandard scheme with multiple dynamical and numerical properties. Most of those properties are thoroughly confirmed using computer simulations. Its easy implementation make this numerical approach a useful tool in the investigation on the propagation of infectious diseases. From the theoretical point of view, the present work is one of the few papers in which a nonstandard scheme is fully and rigorously analyzed not only for the dynamical properties, but also for consistently, stability and convergence.

A Non-Uniform Continuous Cellular Automata for Analyzing and Predicting the Spreading Patterns of COVID-19

During the COVID-19 outbreak, modeling the spread of infectious diseases became a challenging research topic due to its rapid spread and high mortality rate. The main objective of a standard epidemiological model is to estimate the number of infected, suspected, and recovered from the illness by mathematical modeling. This model does not capture how the disease transmits between neighboring regions through interaction. A more general framework such as Cellular Automata (CA) is required to accommodate a more complex spatial interaction within the epidemiological model. The critical issue of modeling in the spread of diseases is how to reduce the prediction error. This research aims to formulate the influence of the interaction of a neighborhood on the spreading pattern of COVID-19 using a neighborhood frame model in a Cellular-Automata (CA) approach and obtain a predictive model for the COVID-19 spread with the error reduction to improve the model. We propose a non-uniform continuous CA (N-CCA) as our contribution to demonstrate the influence of interactions on the spread of COVID-19. The model has succeeded in demonstrating the influence of the interaction between regions on the COVID-19 spread, as represented by the coefficients obtained. These coefficients result from multiple regression models. The coefficient obtained represents the population’s behavior interacting with its neighborhood in a cell and influences the number of cases that occur the next day. The evaluation of the N-CCA model is conducted by root mean square error (RMSE) for the difference in the number of cases between prediction and real cases per cell in each region. This study demonstrates that this approach improves the prediction of accuracy for 14 days in the future using data points from the past 42 days, compared to a baseline model.

Optimal control and comprehensive cost-effectiveness analysis for COVID-19

Cost-effectiveness analysis is a mode of determining both the cost and economic health outcomes of one or more control interventions. In this work, we have formulated a non-autonomous nonlinear deterministic model to study the control of COVID-19 to unravel the cost and economic health outcomes for the autonomous nonlinear model proposed for the Kingdom of Saudi Arabia. We calculated the strength number and noticed the strength number is less than zero, meaning the proposed model does not capture multiple waves, hence to capture multiple wave new compartmental model may require for the Kingdom of Saudi Arabia. We proposed an optimal control problem based on a previously studied model and proved the existence of the proposed optimal control model. The optimality system associated with the non-autonomous epidemic model is derived using Pontryagin's maximum principle. The optimal control model captures four time-dependent control functions, thus,u 1 -practising physical or social distancing protocols;u 2 -practising personal hygiene by cleaning contaminated surfaces with alcohol-based detergents;u 3 -practising proper and safety measures by exposed, asymptomatic and symptomatic infected individuals;u 4 -fumigating schools in all levels of education, sports facilities, commercial areas and religious worship centres. We have performed numerical simulations to investigate extensive cost-effectiveness analysis for fourteen optimal control strategies. Comparing the control strategies, we noticed that; Strategy 1 (practising physical or social distancing protocols) is the most cost-saving and most effective control intervention in Saudi Arabia in the absence of vaccination. But, in terms of the infection averted, we saw that strategy 6, strategy 11, strategy 12, and strategy 14 are just as good in controlling COVID-19.

Assessing population-sampling strategies for reducing the COVID-19 incidence

As long as critical levels of vaccination have not been reached to ensure heard immunity, and new SARS-CoV-2 strains are developing, the only realistic way to reduce the infection speed in a population is to track the infected individuals before they pass on the virus. Testing the population via sampling has shown good results in slowing the epidemic spread. Sampling can be implemented at different times during the epidemic and may be done either per individual or for combined groups of people at a time. The work we present here makes two main contributions. We first extend and refine our scalable agent-based COVID-19 simulator to incorporate an improved socio-demographic model which considers professions, as well as a more realistic population mixing model based on contact matrices per country. These extensions are necessary to develop and test various sampling strategies in a scenario including the 62 largest cities in Spain; this is our second contribution. As part of the evaluation, we also analyze the impact of different parameters, such as testing frequency, quarantine time, percentage of quarantine breakers, or group testing, on sampling efficacy. Our results show that the most effective strategies are pooling, rapid antigen test campaigns, and requiring negative testing for access to public areas. The effectiveness of all these strategies can be greatly increased by reducing the number of contacts for infected individual.

