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Recently, Karapinar introduced a new Hardy-Rogers type contractive mapping using the concept of interpolation and proved a fixed point theorem in complete metric space. This new type of mapping, called "interpolative Hardy-Rogers type contractive mapping" is a generalization of Hardy-Rogers's fixed point theorem. Following this direction of research, in this paper, we will present some fixed point results of Hardy-Rogers-type for cyclic mappings on complete metric spaces. Moreover, an example is given to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce four new types of contractions called in this order Kannan-type cyclic contraction via interpolation, interpolative Ćirić-Reich-Rus type cyclic contraction, and we prove the existence and uniqueness for a fixed point for each situation. [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 this article, we consider a stochastic SIR model with a saturated incidence rate and saturated treatment function incorporating Lévy noise. First, we prove the existence of a unique global positive solution to the model. We investigate the stability of the free equilibria E0 by using the Lyapunov method. We give sufficient conditions for the persistence in the mean. We show the dynamic properties of the solution around endemic equilibria point of the deterministic model. Moreover, we display some numerical results to confirm our theoretical results. [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]

In this paper, we investigate a stochastic delayed epidemic model with double epidemic hypothesis and vaccination incorporating Lévy noise. First, we show that this model has a unique global positive solution. Furthermore, we give sufficient conditions for extinction and persistence in the mean of the two epidemics and we prove that the two diseases can coexist under some conditions. Finally, we present some examples to illustrate the analytical results by numerical simulations. [ABSTRACT FROM AUTHOR]

At the end of 2019, the world knew the propagation of a new pandemic named COVID-19. This disease harmed the exercises of humankind and changed our way of life. For modeling and studying infectious illness transmission, mathematical models are helpful tools. Thus, in this paper, taking into account the effect of the intensity of the noises, we define a threshold value Π s of the model, which determines the extinction and persistence of the COVID-19 pandemic. We give numerical simulations to illustrate the analytical results. [ABSTRACT FROM AUTHOR]

In this work, we study a stochastic SIS epidemic model with Lévy jumps and nonlinear incidence rates. Firstly, we present our proposed model and its parameters. We establish sufficient conditions for the extinction and persistence of the disease in the population using some stochastic analysis background. We illustrate our theoretical results by numerical simulations. We conclude that the white noise and Lévy jump influence the transmission of the epidemic. [ABSTRACT FROM AUTHOR]

In recent years, the world knew many challenges concerning the propagation of infectious diseases such as avian influenza, Ebola, SARS-CoV-2, etc. These epidemics caused a change in the healthy balance of humanity. Also, the epidemics disrupt the economies and social activities of countries around the world. Mathematical modeling is a vital means to represent and control the propagation of infectious diseases. In this paper, we consider a stochastic epidemic model with a Markov process and delay, which generalizes many models existing in the literature. In addition, we show the stochastic threshold for the extinction of the disease. Furthermore, numerical examples are discussed to confirm the theoretical result. [ABSTRACT FROM AUTHOR]

In this paper, we study a stochastic epidemic model with double epidemics which includes white noise and telegraph noise modeled by Markovian switching. Sufficient conditions for the extinction and persistence of the diseases are established. In the end, some numerical simulations are presented to demonstrate our analytical results. [ABSTRACT FROM AUTHOR]

We expand an SIR epidemic model with vertical and nonlinear incidence rates from a deterministic frame to a stochastic one. The existence of a positive global analytical solution of the proposed stochastic model is shown, and conditions for the extinction and persistence of the disease are established. The presented results are demonstrated by numerical simulations. [ABSTRACT FROM AUTHOR]