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The SEIR model of COVID-19 is developed to investigate the roles of physical distancing, lockdowns, and asymptomatic cases in Italy. In doing so, two types of policies including behavioral measures and lockdown measures are embedded in the model. Compared with existing models, the model successfully reproduces similar multiple observed outputs such as infected and recovered patients in Italy by July 2020. This study concludes that the first policy is important once the number of infected cases is relatively low. However, once the number of infected cases is too high, so the society cannot identify infected and disinfected people, the second policy must be applied soon. It is thus this study suggests that relaxed lockdowns lead to the second wave of the COVID-19 around the world. It is hoped that the model can enhance our understanding of the roles of behavioral measures, lockdowns, and undocumented cases, so-called asymptomatic cases, on the COVID-19 flow. Doi: 10.28991/SciMedJ-2021-0303-8 Full Text: PDF

Abstract Background Lumpy Skin Disease (LSD) is an infectious disease induced by the Capripoxvirus, causing epidemics in Turkey and several countries worldwide and inducing significant economic losses. Although this disease occurs in Turkish cattle every year, it is a notifiable disease. In this study, LSD in Turkey was modelled using the Susceptible, Exposed, Infectious, and Recovered (SEIR) epidemiological model, and production losses were estimated with predictions of the course of the disease. The animal population was categorized into four groups: Susceptible, Exposed, Infectious, and Recovered, and model parameters were obtained. The SEIR model was formulated with an outbreak calculator simulator applied for demonstration purposes. Results Production losses caused by the LSD epidemic and the SEIR model’s predictions on the disease’s course were evaluated. Although 1282 cases were identified in Turkey during the study period, the prevalence of LSD was calculated as 4.51%, and the mortality rate was 1.09%. The relationship between the disease duration and incubation period was emphasized in the simulated SEIR model to understand the dynamics of LSD. Early detection of the disease during the incubation period significantly affected the peak time of the disease. According to the model, if the disease was detected during the incubation period, the sick animal's time could transmit the disease (Tinf) was calculated as 2.66 days. Production loss from LSD infection was estimated at US $ 886.34 for dairy cattle and the US $ 1,066.61 for beef cattle per animal. Conclusion Detection of LSD infection during the incubation period changes the course of the disease and may reduce the resulting economic loss.

Abstract Objective There has been much discussion and debate around the underreporting of COVID-19 infections and deaths in India. In this short report we first estimate the underreporting factor for infections from publicly available data released by the Indian Council of Medical Research on reported number of cases and national seroprevalence surveys. We then use a compartmental epidemiologic model to estimate the undetected number of infections and deaths, yielding estimates of the corresponding underreporting factors. We compare the serosurvey based ad hoc estimate of the infection fatality rate (IFR) with the model-based estimate. Since the first and second waves in India are intrinsically different in nature, we carry out this exercise in two periods: the first wave (April 1, 2020–January 31, 2021) and part of the second wave (February 1, 2021–May 15, 2021). The latest national seroprevalence estimate is from January 2021, and thus only relevant to our wave 1 calculations. Results Both wave 1 and wave 2 estimates qualitatively show that there is a large degree of “covert infections” in India, with model-based estimated underreporting factor for infections as 11.11 (95% credible interval (CrI) 10.71–11.47) and for deaths as 3.56 (95% CrI 3.48–3.64) for wave 1. For wave 2, underreporting factor for infections escalate to 26.77 (95% CrI 24.26–28.81) and to 5.77 (95% CrI 5.34–6.15) for deaths. If we rely on only reported deaths, the IFR estimate is 0.13% for wave 1 and 0.03% for part of wave 2. Taking underreporting of deaths into account, the IFR estimate is 0.46% for wave 1 and 0.18% for wave 2 (till May 15). Combining waves 1 and 2, as of May 15, while India reported a total of nearly 25 million cases and 270 thousand deaths, the estimated number of infections and deaths stand at 491 million (36% of the population) and 1.21 million respectively, yielding an estimated (combined) infection fatality rate of 0.25%. There is considerable variation in these estimates across Indian states. Up to date seroprevalence studies and mortality data are needed to validate these model-based estimates.

Abstract Background Hand, foot, and mouth disease (HFMD) is a common illness in young children. A monovalent vaccine has been developed in China protecting against enterovirus-71, bivalent vaccines preventing HFMD caused by two viruses are under development. Objective To predict and compare the incidence of HFMD under different vaccination scenarios in China. Methods We developed a compartmental model to capture enterovirus transmission and the natural history of HFMD in children aged 0–5, and calibrated to reported cases in the same age-group from 2015 to 2018. We compared the following vaccination scenarios: different combinations of monovalent and bivalent vaccine; a program of constant vaccination to that of pulse vaccination prior to seasonal outbreaks. Results We estimate 1,982,819, 2,258,846, 1,948,522 and 2,398,566 cases from 2015 to 2018. Increased coverage of monovalent vaccine from 0 to 80% is predicted to decrease the cases by 797,262 (49.1%). Use of bivalent vaccine at an 80% coverage level would decrease the cases by 828,560. Use of a 2.0× pulse vaccination for the bivalent vaccine in addition to 80% coverage would reduce cases by over one million. The estimated R 0 for HFMD in 2015–2018 was 1.08, 1.10, 1.35 and 1.17. Conclusions Our results point to the benefit of bivalent vaccine and using a pulse vaccination in specific months over routine vaccination. Other ways to control HFMD include isolation of patients in the early stage of dissemination, more frequent hand-washing and ventilation, and better treatment options for patients.