Pandemic fatigue impact on COVID-19 spread: A mathematical modelling answer to the Italian scenario

The COVID-19 outbreak has generated, in addition to the dramatic sanitary consequences, severe psychological repercussions for the populations affected by the pandemic. Simultaneously, these consequences can have related effects on the spread of the virus. Pandemic fatigue occurs when stress rises beyond a threshold, leading a person to feel demotivated to follow recommended behaviours to protect themselves and others. In the present paper, we introduce a new susceptible-infected-quarantined-recovered-dead (SIQRD) model in terms of a system of ordinary differential equations (ODE). The model considers the countermeasures taken by sanitary authorities and the effect of pandemic fatigue. The latter can be mitigated by fear of the disease's consequences modelled with the death rate in mind. The mathematical well-posedness of the model is proved. We show the numerical results to be consistent with the transmission dynamics data characterising the epidemic of the COVID-19 outbreak in Italy in 2020. We provide a measure of the possible pandemic fatigue impact. The model can be used to evaluate the public health interventions and prevent with specific actions the possible damages resulting from the social phenomenon of relaxation concerning the observance of the preventive rules imposed.

Model with transmission delays for COVID-19 control: Theory and empirical assessment

The paper focuses on modeling of public health measures to control the COVID-19 pandemic. The authors suggest a flexible integral model with distributed lags, which realistically describes COVID-19 infectiousness period from clinical data. It contains susceptible-infectious-recovered (SIR), susceptible-exposed-infectious-recovered (SEIR), and other epidemic models as special cases. The model is used for assessing how government decisions to lockdown and reopen the economy affect epidemic spread. The authors demonstrate essential differences in transition and asymptotic dynamics of the integral model and the SIR model after lockdown. The provided simulation on real data accurately describes several waves of the COVID-19 epidemic in the United States and is in good correspondence with government actions to curb the epidemic.

Activity-based epidemic propagation and contact network scaling in auto-dependent metropolitan areas

We build on recent work to develop a fully mechanistic, activity-based and highly spatio-temporally resolved epidemiological model which leverages person-trajectories obtained from an activity-based model calibrated for two full-scale prototype cities, consisting of representative synthetic populations and mobility networks for two contrasting auto-dependent city typologies. We simulate the propagation of the COVID-19 epidemic in both cities to analyze spreading patterns in urban networks across various activity types. Investigating the impact of the transit network, we find that its removal dampens disease propagation significantly, suggesting that transit restriction is more critical for mitigating post-peak disease spreading in transit dense cities. In the latter stages of disease spread, we find that the greatest share of infections occur at work locations. A statistical analysis of the resulting activity-based contact networks indicates that transit contacts are scale-free, work contacts are Weibull distributed, and shopping or leisure contacts are exponentially distributed. We validate our simulation results against existing case and mortality data across multiple cities in their respective typologies. Our framework demonstrates the potential for tracking epidemic propagation in urban networks, analyzing socio-demographic impacts and assessing activity- and mobility-specific implications of both non-pharmaceutical and pharmaceutical intervention strategies.

Evaluation of the Spatiotemporal Epidemiological Modeler (STEM) during the recent COVID-19 pandemic

In early December 2019, some people in China were diagnosed with an unknown pneumonia in Wuhan, in the Hubei province. The responsible of the outbreak was identified in a novel human-infecting coronavirus which differs both from severe acute respiratory syndrome coronavirus and from Middle East respiratory syndrome coronavirus. The new coronavirus, officially named severe acute respiratory syndrome coronavirus 2 by the International Committee on Taxonomy of Viruses, has spread worldwide within few weeks. Only two vaccines have been approved by regulatory agencies and some others are under development. Moreover, effective treatments have not been yet identified or developed even if some potential molecules are under investigation. In a pandemic outbreak, when treatments are not available, the only method that contribute to reduce the virus spreading is the adoption of social distancing measures, like quarantine and isolation. With the intention of better managing emergencies like this, which are a great public health threat, it is important to dispose of predictive epidemiological tools that can help to understand both the virus spreading in terms of people infected, hospitalized, dead and recovered and the effectiveness of containment measures.

