The relationship between the basic reproduction number R0 and the exponential growth rate, specific to pair approximation models, is derived for the SIS, SIR and SEIR deterministic models without demography. These models are extended by including a random rewiring of susceptible individuals from infectious (and exposed) neighbours. The derived relationship between the exponential growth rate an...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 20 July 2020Accepted: 17 May 2021Published online: 13 September 2021Keywordsepidemic model, varying infectivity, infection-age-dependent deterministic integral equations, early phase epidemic, basic reproduction number $R_0$, Poisson random measureAMS Subject Headings45D0...

We consider a discrete time model of semelparous biennial population dynamics. Interactions between individuals are modelled with the aid of an "environmental" variable I. The impact on and the sensitivity to the environmental condition is age specific. The main result is that competitive exclusion between the year classes is possible as is their coexistence. For moderate values of the basic re...

In this paper, we studied the global dynamics of a SEIR epidemic model in which the latent and immune state were infective. The basic reproductive rate, R0, is derived. If R0 6 1, the disease-free equilibrium is globally stable and the disease always dies out. If R0 > 1, there exists a unique endemic equilibrium which is locally stable. Furthermore, we proved the global stability of the unique ...

Using a multiple stage age of infection model, we derive an expression for the basic reproduction number, R0. We apply this method to find R0 in analogous treatment models. We find, in the model without treatment, R0 depends only on the mean infective period, and not on the infective distribution. In treatment models, R0 depends on the mean infective and mean treatment period, as well as the di...

Schistosomiasis, a health challenge in many communities, is prevalent as the rate of infection one every thirty individuals. In this work, deterministic model for schistosomiasis transmission dynamics studied. The stability properties equilibrium states, disease-free and endemic equilibria are established terms basic reproduction number, R_0. sensitivity analysis R_0 with respect to parameters ...

Abstract Taenia solium taeniasis and cysticercosis are neglected zoonotic diseases that affect human health economies of developing countries. In this work, we formulate analyze deterministic continuous time Markov chain (CTMC) stochastic models to determine parameters drive the likelihood their extinction. The basic reproduction number $$R_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/M...

‎Hepatitis B virus (HBV) infection is a major public health problem in the world today‎. ‎A mathematical model is formulated to describe the spread of hepatitis B‎, ‎which can be controlled by vaccination as well as treatment‎. ‎We study the dynamical behavior of the system with fixed control for both vaccination and treatment‎. ‎The results shows that the dynamics of the model is completely de...

We consider a model for an epidemic in a population that occupies geographically distinct locations. The disease is spread within subpopulations by contacts between infective and susceptible individuals, and is spread between subpopulations by the migration of infected individuals. We show how susceptible individuals can act collectively to limit the spread of disease during the initial phase o...