Given the scarcity of safe and effective COVID-19 vaccines, a chief policy question is how to allocate them among different sociodemographic groups. This paper evaluates COVID-19 vaccine prioritization strategies proposed to date, focusing on their stated goals; the mechanisms through which the selected allocations affect the course and burden of the pandemic; and the main epidemiological, economic, logistical, and political issues that arise when setting the prioritization strategy. The paper uses a simple, age-stratified susceptible–exposed–infectious–recovered model applied to the United States to quantitatively assess the performance of alternative prioritization strategies with respect to avoided deaths, avoided infections, and life-years gained. We demonstrate that prioritizing essential workers is a viable strategy for reducing the number of cases and years of life lost, while the largest reduction in deaths is achieved by prioritizing older adults in most scenarios, even if the vaccine is effective at blocking viral transmission. Uncertainty regarding this property and potential delays in dose delivery reinforce the call for prioritizing older adults. Additionally, we investigate the strength of the equity motive that would support an allocation strategy attaching absolute priority to essential workers for a vaccine that reduces infection-fatality risk.

Human life is deeply influenced by infectious diseases. A vaccine, when available, is one of the most effective ways of controlling the spread of an epidemic. However, vaccine shortage and uncertain vaccine effectiveness in the early stage of vaccine production make vaccine allocation a critical issue. To tackle this issue, we propose a multi-objective framework to optimize the vaccine allocation strategy among different age groups during an epidemic under vaccine shortage in this study. Minimizing total disease onsets and total severe cases are the two objectives of this vaccine allocation optimization problem, and the multistage feature of vaccine allocation are considered in the framework. An improved Strength Pareto Evolutionary Algorithm (SPEA2) is used to solve the optimization problem. To evaluate the two objectives under different strategies, a deterministic age-stratified extended SEIR model is developed. In the proposed framework, different combinations of vaccine effectiveness and vaccine production capacity are investigated, and it is identified that for COVID-19 the optimal strategy is highly related to vaccine-related parameters. When the vaccine effectiveness is low, allocating most of vaccines to 0–19 age group or 65+ age group is a better choice under a low production capacity, while allocating most of vaccines to 20–49 age group or 50–64 age group is a better choice under a relatively high production capacity. When the vaccine effectiveness is high, a better strategy is to allocate vaccines to 65+ age group under a low production capacity, while to allocate vaccines to 20–49 age group under a relatively high production capacity.

ObjectiveAs a heavily populated megacity, Shanghai faces major epidemic risks. However, Shanghai's control of COVID-19 has been successful owing to both the strict government policy and wide community participation. Here, we investigated the impact of these stakeholders and examined who played a major role across different epidemic stages.DesignWe extended the classic susceptible-exposed-infectious-recovered (SEIR) model considering the heterogeneous contact structure in four social sceneries, i.e., school, workplace, public entertainment venues, and neighborhood community, which could reflect the impact of lockdown policy and wide participation of residents happened at the community level.ResultThe simulation results showed that without lockdown policy and only with community participation, the daily new confirmed cases would gradually increase to more than 7,000 [292/1,000,000] at the end of Sep. However, without community participation and only with a lockdown policy, the daily new confirmed cases sharply decreased to 30 [1.2/1,000,000] at the end of the 1st month and remained low for several months. However, when a lockdown policy was gradually lifted, the new confirmed cases increased exponentially, eventually reaching more than 17,000 [708/1,000,000]. Therefore, a government lockdown policy was necessary for the rapid control of COVID-19 during the outbreak stage while community participation is more important in keeping the number of new confirmed cases low during the reopening stage.ConclusionGovernment lockdown policy and community participation play different roles in the control of COVID-19 at different stages of the epidemic: although the government played a leading role in setting up policies, the broader participation of community fever clinics (CFCs) and the general public were especially crucial in winning the battle against COVID-19 in the long run.

This article develops a detailed epidemiological multi-factor model, the K-susceptible–exposed–infected–removed (K-SEIR) model, and several simpler sub-models as its building blocks. The general model enables us to account for all the relevant COVID-19 features, its disparate impact on different population groups, and interactions within and between the groups. It also includes the availability (or lack thereof) of spare hospital beds and intensive care units (ICU) to accommodate the pent-up demand due to the pandemic. We use the most recent hospitalization and mortality data to calibrate the model. Since our model is multi-factor, we can use it to simulate and analyze the consequences of the sheltering-in-place for each specific group and compare the lives saved and lost due to this measure. We show that in countries with well-developed healthcare systems and a population willing to abide by suitable containment and mitigation procedures, the sheltering in place of the entire community is excessive and harmful when considered holistically. At the same time, sealing nursing homes as thoroughly as possible to avoid high infection and mortality rates is an absolute necessity. [ABSTRACT FROM AUTHOR]