Merits and Limitations of Mathematical Modeling and Computational Simulations in Mitigation of COVID-19 Pandemic: A Comprehensive Review

Mathematical models have assisted in describing the transmission and propagation dynamics of various viral diseases like MERS, measles, SARS, and Influenza; while the advanced computational technique is utilized in the epidemiology of viral diseases to examine and estimate the influences of interventions and vaccinations. In March 2020, the World Health Organization (WHO) has declared the COVID-19 as a global pandemic and the rate of morbidity and mortality triggers unprecedented public health crises throughout the world. The mathematical models can assist in improving the interventions, key transmission parameters, public health agencies, and countermeasures to mitigate this pandemic. Besides, the mathematical models were also used to examine the characteristics of epidemiological and the understanding of the complex transmission mechanism. Our literature study found that there were still some challenges in mathematical modeling for the case of ecology, genetics, microbiology, and pathology pose; also, some aspects like political and societal issues and cultural and ethical standards are hard to be characterized. Here, the recent mathematical models about COVID-19 and their prominent features, applications, limitations, and future perspective are discussed and reviewed. This review can assist in further improvement of mathematical models that will consider the current challenges of viral diseases.

Transmission dynamics of novel coronavirus SARS-CoV-2 among healthcare workers, a case study in Iran

One of the main concerns during the COVID-19 pandemic was the protection of healthcare workers against the novel coronavirus. The critical role and vulnerability of healthcare workers during the COVID-19 pandemic leads us to derive a mathematical model to express the spread of coronavirus between the healthcare workers. In the first step, the SECIRH model is introduced, and then the mathematical equations are written. The proposed model includes eight state variables, i.e., Susceptible, Exposed, Carrier, Infected, Hospitalized, ICU admitted, Dead, and finally Recovered. In this model, the vaccination, protective equipment, and recruitment policy are considered as preventive actions. The formal confirmed data provided by the Iranian ministry of health is used to simulate the proposed model. The simulation results revealed that the proposed model has a high degree of consistency with the actual COVID-19 daily statistics. In addition, the roles of vaccination, protective equipment, and recruitment policy for the elimination of coronavirus among the healthcare workers are investigated. The results of this research help the policymakers to adopt the best decisions against the spread of coronavirus among healthcare workers.

An explicit unconditionally stable scheme: application to diffusive Covid-19 epidemic model

An explicit unconditionally stable scheme is proposed for solving time-dependent partial differential equations. The application of the proposed scheme is given to solve the COVID-19 epidemic model. This scheme is first-order accurate in time and second-order accurate in space and provides the conditions to get a positive solution for the considered type of epidemic model. Furthermore, the scheme's stability for the general type of parabolic equation with source term is proved by employing von Neumann stability analysis. Furthermore, the consistency of the scheme is verified for the category of susceptible individuals. In addition to this, the convergence of the proposed scheme is discussed for the considered mathematical model.

Assessing the Spatio-temporal Spread of COVID-19 via Compartmental Models with Diffusion in Italy, USA, and Brazil

The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population under study is divided into compartments based on qualitative characteristics, with different assumptions about the nature and rate of transfer across compartments. Though most commonly formulated as ordinary differential equation models, in which the compartments depend only on time, recent works have also focused on partial differential equation (PDE) models, incorporating the variation of an epidemic in space. Such research on PDE models within a Susceptible, Infected, Exposed, Recovered, and Deceased framework has led to promising results in reproducing COVID-19 contagion dynamics. In this paper, we assess the robustness of this modeling framework by considering different geometries over more extended periods than in other similar studies. We first validate our code by reproducing previously shown results for Lombardy, Italy. We then focus on the U.S. state of Georgia and on the Brazilian state of Rio de Janeiro, one of the most impacted areas in the world. Our results show good agreement with real-world epidemiological data in both time and space for all regions across major areas and across three different continents, suggesting that the modeling approach is both valid and robust.

Risk of COVID-19 variant importation - How useful are travel control measures?

We consider models for the importation of a new variant COVID-19 strain in a location already seeing propagation of a resident variant. By distinguishing contaminations generated by imported cases from those originating in the community, we are able to evaluate the contribution of importations to the dynamics of the disease in a community. We find that after an initial seeding, the role of importations becomes marginal compared to that of community-based propagation. We also evaluate the role of two travel control measures, quarantine and travel interruptions. We conclude that quarantine is an efficacious way of lowering importation rates, while travel interruptions have the potential to delay the consequences of importations but need to be applied within a very tight time window following the initial emergence of the variant.

