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Coronavirus disease 2019 (COVID-19) is an infection that can result in lung issues such as pneumonia and, in extreme situations, the most severe acute respiratory syndrome. COVID-19 is widely investigated by researchers through mathematical models from different aspects. Inspired from the literature, in the present paper, the generalized deterministic COVID-19 model is considered and examined. The basic reproduction number is obtained which is a key factor in defining the nonlinear dynamics of biological and physical obstacles in the study of mathematical models of COVID-19 disease. To better comprehend the dynamical behavior of the continuous model, two unconditionally stable schemes, i.e., mixed Euler and nonstandard finite difference (NSFD) schemes are developed for the continuous model. For the discrete NSFD scheme, the boundedness and positivity of solutions are discussed in detail. The local stability of disease-free and endemic equilibria is demonstrated by constructing Jacobian matrices for NSFD scheme; nevertheless, the global stability of aforementioned equilibria is verified by using Lyapunov functions. Numerical simulations are also presented that demonstrate how both the schemes are effective and suitable for solving the continuous model. Consequently, the outcomes obtained through these schemes are completely according to the solutions of the continuous model. [ABSTRACT FROM AUTHOR]

The hepatitis B infection is a global epidemic disease which is a huge risk to the public health. In this paper, the transmission dynamics of hepatitis B deterministic model are presented and studied. The basic reproduction number is attained and by applying it, the local as well as global stability of disease-free and endemic equilibria of continuous hepatitis B deterministic model are discussed. To better understand the dynamics of the disease, the discrete nonstandard finite difference (NSFD) scheme is produced for the continuous model. Different criteria are employed to check the local and global stability of disease-free and endemic equilibria for the NSFD scheme. Our findings demonstrate that the NSFD scheme is convergent for all step sizes and consequently reasonable in all respect for the continuous deterministic epidemic model. All the aforementioned properties and their effects are also proved numerically at each stage to show their mathematical as well as biological feasibility. The theoretical and numerical findings used in this paper can be employed as a helpful tool for predicting the transmission of other infectious diseases. [ABSTRACT FROM AUTHOR]

In the present paper, the SIR model with nonlinear recovery and Monod type equation as incidence rates is proposed and analyzed. The expression for basic reproduction number is obtained which plays a main role in the stability of disease-free and endemic equilibria. The nonstandard finite difference (NSFD) scheme is constructed for the model and the denominator function is chosen such that the suggested scheme ensures solutions boundedness. It is shown that the NSFD scheme does not depend on the step size and gives better results in all respects. To prove the local stability of disease-free equilibrium point, the Jacobean method is used; however, Schur–Cohn conditions are applied to discuss the local stability of the endemic equilibrium point for the discrete NSFD scheme. The Enatsu criterion and Lyapunov function are employed to prove the global stability of disease-free and endemic equilibria. Numerical simulations are also presented to discuss the advantages of NSFD scheme as well as to strengthen the theoretical results. Numerical simulations specify that the NSFD scheme preserves the important properties of the continuous model. Consequently, they can produce estimates which are entirely according to the solutions of the model. [ABSTRACT FROM AUTHOR]