Ongoing outbreak of pneumonia caused by novel coronavirus (2019-nCoV) began in December 2019 in Wuhan, China, and the number of new patients continues to increase. On the contrary to ongoing outbreak in China, however, there are limited secondary outbreaks caused by exported case outside the country. We here conducted simulations to estimate the impact of potential secondary outbreaks at a community outside China. Simulations using stochastic SEIR model was conducted, assuming one patient was imported to a community. Among 45 possible scenarios we prepared, the worst scenario resulted in total number of persons recovered or removed to be 997 (95% CrI 990-1,000) at day 100 and maximum number of symptomatic infectious patients per day of 335 (95% CrI 232-478). Calculated mean basic reproductive number (R0) was 6.5 (Interquartile range, IQR 5.6-7.2). However, with good case scenarios with different parameter led to no secondary case. Altering parameters, especially time to hospital visit could change the impact of secondary outbreak. With this multiple scenarios with different parameters, healthcare professionals might be able to prepare for this viral infection better.

Rapidly spreading disease, COVID-19 is classified as the human-to-human transmission-able disease and currently is a pandemic in the Globe. In this paper, we propose conceptual mathematical models for COVID-19 outbreak and it's control measurement; quarantine, hospitalization and the effect of panic and anxiety. In this situation, mathematical models are a important tool to employ an effective strategy in order to fight against this pandemic. We establish the positivity and boundedness of solutions, local and global stability analysis of equilibria to examine its epidemiological relevance. To validate the model and estimating the important model parameters and prediction about the disease, we consider the real cases of Italy from $15^{th}$ Feb to $13^{th} $ April 2020. In a series of graphical map, we have presented the comparative study to estimate the current scenarios and to predict the control measurement time boundary of the outbreak.

This study proposes a nonlinear mathematical model of virus transmission based on the SEIR model. In this study, the interaction between viruses and immune cells is investigated using phase-space analysis of a mathematical model. Specifically, it is focused on the dynamics and stability behavior of the mathematical model of a virus spread in a population and its interaction with human immune systems cells. The endemic equilibrium points are found and local stability analysis of all equilibria points of the related model is obtained. Further, the global stability analysis either, at disease-free equilibria, or in endemic equilibria is discussed by constructing the Lyapunov function which shows the validity of the concern model exists. Finally, a simulated solution is achieved and the relationship between viruses and immune cells is highlighted.

The virus SARS-CoV-2 has resulted in numerous modelling approaches arising rapidly to understand the spread of the disease COVID-19 and to plan for future interventions. Herein, we present an SEIR model with a spatial spread component as well as four infectious compartments to account for the variety of symptom levels and transmission rate. The model takes into account the pattern of spatial vulnerability in South Africa through a vulnerability index that is based on socioeconomic and health susceptibility characteristics. Another spatially relevant factor in this context is level of mobility throughout. The thesis of this study is that without the contextual spatial spread modelling, the heterogeneity in COVID-19 prevalence in the South African setting would not be captured. The model is illustrated on South African COVID-19 case counts and hospitalisations.

This study developed a system dynamics model to understand the spread of coronavirus disease (COVID-19) in Japan. The model is built on the generic SEIR (Susceptible, Exposed, Infected, and Recovered) framework adopted by Ghaffarzadegan and Rahmandad (2020) to build a system dynamics model for the spread of COVID-19 in Iran. Japan seems to be successful in containing the spread compared with other countries, and its first peak has passed. However, because this also leaves a large population still susceptible to the virus, it could cause a second and potentially higher peak of infection after the state of emergency aimed at reducing contact rate is lifted. As the government has proposed the “New Lifestyle,” it is critical to behave cautiously so as not to be infected. While the model focuses on the SEIR structure, the reflection of other sub-structures such as economy and hospital capacity that have tradeoffs with reducing contact rate should be beneficial. However, before extending the model, it is also critical to conduct estimates using confidence intervals rather than point estimates to better reflect uncertainties.

In this research, we present the first steps taken towards a data-driven agent-based model (ABM) specifically designed for simulating infectious disease dynamics in Greece. Amidst the ongoing COVID-19 pandemic caused by SARS-CoV-2, this research holds significant importance as it can offer valuable insights into disease transmission patterns and assist in devising effective intervention strategies. To the best of our knowledge, no similar study has been conducted in Greece. We constructed a prototype ABM that utilizes publicly accessible data to accurately represent the complex interactions and dynamics of disease spread in the Greek population. By incorporating demographic information and behavioral patterns, our model captures the specific characteristics of Greece, enabling accurate and context-specific simulations. By using our proposed ABM, we aim to assist policymakers in making informed decisions regarding disease control and prevention. Through the use of simulations, policymakers have the opportunity to explore different scenarios and predict the possible results of various intervention measures. These may include strategies like testing approaches, contact tracing, vaccination campaigns, and social distancing measures. Through these simulations, policymakers can assess the effectiveness and feasibility of these interventions, leading to the development of well-informed strategies aimed at reducing the impact of infectious diseases on the Greek population. This study is an initial exploration toward understanding disease transmission patterns and a first step towards formulating effective intervention strategies for Greece.