A COVID-19 Epidemic Model Predicting the Effectiveness of Vaccination in the US

A model of a COVID-19 epidemic is used to predict the effectiveness of vaccination in the US. The model incorporates key features of COVID-19 epidemics: asymptomatic and symptomatic infectiousness, reported and unreported cases data, and social measures implemented to decrease infection transmission. The model analyzes the effectiveness of vaccination in terms of vaccination efficiency, vaccination scheduling, and relaxation of social measures that decrease disease transmission. The model demonstrates that the subsiding of the epidemic as vaccination is implemented depends critically on the scale of relaxation of social measures that reduce disease transmission.

Modeling the Spread and Control of COVID-19

Data-centric models of COVID-19 have been attempted, but have certain limitations. In this work, we propose an agent-based model of the epidemic in a confined space of agents representing humans. An extension to the SEIR model allows us to consider the difference between the appearance (black-box view) of the spread of disease and the real situation (glass-box view). Our model allows for simulations of lockdowns, social distancing, personal hygiene, quarantine, and hospitalization, with further considerations of different parameters, such as the extent to which hygiene and social distancing are observed in a population. Our results provide qualitative indications of the effects of various policies and parameters, for instance, that lockdowns by themselves are extremely unlikely to bring an end to an epidemic and may indeed make things worse, that social distancing is more important than personal hygiene, and that the growth of infection is significantly reduced for moderately high levels of social distancing and hygiene, even in the absence of herd immunity.

Adaptive SIR model for propagation of SARS-CoV-2 in Brazil

We study the spreading of SARS-CoV-2 in Brazil based on official data available since March 22, 2020. Calculations are done via an adaptive susceptible-infected-removed (SIR) model featuring dynamical recuperation and propagation rates. We are able reproduce the number of confirmed cases over time with less than 5% error and also provide with short- and long-term predictions. The model can also be used to account for the epidemic dynamics in other countries with great accuracy.

The first wave of the SARS-CoV-2 epidemic in Tuscany (Italy): A SI2R2D compartmental model with uncertainty evaluation

With the aim of studying the spread of the SARS-CoV-2 infection in the Tuscany region of Italy during the first epidemic wave (February-June 2020), we define a compartmental model that accounts for both detected and undetected infections and assumes that only notified cases can die. We estimate the infection fatality rate, the case fatality rate, and the basic reproduction number, modeled as a time-varying function, by calibrating on the cumulative daily number of observed deaths and notified infected, after fixing to plausible values the other model parameters to assure identifiability. The confidence intervals are estimated by a parametric bootstrap procedure and a Global Sensitivity Analysis is performed to assess the sensitivity of the estimates to changes in the values of the fixed parameters. According to our results, the basic reproduction number drops from an initial value of 6.055 to 0 at the end of the national lockdown, then it grows again, but remaining under 1. At the beginning of the epidemic, the case and the infection fatality rates are estimated to be 13.1% and 2.3%, respectively. Among the parameters considered as fixed, the average time from infection to recovery for the not notified infected appears to be the most impacting one on the model estimates. The probability for an infected to be notified has a relevant impact on the infection fatality rate and on the shape of the epidemic curve. This stresses the need of collecting information on these parameters to better understand the phenomenon and get reliable predictions.

Cyber Physical Systems Dependability Using CPS-IOT Monitoring

Recently, vast investments have been made worldwide in developing Cyber-Physical Systems (CPS) as solutions to key socio-economic challenges. The Internet-of-Things (IoT) has also enjoyed widespread adoption, mostly for its ability to add “sensing” and “actuation” capabilities to existing CPS infrastructures. However, attention must be paid to the impact of IoT protocols on the dependability of CPS infrastructures. We address the issues of CPS dependability by using an epidemic model of the underlying dynamics within the CPS’ IoT subsystem (CPS-IoT) and an interference-aware routing reconfiguration. These help to efficiently monitor CPS infrastructure—avoiding routing oscillation, while improving its safety. The contributions of this paper are threefold. Firstly, a CPS orchestration model is proposed that relies upon: (i) Inbound surveillance and outbound actuation to improve dependability and (ii) a novel information diffusion model that uses epidemic states and diffusion sets to produce diffusion patterns across the CPS-IoT. Secondly, the proposed CPS orchestration model is numerically analysed to show its dependability for both sensitive and non-sensitive applications. Finally, a novel interference-aware clustering protocol called “INMP”, which enables network reconfiguration through migration of nodes across clusters, is proposed. It is then bench-marked against prominent IoT protocols to assess its impact on the dependability of the CPS.

