In this research, we developed a coinfection model of tuberculosis and COVID-19 with the effect isolation treatment. We obtained two equilibria, namely, disease-free equilibrium endemic equilibrium. Disease-free is state in which no infection occurs. Endemic there occurs not only but also COVID-19. assumed that parameters follow uniform distribution, then, took 1,000 samples each parameter usin...

A general mathematical model for a disease with an exposed (la tent) period and relapse is proposed. Such a model is appropriate for tuberculosis, including bovine tuberculosis in cattle and wildlife, and for herpes. For this model with a general probability of remaining in the exposed class, the basic reproduction number R(0) is identified and its threshold property is discussed. In particular...

Abstract We develop a new transmission model of COVID-19 in the presence waning immunity with isolation and vaccination humans. The spreading disease is determined by basic reproduction number (? 0 ). Based on mathematical analysis, we found that non-endemic equilibrium locally asymptotically stable when ? < 1 whereas endemic > 1. A numerical simulation used to show population dynamics. I...

In this paper we study an epidemic model with nonmonotonic incidence rate, which describes the psychological effect of certain serious diseases on the community when the number of infectives is getting larger. By carrying out a global analysis of the model and studying the stability of the disease-free equilibrium and the endemic equilibrium, we show that either the number of infective individu...

We study a susceptible-infected-susceptible model with distributed delays. By constructing suitable Lyapunov functionals, we demonstrate that the global dynamics of this model is fully determined by the basic reproductive ratio R0. To be specific, we prove that if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable. On the other hand, if R0>1, then the endemic equilibriu...

We investigate a class of multigroup dengue epidemic model. We show that the global dynamics are determined by the basic reproductive number R0. We present that when R0 ≤ 1, there is a unique disease-free equilibrium which is globally asymptotically stable; when R0 > 1, there exists a unique endemic equilibrium and it is globally asymptotically stable proved by a graph-theoretic approach to the...

This paper considers an SIRS model with nonlinear incidence rate and treatment. It is assumed that susceptible and infectious individuals have constant immigration rates. We investigate the existence of equilibrium and prove the global asymptotical stable results of the endemic equilibrium. We then obtained that the model undergoes a Hopf bifurcation and existences a limit cycle. Some numerical...

A model for the transmission of dengue fever with variable human population size is analyzed. We find three threshold parameters which govern the existence of the endemic proportion equilibrium, the increase of the human population size, and the behaviour of the total number of human infectives. We prove the global asymptotic stability of the equilibrium points using the theory of competitive s...

Spatial heterogeneity, habitat connectivity, and rates of movement can have large impacts on the persistence and extinction of infectious diseases. These factors are shown to determine the asymptotic profile of the steady states in a frequency-dependent SIS (susceptible-infectedsusceptible) epidemic model with n patches in which susceptible and infected individuals can both move between patches...

In this paper, we derive and study the classical SIR, SIS, SEIR and SEI models of epidemiological dynamics with time delays and a general incidence rate. By constructing Lyapunov functionals, the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium is shown. This analysis extends and develops further our previous results and can be applied to the other biologi...