Background: Tuberculosis (TB) has a serious impact on people's health. China is one of 30 countries that has a high TB burden. As the currently decreasing speed of the incidence of TB, the WHO's goal of "End TB Strategy" is hard to achieve by 2035. As a result, a SEIR model that determines the impact of different tuberculosis preventive treatments (TPTs) in different age groups, and the effect of different interventions on latent TB infections (LTBIs) in China is developed.Methods: A Susceptible-Exposed-Infectious-Recovered (SEIR) model was established. Goodness-of-fit tests were used to assess model performance. Predictive analysis was used to assess the effect of different interventions on LTBIs and achieving the goals of the "End TB Strategy".Results: The Chi-square test indicated the model provided a good statistical fit to previous data on the incidence of TB (χ2 = 0.3085, p > 0.999). The 1HP treatment regimen (daily rifapentine + isoniazid for 4 weeks) was most effective in reducing the number of TB cases by 2035. The model indicated that several strategies could achieve the 2035 target of the "End TB Strategy": completion of active case finding (ACF) for LTBI and TPT nation-wide within 5 years; completion of ACF for LTBIs and TPT within 2 years in high-incidence areas; completion of TPT in the elderly within 2 years; or introduction of a new vaccine in which the product of annual doses and vaccine efficiency in the three age groups above 14 years old reached 10.5 million.Conclusion: The incidence of TB in China declined gradually from 2005 to 2019. Implementation of ACF for LTBIs and TPT nation-wide or in areas with high incidence, in the elderly, or administration of a new and effective vaccine could greatly reduce the number of TB cases and achieve the 2035 target of the "End TB Strategy" in China. [ABSTRACT FROM AUTHOR]

Currently, the spread of COVID-19 is running at a constant pace. The current situation is not so alarming, but every pandemic has a history of three waves. Two waves have been seen, and now expecting the third wave. Compartmental models are one of the methods that predict the severity of a pandemic. An enhanced SEIR model is expected to predict the new cases of COVID-19. The proposed model has an additional compartment of vaccination. This proposed model is the SEIRV model that predicts the severity of COVID-19 when the population is vaccinated. The proposed model is simulated with three conditions. The first condition is when social distancing is not incorporated, while the second condition is when social distancing is included. The third one condition is when social distancing is combined when the population is vaccinated. The result shows an epidemic growth rate of about 0.06 per day, and the number of infected people doubles every 10.7 days. Still, with imparting social distancing, the proposed model obtained the value of R0 is 1.3. Vaccination of infants and kids will be considered as future work. [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]

The paper formulates a SEIR model with time delay effect to explain the influence of media reports on diseases. Firstly, the basic reproduction number of the model is determined by the method of next generation matrix. The existence and the global stability of the equilibrium point are discussed. Secondly, sufficient conditions of Hopf bifurcation of the model are given. Finally, by numerical simulation, we prove the correctness of the theories. [ABSTRACT FROM AUTHOR]

Abstract Background The new coronavirus disease appeared at the end of 2019, and it is now a global problem over the world. There are multiple epidemiologic indicators used for discussing the spread of pandemics, one of these indicators is the basic reproductive ratio which indicates whether the pandemic is going to spread more or relax, and the aim of this work is estimating this ratio for the Middle East countries for two stages of the pandemic. Main body of the abstract We employ Runge–Kutta method on SEIR model to simulate the basic reproductive ratio values of SARS-CoV-2 disease by using the recorded data of the disease for two stages, up to date May 29, 2020, in the first stage and up to date September 7, 2020, in the second stage. We estimate the coefficient of exposing rate, the coefficient of infection rate, the coefficient of recovery rate and the coefficient of mortality rate of the new coronavirus disease in addition to the basic reproductive ratio values of the disease in the Middle East countries, namely Bahrain, Cyprus, Egypt, Iran, Iraq, Jordan, Kuwait, Lebanon, Oman, Qatar, Saudi Arabia, the Syrian Arab Republic, the United Arab Emirates, Turkey and Yemen where we apply the SEIR epidemic model. Short conclusion We find that the values of the basic reproductive ratio of the new coronavirus disease based on the used model in the Middle East countries start from 1.5583 to 3.0395 in the first stage and from 1.0001 to 4.5757. Besides, we find that the problem of the new coronavirus disease in Lebanon and in the Syrian Arab Republic is not good at all in the recent stage based on the values of the basic reproductive ratio comparing with other Middle East countries. Also, we find that the value of the basic reproductive ratio for the second stage is near one; however, if we apply the method for the following stages, we find that the values return to be larger because lots of people in that stage and after did not follow the governmental procedures for stopping the spreading of the disease.

Meme transmission has become an important way of information dissemination. Three transfer paths were added to the classic infectious disease storehouse model in this study based on characteristics of meme transmission. Individual heterogeneity factors such as individual interest, risk perception and trust perception were used to construct a meme transmission model named Individual Heterogeneity SEIR (IHSEIR) model. Equilibrium of the model and the basic reproduction number were obtained using mean-field theory. Effects of individual heterogeneity factors on meme propagation were analyzed through Multi-Agent simulation. The findings showed that individual interest has a significant effect on the propagation range and speed of meme. A low-level overall trust of the system was correlated with higher risk perception among individuals, which is not conducive for the propagation of meme. Effect of regulation and intervention in the process of meme transmission was significantly lower compared with that at the initial state of transmission.

We consider a SEIR model for the spread (transmission) of an infectious disease. The model has played an important role due to world pandemic disease spread cases. Our contributions in this paper are three folds. Our first contribution is to provide successive approximation and variational iteration methods to obtain analytical approximate solutions to the SEIR model. Our second contribution is to prove that for solving the SEIR model, the variational iteration and successive approximation methods are identical when we have some particular values of Lagrange multipliers in the variational iteration formulation. Third, we propose a new multistage-analytical method for solving the SEIR model. Computational experiments show that the successive approximation and variational iteration methods are accurate for small size of time domain. In contrast, our proposed multistage-analytical method is successful to solve the SEIR model very accurately for large size of time domain. Furthermore, the order of accuracy of the multistage-analytical method can be made higher simply by taking more number of successive iterations in the multistage evolution.