Estimation of COVID-19 outbreak size in Harbin, China

Since the first level response to public health emergencies was launched on January 25, 2020, in Heilongjiang province, China, the outbreak of COVID-19 seems to be under control. However, an outbreak of COVID-19 caused by imported cases developed in Harbin during April 2020. A mathematical model is established to investigate the transmission of COVID-19 in Harbin. Based on the dynamical analysis and data fitting, the research investigates the outbreak of COVID-19 in Harbin and estimates the outbreak size of COVID-19 in Harbin. The outbreak size estimated of COVID-19 in Harbin reaches 174, where 54% of infected cases were identified while 46% of infected cases were not found out. We should maintain vigilance against unfound infected people. Our findings suggest that the effective reproduction number decreased drastically in contrast with the value of 3.6 on April 9; after that the effective interventions were implemented by the Heilongjiang province government. Finally, the effective reproduction number arrived at the value of 0.04 which is immensely below the threshold value 1, which means that the Heilongjiang province government got the outbreak of COVID-19 in Harbin under control.

Simulation of COVID-19 Propagation Scenarios in the Madrid Metropolitan Area

This work presents simulation results for different mitigation and confinement scenarios for the propagation of COVID-19 in the metropolitan area of Madrid. These scenarios were implemented and tested using EpiGraph, an epidemic simulator which has been extended to simulate COVID-19 propagation. EpiGraph implements a social interaction model, which realistically captures a large number of characteristics of individuals and groups, as well as their individual interconnections, which are extracted from connection patterns in social networks. Besides the epidemiological and social interaction components, it also models people's short and long-distance movements as part of a transportation model. These features, together with the capacity to simulate scenarios with millions of individuals and apply different contention and mitigation measures, gives EpiGraph the potential to reproduce the COVID-19 evolution and study medium-term effects of the virus when applying mitigation methods. EpiGraph, obtains closely aligned infected and death curves related to the first wave in the Madrid metropolitan area, achieving similar seroprevalence values. We also show that selective lockdown for people over 60 would reduce the number of deaths. In addition, evaluate the effect of the use of face masks after the first wave, which shows that the percentage of people that comply with mask use is a crucial factor for mitigating the infection's spread.

Pandemic velocity: Forecasting COVID-19 in the US with a machine learning & Bayesian time series compartmental model

Predictions of COVID-19 case growth and mortality are critical to the decisions of political leaders, businesses, and individuals grappling with the pandemic. This predictive task is challenging due to the novelty of the virus, limited data, and dynamic political and societal responses. We embed a Bayesian time series model and a random forest algorithm within an epidemiological compartmental model for empirically grounded COVID-19 predictions. The Bayesian case model fits a location-specific curve to the velocity (first derivative) of the log transformed cumulative case count, borrowing strength across geographic locations and incorporating prior information to obtain a posterior distribution for case trajectories. The compartmental model uses this distribution and predicts deaths using a random forest algorithm trained on COVID-19 data and population-level characteristics, yielding daily projections and interval estimates for cases and deaths in U.S. states. We evaluated the model by training it on progressively longer periods of the pandemic and computing its predictive accuracy over 21-day forecasts. The substantial variation in predicted trajectories and associated uncertainty between states is illustrated by comparing three unique locations: New York, Colorado, and West Virginia. The sophistication and accuracy of this COVID-19 model offer reliable predictions and uncertainty estimates for the current trajectory of the pandemic in the U.S. and provide a platform for future predictions as shifting political and societal responses alter its course.

On the Transmission Dynamics of SARS-CoV-2 in a Temperate Climate

An epidemiological model, which describes the transmission dynamics of SARS-CoV-2 under specific consideration of the incubation period including the population with subclinical infections and being infective is presented. The COVID-19 epidemic in Greece was explored through a Monte Carlo uncertainty analysis framework, and the optimal values for the parameters that determined the transmission dynamics could be obtained before, during, and after the interventions to control the epidemic. The dynamic change of the fraction of asymptomatic individuals was shown. The analysis of the modelling results at the intra-annual climatic scale allowed for in depth investigation of the transmission dynamics of SARS-CoV-2 and the significance and relative importance of the model parameters. Moreover, the analysis at this scale incorporated the exploration of the forecast horizon and its variability. Three discrete peaks were found in the transmission rates throughout the investigated period (15 February–15 December 2020). Two of them corresponded to the timing of the spring and autumn epidemic waves while the third one occurred in mid-summer, implying that relaxation of social distancing and increased mobility may have a strong effect on rekindling the epidemic dynamics offsetting positive effects from factors such as decreased household crowding and increased environmental ultraviolet radiation. In addition, the epidemiological state was found to constitute a significant indicator of the forecast reliability horizon, spanning from as low as few days to more than four weeks. Embedding the model in an ensemble framework may extend the predictability horizon. Therefore, it may contribute to the accuracy of health risk assessment and inform public health decision making of more efficient control measures.

An Epidemic Grid Model to Address the Spread of Covid-19: A Comparison between Italy, Germany and France

This paper presents a discrete compartmental Susceptible–Exposed–Infected–Recovered/Dead (SEIR/D) model to address the expansion of Covid-19. This model is based on a grid. As time passes, the status of the cells updates by means of binary rules following a neighborhood and a delay pattern. This model has already been analyzed in previous works and successfully compared with the corresponding continuous models solved by ordinary differential equations (ODE), with the intention of finding the homologous parameters between both approaches. Thus, it has been possible to prove that the combination neighborhood-update rule is responsible for the rate of expansion and recovering/death of the disease. The delays (between Susceptible and Asymptomatic, Asymptomatic and Infected, Infected and Recovered/Dead) may have a crucial impact on both height and timing of the peak of Infected and the Recovery/Death rate. This theoretical model has been successfully tested in the case of the dissemination of information through mobile social networks and in the case of plant pests.

Adaptive mesh refinement and coarsening for diffusion-reaction epidemiological models

The outbreak of COVID-19 in 2020 has led to a surge in the interest in the mathematical modeling of infectious diseases. Disease transmission may be modeled as compartmental models, in which the population under study is divided into compartments and has assumptions about the nature and time rate of transfer from one compartment to another. Usually, they are composed of a system of ordinary differential equations in time. A class of such models considers the Susceptible, Exposed, Infected, Recovered, and Deceased populations, the SEIRD model. However, these models do not always account for the movement of individuals from one region to another. In this work, we extend the formulation of SEIRD compartmental models to diffusion-reaction systems of partial differential equations to capture the continuous spatio-temporal dynamics of COVID-19. Since the virus spread is not only through diffusion, we introduce a source term to the equation system, representing exposed people who return from travel. We also add the possibility of anisotropic non-homogeneous diffusion. We implement the whole model in libMesh, an open finite element library that provides a framework for multiphysics, considering adaptive mesh refinement and coarsening. Therefore, the model can represent several spatial scales, adapting the resolution to the disease dynamics. We verify our model with standard SEIRD models and show several examples highlighting the present model's new capabilities.

Evaluation of the effect of different policies in the containment of epidemic spreads for the COVID-19 case

The paper presents a new mathematical model for the SARS-CoV-2 virus propagation, designed to include all the possible actions to prevent the spread and to help in the healing of infected people. After a discussion on the equilibrium and stability properties of the model, the effects of each different control actions on the evolution of the epidemic spread are analysed, through numerical evaluations for a more intuitive and immediate presentation, showing the consequences on the classes of the population.

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A new mathematical model for the spread of the SARS-CoV-2 is proposed and analysed.

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Available control actions are considered including social and political decisions.

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The effects on populations of containment policies and medical efforts are described.

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The model can support choices for large scale strategies of diseases contrast.

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Control actions can be defined according to economic, healthy and social issues.

Mathematical model for spreading of COVID-19 virus with the Mittag-Leffler kernel

In the Nidovirales order of the Coronaviridae family, where the coronavirus (crown-like spikes on the surface of the virus) causing severe infections like acute lung injury and acute respiratory distress syndrome. The contagion of this virus categorized as severed, which even causes severe damages to human life to harmless such as a common cold. In this manuscript, we discussed the SARS-CoV-2 virus into a system of equations to examine the existence and uniqueness results with the Atangana-Baleanu derivative by using a fixed-point method. Later, we designed a system where we generate numerical results to predict the outcome of virus spreadings all over India.

Spatio-temporal estimation of the daily cases of COVID-19 in worldwide using random forest machine learning algorithm

Novel Coronavirus pandemic, which negatively affected public health in social, psychological and economical terms, spread to the whole world in a short period of 6 months. However, the rate of increase in cases was not equal for every country. The measures implemented by the countries changed the daily spreading speed of the disease. This was determined by changes in the number of daily cases. In this study, the performance of the Random Forest (RF) machine learning algorithm was investigated in estimating the near future case numbers for 190 countries in the world and it is mapped in comparison with actual confirmed cases results. The number of confirmed cases between 23/01/2020 - 17/06/2020 were divided into 3 main sub-datasets: training sub-data, testing sub-data (interpolation data) and estimating sub-data (extrapolation data) for the random forest model. At the end of the study, it has been found that R2 values for testing sub-data of RF model estimates range between 0.843 and 0.995 (average R2= 0.959), and RMSE values between 141.76 and 526.18 (mean RMSE = 259.38); and that R2 values for estimating sub-data range between 0.690 and 0.968 (mean R2 = 0.914), and RMSE values between 549.73 and 2500.79 (mean RMSE = 909.37). These results show that the random forest machine learning algorithm performs well in estimating the number of cases for the near future in case of an epidemic like Novel Coronavirus, which outbreaks suddenly and spreads rapidly.

COVID-ABS: An agent-based model of COVID-19 epidemic to simulate health and economic effects of social distancing interventions

The COVID-19 pandemic due to the SARS-CoV-2 coronavirus has directly impacted the public health and economy worldwide. To overcome this problem, countries have adopted different policies and non-pharmaceutical interventions for controlling the spread of the virus. This paper proposes the COVID-ABS, a new SEIR (Susceptible-Exposed-Infected-Recovered) agent-based model that aims to simulate the pandemic dynamics using a society of agents emulating people, business and government. Seven different scenarios of social distancing interventions were analyzed, with varying epidemiological and economic effects: (1) do nothing, (2) lockdown, (3) conditional lockdown, (4) vertical isolation, (5) partial isolation, (6) use of face masks, and (7) use of face masks together with 50% of adhesion to social isolation. In the impossibility of implementing scenarios with lockdown, which present the lowest number of deaths and highest impact on the economy, scenarios combining the use of face masks and partial isolation can be the more realistic for implementation in terms of social cooperation. The COVID-ABS model was implemented in Python programming language, with source code publicly available. The model can be easily extended to other societies by changing the input parameters, as well as allowing the creation of a multitude of other scenarios. Therefore, it is a useful tool to assist politicians and health authorities to plan their actions against the COVID-19 epidemic.

A model of COVID-19 transmission to understand the effectiveness of the containment measures: application to data from France

The main objective of this paper is to address the following question: are the containment measures imposed by most of the world governments effective and sufficient to stop the epidemic of COVID-19 beyond the lock-down period? In this paper, we propose a mathematical model which allows us to investigate and analyse this problem. We show by means of the reproductive number, that the containment measures appear to have slowed the growth of the outbreak. Nevertheless, these measures remain only effective as long as a very large fraction of population, p, greater than the critical value remains confined. Using French current data, we give some simulation experiments with five scenarios including: (i) the validation of model with p estimated to 93%, (ii) the study of the effectiveness of containment measures, (iii) the study of the effectiveness of the large-scale testing, (iv) the study of the social distancing and wearing masks measures and (v) the study taking into account the combination of the large-scale test of detection of infected individuals and the social distancing with linear progressive easing of restrictions. The latter scenario was shown to be effective at overcoming the outbreak if the transmission rate decreases to 75% and the number of tests of detection is multiplied by three. We also noticed that if the measures studied in our five scenarios are taken separately then the second wave might occur at least as far as the parameter values remain unchanged.

Analysis of the outbreak of COVID-19 in Japan by SIQR model

The SIQR model is exploited to analyze the outbreak of COVID-19 in Japan where the number of the daily confirmed new cases is explicitly treated as an observable. It is assumed that the society consists of four compartments; susceptible individuals (S), infected individuals at large (I), quarantined patients (Q) and recovered individuals (R), and the time evolution of the pandemic is described by a set of ordinary differential equations. It is shown that the quarantine rate can be determined from the time dependence of the daily confirmed new cases, from which the number of infected individuals can be estimated. The infection rate and quarantine rate are determined for the period from mid-February to mid-April in Japan and transmission characteristics of the initial stages of the outbreak in Japan are analyzed in connection with the policies employed by the government. The effectiveness of different measures is discussed for controlling the outbreak and it is shown that identifying patients through PCR (Polymerase Chain Reaction) testing and isolating them in a quarantine is more effective than lockdown measures aimed at inhibiting social interactions of the general population. An effective reproduction number for infected individuals at large is introduced which is appropriate to epidemics controlled by quarantine measures.

Mathematical Modeling for Prediction Dynamics of the Coronavirus Disease 2019 (COVID-19) Pandemic, Quarantine Control Measures

A mathematical model for forecasting the transmission of the COVID-19 outbreak is proposed to investigate the effects of quarantined and hospitalized individuals. We analyze the proposed model by considering the existence and the positivity of the solution. Then, the basic reproduction number (R0)—the expected number of secondary cases produced by a single infection in a completely susceptible population—is computed by using the next-generation matrix to carry out the stability of disease-free equilibrium and endemic equilibrium. The results show that the disease-free equilibrium is locally asymptotically stable if R0<1, and the endemic equilibrium is locally asymptotically stable if R0>1. Numerical simulations of the proposed model are illustrated. The sensitivity of the model parameters is considered in order to control the spread by intervention strategies. Numerical results confirm that the model is suitable for the outbreak that occurred in Thailand.

Infectious Disease Modeling and Epidemic Response Measures Analysis Considering Asymptomatic Infection

Classical SIR dynamic model and its derivative improved model may not accurately describe the epidemic situation similar to COVID-19 with characteristics of relative long incubation period and a large number of asymptomatic infections. Based on the existing epidemic compartment model, a novel compartment dynamic model considering actual transmission path of the symptomatic and asymptomatic infected is presented. Theoretical analysis and numerical simulation are employed to conduct prediction of development of the epidemic. According to different epidemic response measures, i.e., mitigation measures, suppression measures, medical treatment, evolutionary trend of epidemic situation under the initial population distribution structure are discussed. Results show that the control effects of different response measures on the number of deaths depend on the timing of the implementation of the measures. For mitigation response measures, the timing of the implementation of the measures has no obvious effect on the final epidemic, while for suppression response measures, the effect of suppression response measures in the early stage of the epidemic is significantly better than that in the middle and late stage of the epidemic development. Furthermore, no matter which stage the epidemic is in, the improvement of medical treatment level will play an important role in effectively reducing mortality. This study provides useful enlightenment and decision-making reference for policy makers to choose appropriate epidemic prevention and response measures in practice.

Adequacy of Logistic models for describing the dynamics of COVID-19 pandemic

Logistic models have been widely used for modelling the ongoing COVID-19 pandemic. This study used the data for Kuwait to assess the adequacy of the two most commonly used logistic models (Verhulst and Richards models) for describing the dynamics COVID-19. Specifically, the study assessed the predictive performance of these two models and the practical identifiability of their parameters. Two model calibration approaches were adopted. In the first approach, all the data was used to fit the models as per the heuristic model fitting method. In the second approach, only the first half of the data was used for calibrating the models, while the other half was left for validating the models. Analysis of the obtained calibration and validation results have indicated that parameters of the two models cannot be identified with high certainty from COVID-19 data. Further, the models shown to have structural problems as they could not predict reasonably the validation data. Therefore, they should not be used for long-term predictions of COVID-19. Suggestion have been made for improving the performances of the models.

Modelling scenarios of the epidemic of COVID-19 in Canada

BACKGROUND

Severe acute respiratory syndrome virus 2 (SARS-CoV-2), likely a bat-origin coronavirus, spilled over from wildlife to humans in China in late 2019, manifesting as a respiratory disease. Coronavirus disease 2019 (COVID-19) spread initially within China and then globally, resulting in a pandemic.

OBJECTIVE

This article describes predictive modelling of COVID-19 in general, and efforts within the Public Health Agency of Canada to model the effects of non-pharmaceutical interventions (NPIs) on transmission of SARS-CoV-2 in the Canadian population to support public health decisions.

METHODS

The broad objectives of two modelling approaches, 1) an agent-based model and 2) a deterministic compartmental model, are described and a synopsis of studies is illustrated using a model developed in Analytica 5.3 software.

RESULTS

Without intervention, more than 70% of the Canadian population may become infected. Non-pharmaceutical interventions, applied with an intensity insufficient to cause the epidemic to die out, reduce the attack rate to 50% or less, and the epidemic is longer with a lower peak. If NPIs are lifted early, the epidemic may rebound, resulting in high percentages (more than 70%) of the population affected. If NPIs are applied with intensity high enough to cause the epidemic to die out, the attack rate can be reduced to between 1% and 25% of the population.

CONCLUSION

Applying NPIs with intensity high enough to cause the epidemic to die out would seem to be the preferred choice. Lifting disruptive NPIs such as shut-downs must be accompanied by enhancements to other NPIs to prevent new introductions and to identify and control any new transmission chains.