Italy suffered heavily with the new pandemic crisis caused by the novel coronavirus SARS-CoV-2. Given the low number of tests performed on the early stages of the outbreak, Italy lost track of most of infections. We use a modified SEIR model to reconstruct the most realistic infection curve using the hospitalization curve of the registered data. Using this method we estimated that, by the end of the first infection wave, about 3-4% of the population will have been infected by the virus. Following the same process, the number of deaths is projected to be between 100000 to 115000. We also find a significant correlation between the number of tests performed, the fraction of undocumented infections and the rate of change dI/dt of the real infection curve. We conclude that herd immunity is not enough to contain further spread of the disease inside the country.

In this paper, we proposed the numerical method called the variational iteration orthogonal collocation method (VIOCM), for the approximate solution of the deadly Corona virus model using Mamadu-Njoseh polynomials as basis functions. The proposed method is an elegant mixture of the variational iteration method (VIM) and the orthogonal collocation method (OCM). It was observed that the proposed method converges rapidly to the exact solution even as N increases. This suggests that the use of orthogonal polynomials as trial functions for the SEIR model is indeed an effective approximant as it produces the analytic solution at just few iterations. Resulting numerical evidences were compared with the standard variational iteration method as available in literature. All computational frameworks were executed with MAPLE software.

In this paper, drug treatment and vaccination are compared healthy and economically. In this comparison, in addition to comparing economic costs, it has paid attention to patients' recovery. To reach the goal, the prevalence of Covid-19 virus in New York is modeled by using the SEIR dynamic model. The SEIR dynamic model is used to model the period of epidemic diseases. Then, three disease control scenarios are evaluated economically. Treatment and vaccination are two important issues in controlling epidemic diseases. To control the disease, each of these two methods has economic costs and benefits. The main purpose of this paper is to compare the two methods of vaccination and treatment economically. Although the results of the study show that vaccination can be effective in preventing the epidemic of the disease than treatment, but due to the high cost and genetic mutation of the virus, vaccination is not the optimal method for both health and the economy in the long term.

The outbreak of coronavirus disease 2019 (COVID-19) was identified in Wuhan, China, in December 2019. As of April 17, 2020, more than 2 million cases of COVID-19 have been reported worldwide. Northern Italy is one of the world’s centers of active coronavirus cases. In this study, we predicted the spread of COVID-19 and its burden on hospital care under different conditions of social distancing in Lombardy and Emilia-Romagna, the two regions of Italy most affected by the epidemic. To do this, we used a Susceptible-Exposed-Infectious-Recovered (SEIR) deterministic model, which encompasses compartments relevant to public health interventions such as quarantine. A new compartment L was added to the model for isolated infected population, i.e., individuals tested positives that do not need hospital care. We found that in Lombardy restrictive containment measures should be prolonged at least until early July to avoid a resurgence of hospitalizations; on the other hand, in Emilia-Romagna the number of hospitalized cases could be kept under a reasonable amount with a higher contact rate. Our results suggest that territory-specific forecasts under different scenarios are crucial to enhance or take new containment measures during the epidemic.

We have considered a SEIR-SEI Vector-host mathematical model which captures malaria transmission dynamics, described and built on 7-dimensional nonlinear ordinary differential equations. We compute the basic reproduction number of the model; examine the positivity and boundedness of the model compartments in a region using well established methods viz: Cauchy’s differential theorem, Birkhoff & Rota’s theorem which verifies and reveals the well-posedness, and carrying capacity of the model respectively, the existence of the Disease-Free (DFE) and Endemic (EDE) equilibrium points were determined and examined. Using the Gaussian elimination method and the Routh-hurwitz criterion, we convey stability analyses at DFE and EDE points which indicates that the DFE (malaria-free) and the EDE (epidemic outbreak) point occurs when the basic reproduction number is less than unity (one) and greater than unity (one) respectively. We obtain a solution to the model using the Variational iteration method (VIM) (an unprecedented method) to each population compartments and verify the efficacy, reliability and validity of the proposed method by comparing the respective solutions via tables and combined plots with the computer in-built Runge-kutta-Felhberg of fourth-fifths order (RKF-45). We illustrate the combined plot profiles of each compartment in the model, showing the dynamic behavior of these compartments; then we speculate that VIM is efficient and capable to conduct analysis on Malaria models and other epidemiological models.