In this paper, deterministic and stochastic models are proposed to study the transmission dynamics of the Coronavirus Disease 2019 (COVID-19) in Wuhan, China. The deterministic model is formulated by a system of ordinary differential equations (ODEs) that is built upon the classical SEIR framework. The stochastic model is formulated by a continuous-time Markov chain (CTMC) that is derived based on the ODE model with constant parameters. The nonlinear CTMC model is approximated by a multitype branching process to obtain an analytical estimate for the probability of a disease outbreak. The local and global dynamics of the disease are analyzed by using the deterministic model with constant parameters, and the result indicates that the basic reproduction number {$\mathcal{R}_0$ serves} as a sharp disease threshold: the disease dies out if $\mathcal{R}_0\le 1$ and persists if $\mathcal{R}_0>1$. In contrast to the deterministic dynamics, the stochastic dynamics indicate that the disease may not persist when $\mathcal{R}_0>1$. Parameter estimation and validation are performed to fit our ODE model to the public reported data. Our result indicates that both the exposed and infected classes play an important role in shaping the epidemic dynamics of COVID-19 in Wuhan, China. In addition, numerical simulations indicate that a second wave of the ongoing pandemic is likely to occur if the prevention and control strategies are not implemented properly.

Introduction: In Hungary, where MMR vaccine coverage is 99%, in 2017, a minor measles epidemic started from imported cases due to two major factors – latent susceptible cohorts among the domestic population and the vicinity of measles-endemic countries. Suspended immunization activities due to the COVID-19 surge are an ominous precursor to a measles resurgence. This epidemiological demonstration is aimed at promoting a better public understanding of epidemiological data. Materials and Methods: Our previous MMR sero-epidemiological measurements (N of total measles cases = 3919, N of mumps cases = 2132, and N of rubella cases = 2132) were analyzed using open-source epidemiological data (ANTSZ) of a small-scale measles epidemic outbreak (2017, Hungary). A simplified SEIR model was applied in the analysis. Results: In case of measles, due to a cluster-specific inadequacy of IgG levels, the cumulative seropositivity ratios (measles = 89.97%) failed to reach the herd immunity threshold (HIT Measles = 92–95%). Despite the fact that 90% of overall vaccination coverage is just slightly below the HIT, unprotected individuals may pose an elevated epidemiological risk. According to the SEIR model, ≥74% of susceptible individuals are expected to get infected. Estimations based on the input data of a local epidemic may suggest an even lower effective coverage rate (80%) in certain clusters of the population. Conclusion: Serological survey-based, historical and model-computed results are in agreement. A practical demonstration of epidemiological events of the past and present may promote a higher awareness of infectious diseases. Because of the high R0 value of measles, continuous large-scale monitoring of humoral immunity levels is important.

ObjectiveTo evaluate epidemiological characteristics of the COVID-19 outbreak that resurged in Yangzhou and to simulate the impact of different control measures at different regional scales.MethodsWe collected personal information from 570 laboratory-confirmed cases in Yangzhou from 28 July to 26 August 2021, and built a modified susceptible-exposed-infected-removed (SEIR) model and an agent-based model.ResultsThe SEIR model showed that for passengers from medium-high risk areas, pre-travel nucleic acid testing within 3 days could limit the total number of infected people in Yangzhou to 50; among elderly persons, a 60% increase in vaccination rates could reduce the estimated infections by 253. The agent-based model showed that when the population density of the chess and card room dropped by 40%, the number of infected people would decrease by 54 within 7 days. A ventilation increase in the chess and card room from 25 to 50% could reduce the total number of infections by 33 within 7 days; increasing the ventilation from 25 to 75% could reduce the total number of infections by 63 within 7 days.ConclusionsThe SEIR model and agent-based model were used to simulate the impact of different control measures at different regional scales successfully. It is possible to provide references for epidemic prevention and control work.

Abstract 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.

Goal: Because a fast vaccination rollout against coronavirus disease 2019 (COVID-19) is critical to restore daily life and avoid virus mutations, it is tempting to have a relaxed vaccination-administration management system. However, a rigorous management system can support the enforcement of preventive measures, and in turn, reduce incidence and deaths. Here, we model a trustable and reliable management system based on blockchain for vaccine distribution by extending the Susceptible-Exposed-Infected-Recovery (SEIR) model. The model includes prevention measures such as mask-wearing, social distancing, vaccination rate, and vaccination efficiency. It also considers negative social behavior, such as violations of social distance and attempts of using illegitimate vaccination proofs. By evaluating the model, we show that the proposed system can reduce up to 2.5 million cases and half a million deaths in the most demanding scenarios.

While the Coronavirus Disease 2019 (COVID-19) pandemic continues to threaten public health and safety, every state has strategically reopened the business in the United States. It is urgent to evaluate the effect of reopening policies on the COVID-19 pandemic to help with the decision-making on the control measures and medical resource allocations. In this study, a novel SEIR model was developed to evaluate the effect of reopening policies based on the real-world reported COVID-19 data in Texas. The earlier reported data before the reopening were used to develop the SEIR model; data after the reopening were used for evaluation. The simulation results show that if continuing the “stay-at-home order” without reopening the business, the COVID-19 pandemic could end in December 2020 in Texas. On the other hand, the pandemic could be controlled similarly as the case of no-reopening only if the contact rate was low and additional high magnitude of control measures could be implemented. If the control measures are only slightly enhanced after reopening, it could flatten the curve of the COVID-19 epidemic with reduced numbers of infections and deaths, but it might make the epidemic last longer. Based on the reported data up to July 2020 in Texas, the real-world epidemic pattern is between the cases of the low and high magnitude of control measures with a medium risk of contact rate after reopening. In this case, the pandemic might last until summer 2021 to February 2022 with a total of 4–10 million infected cases and 20,080–58,604 deaths.

This article attempts to establish a mathematical epidemic model for the outbreak of the new COVID-19 coronavirus. A new consideration for evaluating and controlling the COVID-19 outbreak will be constructed based on the SEIQR Pandemic Model. In this paper, the real data of COVID-19 spread in Saudi Arabia has been used for the mathematical model and dynamic analyses. Including the new reproductive number and detailed stability analysis, the dynamics of the proposed SEIQR model have been applied. The local sensitivity of the reproduction number has been analyzed. The domain of solution and equilibrium based on the SEIQR model have been proved using a Jacobian linearization process. The state of equilibrium and its significance have been proved, and a study of the integrity of the disease-free equilibrium has been carried out. The Lyapunov stability theorem demonstrated the global stability of the current model equilibrium. The SEIQR model has been numerically validated and projected by contrasting the results from the SEIQR model with the actual COVID-19 spread data in Saudi Arabia. The result of this paper shows that the SEIQR model is a model that is effective in analyzing epidemic spread, such as COVID-19. At the end of the study, we have implemented the protocol which helped the Saudi population to stop the spread of COVID-19 rapidly.

Infectious disease is a great enemy of humankind. The ravages of COVID-19 are leading to profound crises across the world. There is an urgent requirement for analyzing the current pandemic situation, predicting trends over time, and assessing the effectiveness of containment measures. Thus, numerous statistical models, primarily based on the susceptible–exposed–infected–recovered or removed (SEIR) model, have been established. However, these models are highly technical, which are difficult for the public and governing bodies to understand and use. To address this issue, we developed a simple operating software based on our improved K-SEIR model termed as the kernel SEIR simulator (K-SEIR-Sim). This software includes natural propagation parameters, containment measure parameters, and certain characteristic parameters that can deduce the effects of natural propagation and containment measures. Further, the applicability of the proposed software was demonstrated using the examples of the COVID-19 outbreak in the United States, Wuhan city of China, Diamond Princess, and France. Operating results verified the potency of the proposed software in evaluating the epidemic situation and human intervention during COVID-19. Importantly, no installation is required and the software can perform real-time, backward-looking, and forward-looking analysis by functioning in data-driven and model-driven ways. All of them have considerable practical values in their applications according to the actual needs of personal use. Conclusively, K-SEIR-Sim is the first simple customized operating software that is highly valuable for the global fight against COVID-19 and other infectious diseases.

The convenient transport network enables people to travel quickly and frequently across regions, but it also brings serious challenges to the emergency management of infectious diseases. This work extends the classical SEIR model by incorporating trans-regional population movements and contact infections during travel. It also includes cross-regional population testing and treatment measures to curb the spread of infectious diseases across regions. According to these characteristics, a Net-SEIHR model is established and its diffusion properties are deduced. Further, the cooperative allocation problem of limited detection resources and its control strategy are discussed. Numerical experiments show that the control measures can reduce the speed of trans-regional transmission of infectious diseases and the peak of treatment. In the case of limited testing resources, it is necessary to strengthen the detection of people in the inflow regions. [ABSTRACT FROM AUTHOR]

This work presents a new polymorphic, reusable, and comprehensive mathematical model for COVID-19 epidemic transition cycle dynamics. This model has the following characteristics: (1) The core SEIR model includes asymptomatic and symptomatic infections; (2) the symptomatic infection is a multi-variant; (3) the recovery stage provides a partial feed to the symptomatic infection; and (4) the symptomatic and asymptomatic stages have additional feed streams from the protected stage. The proposed formalisation template is a canonical way to achieve different models for the underlying health control environment. This template approach endows the model with polymorphic and reusable capability across different scenarios. To verify the model’s reliability and validity, this work utilised two sets of initial conditions: date range and COVID-19 data for Canada and Saudi Arabia.

Nowadays, a lot of research papers are concentrating on the diffusion dynamics of infectious diseases, especially the most recent one: COVID-19. The primary goal of this work is to explore the stability analysis of a new version of the SEIR model formulated with incommensurate fractional-order derivatives. In particular, several existence and uniqueness results of the solution of the proposed model are derived by means of the Picard–Lindelöf method. Several stability analysis results related to the disease-free equilibrium of the model are reported in light of computing the so-called basic reproduction number, as well as in view of utilising a certain Lyapunov function. In conclusion, various numerical simulations are performed to confirm the theoretical findings.

Due to insufficient epidemic detection and control, untimely government interventions, and high epidemic prevention costs in the early stages of the epidemic outbreak, the spread of the epidemic may become out of control and pose a great threat to human society. This paper optimized and improved the traditional Susceptible-Exposed-Infectious-Removed (SEIR) model for investigating epidemic control and public health emergency management. Using the Corona Virus Disease 2019 (COVID-19) outbreak as an example, this paper simulates and analyzes the development of an epidemic outbreak during various periods with the optimized SEIR model, to explore the emergency control capacity of conventional medical control measures, such as large-scale outbreak testing capacity, hospital admission capacity, or daily protection of key personnel, and analyze the government’s emergency management strategies to achieve low-cost epidemic control. The model developed in this study and the results of its analysis demonstrate the differences in outbreak emergency control capacity under different conditions and different implementation strategies. A low-cost local outbreak emergency management strategy and the timing of the government’s resumption of work and school are discussed on this basis.

In 2020, coronavirus (COVID-19) was declared a global pandemic and it remains prevalent today. A necessity to model the transmission of the virus has emerged as a result of COVID-19’s exceedingly contagious characteristics and its rapid propagation throughout the world. Assessing the incidence of infection could enable policymakers to identify measures to halt the pandemic and gauge the required capacity of healthcare centers. Therefore, modeling the susceptibility, exposure, infection, and recovery in relation to the COVID-19 pandemic is crucial for the adoption of interventions by regulatory authorities. Fundamental factors, such as the infection rate, mortality rate, and recovery rate, must be considered in order to accurately represent the behavior of the pandemic using mathematical models. The difficulty in creating a mathematical model is in identifying the real model variables. Parameters might vary significantly across models, which can result in variations in the simulation results because projections primarily rely on a particular dataset. The purpose of this work was to establish a susceptible–exposed–infected–recovered (SEIR) model describing the propagation of the COVID-19 outbreak throughout the Kingdom of Saudi Arabia (KSA). The goal of this study was to derive the essential COVID-19 epidemiological factors from actual data. System dynamics modeling and design of experiment approaches were used to determine the most appropriate combination of epidemiological parameters and the influence of COVID-19. This study investigates how epidemiological variables such as seasonal amplitude, social awareness impact, and waning time can be adapted to correctly estimate COVID-19 scenarios such as the number of infected persons on a daily basis in KSA. This model can also be utilized to ascertain how stress (or hospital capacity) affects the percentage of hospitalizations and the number of deaths. Additionally, the results of this study can be used to establish policies or strategies for monitoring or restricting COVID-19 in Saudi Arabia.

• Developing a time-fractional compartmental model that incorporates the effect of contact tracing for Covid-19. • Describe the effective reproduction number in terms of observable quantities. • Discuss effects of tracking, reporting and monitoring in contact tracing. • Monitoring proportion of reported cases which must be tracked to ensure that the reproduction number is below one. • Numerical simulations are done to discuss the impact of contact tracing on the pandemic. Contact Tracing (CT) is one of the measures taken by government and health officials to reduce the spread of the novel coronavirus. In this paper, we investigate its efficacy by developing a compartmental model for assessing its impact on mitigating the spread of the virus. We describe the impact on the reproduction number R 0 of COVID-19. In particular, we discuss the importance and relevance of parameters of the model such as the number of reported cases, effectiveness of tracking and monitoring policy, and the transmission rates to contact tracing. We describe the terms "perfect tracking", "perfect monitoring" and "perfect reporting" to indicate that traced contacts will be tracked while incubating, tracked contacts are efficiently monitored so that they do not cause secondary infections, and all infected persons are reported, respectively. We consider three special scenarios: (1) perfect monitoring and perfect tracking of contacts of a reported case, (2) perfect reporting of cases and perfect monitoring of tracked reported cases and (3) perfect reporting and perfect tracking of contacts of reported cases. Furthermore, we gave a lower bound on the proportion of contacts to be traced to ensure that the effective reproduction, R c , is below one and describe R c in terms of observable quantities such as the proportion of reported and traced cases. Model simulations using the COVID-19 data obtained from John Hopkins University for some selected states in the US suggest that even late intervention of CT may reasonably reduce the transmission of COVID-19 and reduce peak hospitalizations and deaths. In particular, our findings suggest that effective monitoring policy of tracked cases and tracking of traced contacts while incubating are more crucial than tracing more contacts. The use of CT coupled with other measures such as social distancing, use of face mask, self-isolation or quarantine and lockdowns will greatly reduce the spread of the epidemic as well as peak hospitalizations and total deaths. [ABSTRACT FROM AUTHOR]

COVID-19 has threatened human lives. Countries have implemented various interventions such as vaccination, mask-wearing, body temperature screening, and isolation. However, the effectiveness of single and combined interventions has not yet been accurately analyzed. In this study, an improved SEIR model considering both real human indoor close contact behaviors and susceptibility to COVID-19 was established. Taking Hong Kong as an example, a quantitative assessment of the relationship between the efficiency of single and combined interventions and implementation time and intensity was carried out. The results showed that the infection risk (one-hour close contact with an infected person) of COVID-19 of students, workers, and non-workers/non-students was 3.1%, 8.7%, and 13.6%, respectively. Workplace closures were more effective among built environment interventions. If mask-wearing was mandatorily required in schools, workplaces, supermarkets, shopping centers, and public transport, COVID-19 could not be totally restricted. Workers should be prioritized for vaccination, followed by non-workers/non-students and students. Among all interventions, reducing close contact rate and increasing vaccination rate were better interventions. There was no COVID-19 outbreak (basic reproduction number R0 = 1) if the close contact reduction rate was 59.9% or the vaccination rate reached 89.5%. The results may provide scientific support for COVID-19 prevention and control. [ABSTRACT FROM AUTHOR]

