*Correspondence: [email protected] School of Mathematics and Computer Science, Shanxi Normal University, Linfen, P.R. China Abstract In this paper, we study a new SEIRS epidemic model describing nonlinear incidence with a more general form and the transmission of influenza virus with disease resistance. The basic reproductive number 0 is obtained by using the method of next generating matrix. ...

In this paper, we study a vaccination model for tuberculosis (TB) dynamics at the population level. We prove that the solution to the model is positive and bounded. The basic reproduction number is determined. We show that the disease-free equilibrium (DFE) is globally asymptotically stable if and the existence of at least one endemic equilibrium of the model. Numerical simulations of the model...

We study an epidemic model with a nonlinear incidence rate which describes the psychological effect of certain serious diseases on the community when the ratio of the number of infectives to that of the susceptibles is getting larger. The model has set up a challenging issue regarding its dynamics near the origin since it is not well defined there. By carrying out a global analysis of the model...

This article concerns the SIRC epidemiological model for influenza A, which efficiently describes the mechanism of disease spreading, including the susceptible (S), the infected (I) and the recovered (R), along with a crossimmune class (C) that recovers after being inflected by different strains of the same viral subtype. The dynamics of the model is completely determined by the basic reproduct...

A disease transmission model of SEIRS type with distributed delays in latent and temporary immune periods is discussed. With general/particular probability distributions in both of these periods, we address the threshold property of the basic reproduction number R0 and the dynamical properties of the disease-free/endemic equilibrium points present in the model. More specifically, we 1. show the...

A recent randomized controlled trial shows a significant reduction in women-to-men transmission of HIV due to male circumcision. Such development calls for a rigorous mathematical study to ascertain the full impact of male circumcision in reducing HIV burden, especially in resource-poor nations where access to anti-retroviral drugs is limited. First of all, this paper presents a compartmental m...

We formulate a deterministic model with two latent periods in the non-constant host and vector populations, in order to theoretically assess the potential impact of personal protection, treatment and possible vaccination strategies on the transmission dynamics of malaria. The thresholds and equilibria for the model are determined. The model is analysed qualitatively to determine criteria for co...

Background: HIV is a virus that directed at destroying the human immune system thereby exposing body to risk of been affected by other common illnesses and if it not treated, generates more chronic illness called AIDS. Materials Methods: In this paper, we employed fixed-point theory in developing uniqueness existence solution fractional order HIV/AIDS model having Caputo-Fabrizio operator. This...

many recent studies overshadow the effects of gluten-free diet. gluten-free diet positive effects were observed in celiac disease patients: increase in body mass index, higher energy intakes, reducing adiposity gain, moderates the risk of the associated complications. however, adhering to a gluten-free diet is difficult for many people. a new solution is needed for quality of life of celiac dis...

In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlinear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotica...