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In this work, we examine a fractional-order model for simulating the spread of the monkeypox virus in the human host and rodent populations. The employment of the fractional form of the model gives a better insight into the dynamics and spread of the virus, which will help in providing some new control measures. The model is formulated into eight mutually exclusive compartments and the form of a nonlinear system of differential equations. The reproduction number for the present epidemic system is found. In addition, the equilibrium points of the model are investigated and the associated stability analysis is carried out. The influences of key parameters in the model and the ways to control the monkeypox epidemic have been thoroughly examined for the fractional model. To ensure that the model accurately simulates the nonlinear phenomenon, we adapt an efficient numerical technique to solve the presented model, and the acquired results reveal the dynamic behaviors of the model. It is observed that when memory influences are considered for the present model, through Caputo fractional-order derivatives, they affect the speed and time taken by solution trajectories towards steady-state equilibria.
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The forecasting of the nature and dynamics of emerging coronavirus (COVID-19) pandemic has gained a great concern for health care organizations and governments. The efforts aim to to suppress the rapid and global spread of its tentacles and also control the infection with the limited available resources. The aim of this work is to employ real data set to propose and analyze a compartmental discrete time COVID-19 pandemic model with non-linear incidence and hence predict and control its outbreak through dynamical research. The Basic Reproduction Number ( R 0 ) is calculated analytically to study the disease-free steady state ( R 0 < 1 ), and also the permanency case ( R 0 > 1 ) of the disease. Numerical results show that the transmission rates α > 0 and ß > 0 are quite effective in reducing the COVID-19 infections in India or any country. The fitting and predictive capability of the proposed discrete-time system are presented for relishing the effect of disease through stability analysis using real data sets.
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In this study, a novel reaction-diffusion model for the spread of the new coronavirus (COVID-19) is investigated. The model is a spatial extension of the recent COVID-19 SEIR model with nonlinear incidence rates by taking into account the effects of random movements of individuals from different compartments in their environments. The equilibrium points of the new system are found for both diffusive and non-diffusive models, where a detailed stability analysis is conducted for them. Moreover, the stability regions in the space of parameters are attained for each equilibrium point for both cases of the model and the effects of parameters are explored. A numerical verification for the proposed model using a finite difference-based method is illustrated along with their consistency, stability and proving the positivity of the acquired solutions. The obtained results reveal that the random motion of individuals has significant impact on the observed dynamics and steady-state stability of the spread of the virus which helps in presenting some strategies for the better control of it.
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In this study, an extended spatiotemporal model of a human immunodeficiency virus (HIV) CD4+ T cell with a drug therapy effect is proposed for the numerical investigation. The stability analysis of equilibrium points is carried out for temporal and spatiotemporal cases where stability regions in the space of parameters for each case are acquired. Three numerical techniques are used for the numerical simulations of the proposed HIV reaction-diffusion system. These techniques are the backward Euler, Crank-Nicolson, and a proposed structure preserving an implicit technique. The proposed numerical method sustains all the important characteristics of the proposed HIV model such as positivity of the solution and stability of equilibria, whereas the other two methods have failed to do so. We also prove that the proposed technique is positive, consistent, and Von Neumann stable. The effect of different values for the parameters is investigated through numerical simulations by using the proposed method. The stability of the proposed model of the HIV CD4+ T cell with the drug therapy effect is also analyzed.