Is it possible that the origin of Mycobacterium tuberculosis (Mtb) infection was around 70,000 years before the common era? At that time Homo sapiens was just another primate species with discrete growth and a very low-density geographic occupation. Therefore, it is difficult to understand the origin of a highly virulent obligate human pathogen. We have designed a new SEIR model (TBSpectr) that allows the differentiation of smear-positive and -negative tuberculosis. The model reconciles currently accepted growth rates for the Middle Paleolithic (0.003%/year) and Neolithic (0.1%/year). The obtained data link the origin of Mtb infection in the Middle Paleolithic to the induction of smear-negative TB, and reveal that its persistence required interrelations among hunter–gatherer groups, while the risk of human extinction was negligible. It also highlights the number of people infected per case and the fast progression to disease for Mtb infection maintenance, as well as the link between poor health in the Neolithic with the increased incidence of more severe forms of TB (smear-positive). In conclusion, our data support the origin of TB as a well-tolerated, highly persistent disease, even in low-density populations, showing the difficulty of its eradication and highlighting the necessity for providing better health conditions to humans to reduce its severity. [ABSTRACT FROM AUTHOR]

This paper takes COVID-19-related online rumors as the research object, and explores the law of spreading public opinion in social networks. The paper also conducts empirical research on the relationship between rumor spreading, user characteristics and subject interest differences, and analyzes the common influence of individual factors and social environment. In the process of public opinion dissemination, measures that can effectively regulate the dissemination of public opinion are proposed. Based on the susceptible-exposed-infected-recovered (SEIR) model, this paper analyzes the influence of individual differentiation characteristics, friend factors, and time-dependent decline on user status changes. The study found that the user's environment can affect the spread and popularity of public opinion information, and prolong the survival time of public Controlling the propagation threshold and exit threshold of the platform helps to control the large-scale dissemination of online public opinion. The extinction of public opinion is affected by the decline of time and heat rather than certain probability. [ABSTRACT FROM AUTHOR]

Inspired by infectious disease dynamics and modern psychology, this paper aims at constructing a multi-dimensional function to get the model of information dissemination on social networks under epidemic-related panic base on the characteristics of individual differences and global characteristics, like emotional cumulative effect, herd effect, time-sensitive decline effect, cognitive level, intimacy, personal influence, etc. The results show that the psychological effect has a significant effect on the increase of the spread of panic news; When netizens are in an emotional atmosphere, their emotional self-regulation ability is limited; when the infection rate is relatively low, the characteristics of individual differences play a leading role in affecting the spreading process. When the infection rate is high enough, the herd effect and emotional cumulative effect play a major role in promoting information dissemination; In a society with a higher rate of emotional contact, it is easier to form a kind of collective wisdom, which can help the collective quickly identify rumors. Moreover, in this kind of society, the role of opinion leaders is limited, and timely refutation of rumors can significantly reduce the spread of panic news. [ABSTRACT FROM AUTHOR]

Today, the entire world is witnessing an enormous upsurge in coronavirus pandemic (COVID-19 pandemic). Confronting such acute infectious disease, which has taken multiple victims around the world, requires all specialists in all fields to devote their efforts to seek effective treatment or even control its disseminate. In the light of this aspect, this work proposes two new fractional-order versions for one of the recently extended forms of the SEIR model. These two versions, which are established in view of two fractional-order differential operators, namely, the Caputo and the Caputo–Fabrizio operators, are numerically solved based on the Generalized Euler Method (GEM) that considers Caputo sense, and the Adams–Bashforth Method (ABM) that considers Caputo–Fabrizio sense. Several numerical results reveal the impact of the fractional-order values on the two established disease models, and the continuation of the COVID-19 pandemic outbreak to this moment. In the meantime, some novel results related to the stability analysis and the basic reproductive number are addressed for the proposed fractional-order Caputo COVID-19 model. For declining the total of individuals infected by such pandemic, a new compartment is added to the proposed model, namely the disease prevention compartment that includes the use of face masks, gloves and sterilizers. In view of such modification, it is turned out that the performed addition to the fractional-order Caputo COVID-19 model yields a significant improvement in reducing the risk of COVID-19 spreading. [ABSTRACT FROM AUTHOR]

This paper is considering the problem of traveling wave solutions (TWS) for a susceptible‐exposed‐infectious‐recovered (SEIR) epidemic model with discrete diffusion. The threshold condition for the existence and nonexistence of TWS is obtained. More specifically, such kind of solutions are governed by the threshold number ℜ0. We can find a critical wave speed c∗ if ℜ0 > 1, by employing the Schauder's fixed point theorem, limiting argument and two‐sided Laplace transform, we confirm that there exists TWS for c > c∗, while there exists no TWS for c < c∗. We also obtain the nonexistence of TWS for ℜ0 ≤ 1. At last, we give some biological explanations from the epidemiological perspective. [ABSTRACT FROM AUTHOR]

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has the potential for rapid transmission in congregate settings. We describe the multidisciplinary response to an outbreak of coronavirus disease (COVID-19) in a large homeless shelter in Chicago, Illinois, USA. The response to the outbreak included 4 rounds of mass PCR testing of all staff and residents and subsequent isolation of persons who tested positive for SARS-CoV-2. We further describe the dynamics of the shelter outbreak by fitting a modified susceptible-exposed-infectious-recovered compartmental model incorporating the widespread SARS-CoV-2 testing and isolation measures implemented in this shelter. Our model demonstrates that rapid transmission of COVID-19 in the shelter occurred before the outbreak was detected; rates of transmission declined after widespread testing and isolation measures were put in place. Overall, we demonstrate the feasibility of mass PCR testing and isolation in congregate settings and suggest the necessity of prompt response to suspected COVID-19 outbreaks in homeless shelters. [ABSTRACT FROM AUTHOR]

