Search

Corona virus disease which has caused frustration in the human community remains the concern of the globe as every government struggles to defeat the pandemic. In this manuscript, we have extensively studied a new deterministic SEQIHR model of deadly Corona virus pandemic governed by nonlinear ordinary differential equations to provide deep insight into the dynamics of the disease. The purpose is to perform a complete mathematical analysis and the design of an optimal control strategy for the developed deterministic model by utilizing the preventive measures of quarantine and hospitalization. Some comprehensive mathematical techniques are employed to demonstrate the positivity and boundedness of solutions. Two main equilibrium points of the pandemic model are stated. To handle the future dynamical behavior of the pandemic, the threshold parameter value is computed using the next-generation method. The local and global asymptotic stability conditions of both the equilibria are obtained successfully. A numerical analysis to observe the effectiveness of quarantine and hospitalization strategies is performed and illustrated by graphs. We implemented the well known Non-Standard Finite Difference (NSFD) method to find the numerical solution of model. Numerical simulations are conducted to support our analytic results. The developed model is subjected to sensitivity analysis and the most sensitive parameters are identified. The bifurcation nature of the developed model is examined. An optimal control problem is introduced for the proposed model to determine the best controls for the implemented hospitalization and quarantine strategies. With the attention of reducing the number of exposed and infected persons, an optimum control problem and its derived associated optimality conditions of Pontryagin type are explored. An important feature of this study is to employ NSFD method backward in time for the first time to solve optimal control problem instead of other standard methods. The extremals are obtained numerically. Moreover, we have shown the effectiveness of optimal controls on the human community to view more features of the state variables in the proposed model. • We develop a Covid-19 SEQIHR pandemic model and derive analytically several essential properties. • Necessary and sufficient conditions for the stability of equilibrium points are established. • The impact of quarantine and hospitalization on human community is demonstrated numerically. • An optimal control problem is introduced to determine the best controls for both the strategies. • Numerical simulations using an efficient NSFD scheme confirm the derived analytical results. [ABSTRACT FROM AUTHOR]

In this paper, by considering the development of antivirus software always lags behind the emergence of new virus and the point-to-group information propagation mode, a new computer virus model with point to group and discontinuous anti-virus strategy is presented. To the best of our knowledge, this is the first computer virus model that takes into account the effect of discontinuous anti-virus strategy. The dynamic properties of this model are investigated comprehensively. Specifically, it is found that in the case that the equilibrium is asymptotically stable, the convergence to the equilibrium can actually be achieved in finite time, and the time can be estimated in terms of the model parameters, the initial number of the uninfected computer and latent computer and the initial anti-virus strength, which means the virus in the network can be controlled or eliminated in finite time by increasing the anti-virus strength. Finally, two illustrative examples are also given to support the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with a stochastic predator–prey system with Beddington–DeAngelis functional response and time delay. Sufficient conditions for global asymptotic stability of the positive equilibrium point are established. The result demonstrates that the delay is harmless for global stability of the stochastic system in some cases. Some figures are given to validate the analytical results. [Copyright &y& Elsevier]

Abstract: In this work, we investigate the spatiotemporal dynamics of reaction–diffusion equations subject to cross-diffusion in the frame of a two-dimensional ratio-dependent predator–prey model. The conditions for diffusion-driven instability are obtained and the Turing space in the parameters space is achieved. Moreover, the criteria for local and global asymptotic stability of the unique positive homogeneous steady state without diffusion are discussed. Numerical simulations are carried out in order to validate the feasibility of the obtained analytical findings. Different types of spatial patterns through diffusion-driven instability of the proposed model are portrayed and analysed. Lastly, the paper finishes with an external discussion of biological relevance of the analysis regarding cross-diffusion and pattern issues. [Copyright &y& Elsevier]

Abstract: A new deterministic model for the transmission dynamics of two strains of influenza is designed and used to qualitatively assess the role of cross-immunity on the transmission process. It is shown that incomplete cross-immunity could induce the phenomenon of backward bifurcation when the associated reproduction number is less than unity. The model undergoes competitive exclusion (where Strain drives out Strain to extinction whenever ). For the case where infection with one strain confers complete immunity against infection with the other strain, it is shown that the disease-free equilibrium of the model is globally-asymptotically stable whenever the reproduction number is less than unity. In the absence of cross-immunity, the model can have a continuum of co-existence endemic equilibria (which is shown to be globally-asymptotically stable for a special case). When infection with one strain confers incomplete immunity against the other, numerical simulations of the model show that the two strains co-exist, with Strain dominating (but not driving out Strain ), whenever . [Copyright &y& Elsevier]