Abstract. A mathematical model describing the transmission dynamics of an infectious disease with an exposed (latent) period, relapse and a saturation incidence rate is investigated. By analyzing the corresponding characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium is established. By using suitable Lyapunov functionals and LaSalle’s invariance ...

In this paper, an SIR epidemic model involving information-related vaccination, non-linear incidence rate and the information variable is studied. We get a critical value 0  . When 1 < ) (1 0 0  p  , the disease-free Equilibrium is stable, on the contrary, if 1 > ) (1 0 0  p  , the disease-free equilibrium is unstable and an endemic equilibrium appears. We study the local stability and glo...

We use a model to study the dynamics of malaria in the human and mosquito population to explain the stability patterns of malaria. The model results show that the disease-free equilibrium is globally asymptotically stable and occurs whenever the basic reproduction number, R0 is less than unity. We also note that when R0 . 1, the disease-free equilibrium is unstable and the endemic equilibrium i...

In this paper the spreading of epidemic model on complex networks with a generalized nonlinear incidence rate is presented. Firstly the SIS model on homogeneous networks with nonlinear incidence rate is considered, and the existence conditions about the disease-free equilibrium and the endemic equilibrium are given. And then the model on heterogenous scale-free (SF) networks is considered, wher...

free radicals are produced continuously in the cells as part of normal cellular function, however excess production might play a role in pathophysiology of many disease conditions, including cancer, alzheimer's disease, atherosclerosis and some of the drug-induced toxicity. many basic research studies and observational epidemiologic studies in human suggest that antioxidants can prevent oxidati...

background : â  celiac disease (cd) is an immune-mediated inflammation of the small intestine caused by sensitivity to dietary gluten and related proteins in genetically sensitive individuals . recurrent aphthous stomatitis (ras) is an inflammatory condition characterized by painful recurrent, single or multiple ulcerations of the oral mucosa. the association between cd and ras has been evaluat...

The basic reproduction number, R0 is a measure of the potential for disease spread in a population. Mathematically, R0 is a threshold for stability of a disease-free equilibrium and is related to the peak and final size of an epidemic. The purpose of these notes is to give a precise definition and algorithm for obtaining R0 for a general compartmental ordinary differential equation model of dis...

A multi-stage model of disease transmission, which incorporates a generalized non-linear incidence function, is developed and analysed qualitatively. The model exhibits two steady states namely: a disease-free state and a unique endemic state. A global stability of the model reveals that the disease-free equilibrium is globally asymptotically stable (and therefore the disease can be eradicated)...

In this study, we constructed and analysed a mathematical model of COVID-19 in order to comprehend the transmission dynamics disease. The reproduction number (RC) was calculated via next generation matrix method. We also used Lyaponuv method show global stability both disease free endemic equilibrium points. results showed that disease-free point is globally asymptotically stable if RC > 1. fur...