Background: With the global spreading of Coronavirus disease (COVID-19), many primary care medical workers have been infected, particularly in the early stages of this pandemic. Although extensive studies have explored the COVID-19 transmission patterns and (non-) pharmaceutical intervention to protect the general public, limited research has analysed the measures to prevent nosocomial transmission based upon detailed interpersonal contacts between medical staff and patients. Aim: This paper aims to develop and evaluate proactive prevention measures to contain the nosocomial transmission of COVID-19. The specific objectives are (1) to understand the virus transmission via interpersonal contacts among medical staff and patients; (2) to define proactive measures to reduce the risk of infection of medical staff and (3) evaluate the effectiveness of these measures to control the COVID-19 epidemic in hospitals. Methods: We observed the operation of a typical primary hospital in China to understand the interpersonal contacts among medical staff and patients. We defined effective distance as the indicator for risk of transmission. Then three proactive measures were proposed based upon the observations, including a medical staff rotation system, the establishment of a separate fever clinic and medical staff working alone. Finally, the impacts of these measures are evaluated with a modified Susceptible-Exposure-Infected-Removed model accommodating the situation of hospitals and asymptomatic and latent infection of COVID-19. The case study was conducted with the hospital observed in December 2019 and February 2020. Findings: The implementation of the medical staff rotation system has the most significant impact on containing the epidemic. The establishment of a separate fever clinic and medical staff working alone also benefits from inhibiting the epidemic outbreak. The simulation finds that if effective prevention and control measures are not taken in time, it will lead to a surge of infection cases in all asymptomatic probabilities and incubation periods. [ABSTRACT FROM AUTHOR]

In this paper, we propose and investigate an almost periodic SEIR model with stage structure and latency, in which time-dependent maturation and incubation periods are incorporated. Two threshold parameters for the persistence and extinction of population and disease are introduced: the basic reproduction ratio $\hat{R}_{0}$ for population and the basic reproduction ratio $R_{0}$ for disease. If $\hat{R}_{0}1$, it is shown that the disease tends to die out if $R_{0}1$. By virtue of numerical simulations, we verify the analytic results and investigate the effects of the fluctuations of maturation and incubation periods on disease transmission.

Abstract Background Efficient control and management in the ongoing COVID-19 pandemic needs to carefully balance economical and realizable interventions. Simulation models can play a cardinal role in forecasting possible scenarios to sustain decision support. Methods We present a sophisticated extension of a classical SEIR model. The simulation tool CovidSIM Version 1.0 is an openly accessible web interface to interactively conduct simulations of this model. The simulation tool is used to assess the effects of various interventions, assuming parameters that reflect the situation in Austria as an example. Results Strict contact reduction including isolation of infected persons in quarantine wards and at home can substantially delay the peak of the epidemic. Home isolation of infected individuals effectively reduces the height of the peak. Contact reduction by social distancing, e.g., by curfews, sanitary behavior, etc. are also effective in delaying the epidemic peak. Conclusions Contact-reducing mechanisms are efficient to delay the peak of the epidemic. They might also be effective in decreasing the peak number of infections depending on seasonal fluctuations in the transmissibility of the disease.

Abstract Background Mathematical modeling studies have suggested that pre-emptive school closures alone have little overall impact on SARS-CoV-2 transmission, but reopening schools in the background of community contact reduction presents a unique scenario that has not been fully assessed. Methods We adapted a previously published model using contact information from Shanghai to model school reopening under various conditions. We investigated different strategies by combining the contact patterns observed between different age groups during both baseline and “lockdown” periods. We also tested the robustness of our strategy to the assumption of lower susceptibility to infection in children under age 15 years. Results We find that reopening schools for all children would maintain a post-intervention R0

SEIR model is a widely used and acceptable model to distinguish the outbreak of the COVID-19 epidemic in many countries. In the current work, a new proposed SEIR model as a mathematical model for the outbreak of novel coronaviruses COVID-19 will be constructed. The new proposed SEIR pandemic model provides a new vision for evaluations and management of the epidemic of COVID-19 infection. For mathematical modeling and dynamic analyses, this paper uses the real data of spreading COVID-19 in Saudi Arabia. The dynamics of the proposed SEIR model are presented with the reproduction number and the extensive stability analysis. We discussed the domain of the solution and equilibrium situation based on the proposed SEIR model by using Jacobian's method of linearization. The condition of equilibrium and its uniqueness has been proved, and the stability analysis of disease-free equilibrium has been introduced. A sensitivity analysis of the reproduction number against its internal parameters has been done. The global stability of the equilibrium of this model has been proved by using Lyapunov's Stability theorem. A numerical verification and predictions of the proposed SEIR model have been made with comparing the results based on the SEIR model and the real data due to the spreading of the COVID-19 in Saudi Arabia. The proposed SEIR model is a successful model to analyze the spreading of epidemics like COVID-19. This work introduces the ideal protocol, which can help the Saudi population to breakdown spreading COVID-19 in a fast way.

Abstract 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.