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This paper explores the impact of various distancing measures on the spread of infectious diseases, focusing on the spread of COVID-19 in the Moroccan population as a case study. Contact matrices, generated through a social force model, capture population interactions within distinct activity locations and age groups. These matrices, tailored for each distancing scenario, have been incorporated into an SEIR model. The study models the region as a network of interconnected activity locations, enabling flexible analysis of the effects of different distancing measures within social contexts and between age groups. Additionally, the method assesses the influence of measures targeting potential superspreaders (i.e., agents with a very high contact rate) and explores the impact of inter-activity location flows, providing insights beyond scalar contact rates or survey-based contact matrices. The results suggest that implementing intra-activity location distancing measures significantly reduces in the number of infected individuals relative to the act of imposing restrictions on individuals with a high contact rate in each activity location. The combination of both measures proves more advantageous. On a regional scale, characterized as a network of interconnected activity locations, restrictions on the movement of individuals with high contact rates was found to result in a $ 2 \% $ reduction, while intra-activity location-based distancing measures was found to achieve a $ 44 \% $ reduction. The combination of these two measures yielded a $ 48\% $ reduction.

Epidemiologists have used the timing of the peak of an epidemic to guide public health interventions. By determining the expected peak time, they can allocate resources effectively and implement measures such as quarantine, vaccination, and treatment at the right time to mitigate the spread of the disease. The peak time also provides valuable information for those modeling the spread of the epidemic and making predictions about its future trajectory. In this study, we analyze the time needed for an epidemic to reach its peak by presenting a straightforward analytical expression. Utilizing two epidemiological models, the first is a generalized $ SEIR $ model with two classes of latent individuals, while the second incorporates a continuous age structure for latent infections. We confirm the conjecture that the peak occurs at approximately $ T\sim(\ln N)/\lambda $, where $ N $ is the population size and $ \lambda $ is the largest eigenvalue of the linearized system in the first model or the unique positive root of the characteristic equation in the second model. Our analytical results are compared to numerical solutions and shown to be in good agreement.

In this work, we investigate the transmission dynamics of the Zika virus, considering both a compartmental model involving humans and mosquitoes and an extended model that introduces a non-human primate (monkey) as a second reservoir host. The novelty of our approach lies in the later generalization of the model using a fractional time derivative. The significance of this study is underscored by its contribution to understanding the complex dynamics of Zika virus transmission. Unlike previous studies, we incorporate a non-human primate reservoir host into the model, providing a more comprehensive representation of the disease spread. Our results reveal the importance of utilizing a nonstandard finite difference (NSFD) scheme to simulate the disease's dynamics accurately. This NSFD scheme ensures the positivity of the solution and captures the correct asymptotic behavior, addressing a crucial limitation of standard solvers like the Runge-Kutta Fehlberg method (ode45). The numerical simulations vividly demonstrate the advantages of our approach, particularly in terms of positivity preservation, offering a more reliable depiction of Zika virus transmission dynamics. From these findings, we draw the conclusion that considering a non-human primate reservoir host and employing an NSFD scheme significantly enhances the accuracy and reliability of modeling Zika virus transmission. Researchers and policymakers can use these insights to develop more effective strategies for disease control and prevention.

Media coverage can greatly impact the spread of infectious diseases. Taking into consideration the impacts of media coverage, we propose an SEIR model with a media coverage mediated nonlinear infection force. For this novel disease model, we identify the basic reproduction number using the next generation matrix method and establish the global threshold results: If the basic reproduction number $ \mathcal{R}_{0} < 1 $, then the disease-free equilibrium $ P_{0} $ is stable, and the disease dies out. If $ \mathcal{R}_{0} > 1 $, then the endemic equilibrium $ P^{*} $ is stable, and the disease persists. Sensitivity analysis indicates that the basic reproduction number $ \mathcal{R}_{0} $ is most sensitive to the population recruitment rate $ \Lambda $ and the disease transmission rate $ \beta _{1} $.

We build a model that consider the falling antibody levels and vaccination to assess the impact of falling antibody levels and vaccination on the spread of the COVID-19 outbreak, and simulate the influence of vaccination rates and failure rates on the number of daily new cases in England. We get that the lower the vaccine failure rate, the fewer new cases. Over time, vaccines with low failure rates are more effective in reducing the number of cases than vaccines with high failure rates and the higher the vaccine efficiency and vaccination rate, the lower the epidemic peak. The peak arrival time is related to a boundary value. When the failure rate is less than this boundary value, the peak time will advance with the decrease of failure rate; when the failure rate is greater than this boundary value, the peak time is delayed with the decrease of failure rate. On the basis of improving the effectiveness of vaccines, increasing the vaccination rate has practical significance for controlling the spread of the epidemic.

In this work we use simple mathematical models to study the impact of vaccination against COVID-19 in Portugal. First, we fit a SEIR type model without vaccination to the Portuguese data on confirmed cases of COVID-19 by the date of symptom onset, from the beginning of the epidemic until the 23rd January of 2021, to estimate changes in the transmission intensity. Then, by including vaccination in the model we develop different scenarios for the fade-out of the non pharmacological intervention (NPIs) as vaccine coverage increases in the population according to Portuguese vaccination goals. We include a feedback function to mimic the implementation and relaxation of NPIs, according to some disease incidence thresholds defined by the Portuguese health authorities.

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.

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.

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.

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.

We explore the spread of the Coronavirus disease 2019 (COVID-19) in Lebanon by adopting two different approaches: the STEIR model, which is a modified SEIR model accounting for the effect of travel, and a repeated iterations model. We fit available daily data since the first diagnosed case until the end of June 2020 and we forecast possible scenarios of contagion associated with different levels of social distancing measures and travel inflows. We determine the initial reproductive transmission rate in Lebanon and all subsequent dynamics. In the repeated iterations (RI) model we iterate the available data of currently infected people to forecast future infections under several possible scenarios of contagion. In both models, our results suggest that tougher mitigation measures would slow down the spread of the disease. On the other hand, the current relaxation of measures and partial resumption of international flights, as the STEIR reveals, would trigger a second outbreak of infections, with severity depending on the extent of relaxation. We recommend strong institutional and public commitment to mitigation measures to avoid uncontrolled spread.

In this paper, we attempt to set a framework of conditions for model-specific predictions of newly arising TB epidemics by e.g. immigration of infected persons from high prevalence countries. In addition, we address the aspect of trained immunity in our model. Using a mathematical approach of a system of ordinary differential equations which can be developed over several time-points we obtained varying infection or attack rates that led to different effects of the vaccination, depending on the setting of certain parameters and starting values in the compartments of a SEIR-model. We finally obtained different graphs of disease progression and were able to outline which upgrades and expansions our system requires in order to be exact and well adapted for predicting the course of future TB outbreaks. The model might also be beneficial in predicting non-specific effects of vaccines.