Human civilizations are under enormous threats due to the outbreak of novel coronavirus (COVID-19) originated from Wuhan, China. The asymptomatic carriers are the potential spreads of this novel virus. Since, guaranteed antiviral treatments have not been available in the market so far, it is really challenging to fight against this contagious disease. To save the living mankind, it is urgent to know more about how the virus transmits itself from one to another quite rapidly and how we can predict future infections. Scientists and Researchers are working hard in investigating to understand its high infection rate and transmission process. One possible way to know is to use our existing COVID-19 infection data and prepare a useful model to predict the future trend. Mathematical modelling is very useful to understand the basic principle of COVID-19 transmission and provide necessary guidelines for future prediction. Here, we have reviewed 9 distinct commonly used models based on Mathematical implementations for COVID-19 transmission and dig into the deep head to head comparison of each model. Finally, we have discussed interesting key behaviour of each model, relevant upcoming important issues, challenges and future directions.

We applied a generalized SEIR epidemiological model to the recent SARS-CoV-2 outbreak in the world, with a focus on Italy and its Lombardia, Piemonte, and Veneto regions. We focus on the application of a stochastic approach in fitting the model numerous parameters using a Particle Swarm Optimization (PSO) solver, to improve the reliability of predictions in the medium term (30 days). We analyze the official data and the predicted evolution of the epidemic in the Italian regions, and we compare the results with data and predictions of Spain and South Korea. We link the model equations to the changes in people’s mobility, with reference to Google’s COVID-19 Community Mobility Reports. We discuss the effectiveness of policies taken by different regions and countries and how they have an impact on past and future infection scenarios.

In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations as approximations of some type of fractional nonlinear birth--death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While FDEs appear more flexible in fitting empirical data, our ODEs offered better fits to two out of three data sets. Important differences in transient dynamics between these modeling approaches are discussed.

We review and assess the classic SIR and SEIR epidemiological models regarding possible applications to the COVID-19 pandemic. In spite of numerous more complicated models, we show how the qualitative features of the solution to the SIR and SEIR models continue to provide valuable public health insights in some scenarios. Using estimated COVID-19 data as of this date, the SEIR model shows that if it were possible to reduce R₀ from 2.5 to 1.25 through social distancing and other measures, the maximum fraction of the population that would become infected at any particular time would drop from 17% to 4%, provided that all of the model assumptions are satisfied. Finally, we compare the classic SIR model with a recent stochastic model with favorable results. Since this comparison underscores the importance of underlying connectivity assumptions, we conclude with Monte-Carlo simulations with specific connectivity that reproduce the classical SIR model with standard incidence.

We present a general approach to define reproduction ratios or numbers to monitor the outbreak of epidemics that are modeled by mathematical evolution equations. This provides a solution to an important topic that has not been completely settled in the literature, especially in the case of complex epidemiological models. We illustrate our procedure with a full implementation of a standard deterministic SEIR model that is applied to examine the Covid-19 outbreaks and the effects of intervention measures in several countries in America (Argentina, Brazil, Mexico, USA) and Europe (France, Italy, Spain and UK) in 2020. Our code is also used to investigate herd immunity levels for Covid-19, indicating values between 85% and 90%.

Acute lower respiratory tract infection is a major health problem that affects more than 15% of the total population of Saudi Arabia each year. Epidemiological studies conducted over the last three decades have indicated that viruses are responsible for the majority of these infections. The epidemiology of respiratory viruses in Saudi Arabia is believed to be affected mainly by the presence and mobility of large numbers of foreign workers and the gathering of millions of Muslims in Mecca during the Hajj and Umrah seasons. Knowledge concerning the epidemiology, circulation pattern, and evolutionary kinetics of respiratory viruses in Saudi Arabia are scant, with the available literature being inconsistent. After reviewing the available data on epidemiology and evolution of respiratory viruses, this study examines the effect of varying vaccination rates across different age groups during the 2019/2020 influenza season in Saudi Arabia. Utilizing an age-structured SEIR (Susceptible–Exposed–Infectious–Recovered) model, it develops customized vaccination policies by considering age-specific incidence rates. This pioneering research segments the population into five age groups—infants and school-aged children, junior and older youth, young adults and adults, middle-aged, and seniors—across five regional areas in Saudi Arabis: Eastern, Central, Northern, Western, and Southern. A contact matrix, compiled from multiple sources, is used to delineate the dynamics of influenza transmission. The study undertakes a thorough comparison of three distinct vaccination scenarios: no vaccination, national vaccination, and optimized vaccine allocation policy, under various potential pandemic situations. It examines their impact on vaccination campaigns in terms of the total number of infections, mortality, and morbidity rates. The results emphasize the crucial impact of population demographics on disease transmission and vaccine distribution. According to the findings, the optimized vaccination scenario proved to be the most effective strategy in all scenarios.