In this paper, global dynamics of an SIR model are investigated in which the incidence rate is being considered as Beddington-DeAngelis type and the treatment rate as Holling type II (saturated). Analytical study of the model shows that the model has two equilibrium points (diseasefree equilibrium (DFE) and endemic equilibrium (EE)). The disease-free equilibrium (DFE) is locally asymptotically ...

We present a deterministic mathematical model for malaria transmission with waning immunity. The model consists of five non-linear system of differential equations. We used next generation matrix to derive the basic reproduction number R0. The disease free equilibrium was computed and its local stability has been shown by the virtue of the Jacobean matrix. Moreover, using Lyapunov function theo...

We analyze local asymptotic stability of an SIRS epidemic model with a distributed delay. The incidence rate is given by a general saturated function of the number of infective individuals. Our first aim is to find a class of nonmonotone incidence rates such that a unique endemic equilibrium is always asymptotically stable. We establish a characterization for the incidence rate, which shows tha...

In this paper, we have proposed and analyzed a nonlinear mathematical model for the spread of Polio in a population with variable size structure including the role of vaccination. A threshold parameter, R , is found that completely determines the stability dynamics and outcome of the disease. It is found that if 1  R , the disease free equilibrium is stable and the disease dies out. However, i...

This paper deals with the nonlinear dynamics of a susceptible-infectious-recovered (SIR) epidemic model with nonlinear incidence rate, vertical transmission, vaccination for the newborns of susceptible and recovered individuals, and the capacity of treatment. It is assumed that the treatment rate is proportional to the number of infectives when it is below the capacity and constant when the num...

This paper considers a mathematical model based on the transmission dynamics of hepatitis C virus (HCV) infection. In addition to the usual compartments for susceptible, exposed, and infected individuals, this model includes compartments for individuals who are under treatment and those who have had vaccination against HCV infection. It is assumed that the immunity provided by the vaccine fades...

In this paper, we establish a discrete-time analog for coupled within-host and between-host systems for an environmentally driven infectious disease with fast and slow two time scales by using the non-standard finite difference scheme. The system is divided into a fast time system and a slow time system by using the idea of limit equations. For the fast system, the positivity and boundedness of...

We develop and analyse an ordinary differential equation model to investigate the transmission dynamics of releasing Wolbachia-infected mosquitoes to establish an endemic infection in a population of wild uninfected mosquitoes. Wolbachia is a genus of endosymbiotic bacteria that can infect mosquitoes and reduce their ability to transmit some viral mosquito-transmitted diseases, including dengue...

In this paper, we formulated a dynamical model of COVID-19 to describe the transmission dynamics of the disease. The well possedness of the formulated model equations was proved. Both local and global stability of the disease free equilibrium and endemic equilibrium point of the model equation was established using basic reproduction number. The results show that, if the basic reproduction numb...

This paper is evolved to have insight of Plankton-Nutrients interactions in the presence of delay in the growth term of phytoplankton species .The conditions for asymptotic stability about endemic equilibrium are derived in the absence of delay.The Nyquist criteria is used to estimate the length of delay to preserve stability .Analytic criterion for the existence of hopf-bifurcation is also dis...