This paper deals with the stability analysis of a simple metabolic system with feedback inhibition. The system is a sequence of monomolecular enzymatic reactions. The last metabolite acts as a feedback regulator for the rst enzyme of the pathway. The enzymatic reactions of the pathway satisfy MichaelisMenten kinetics. The inhibition is described by an hyperbolic model. Without inhibition, it is...

A deterministic model for the transmission dynamics of a communicable disease is developed and rigorously analysed. The model, consisting of five mutually exclusive compartments representing the human dynamics, has a globally asymptotically stable disease-free equilibrium (DFE) whenever a certain epidemiological threshold, known as the basic reproduction number (ℛ₀), is less than unity; in such...

In this paper, a partial differential equation (PDE) model is proposed to explore the transmission dynamics of vector-borne diseases. The model includes both incubation age of the exposed hosts and infection age of the infectious hosts which describe incubation-age dependent removal rates in the latent period and the variable infectiousness in the infectious period, respectively. The reproducti...

This paper addresses the spread of tuberculosis through one-strain and two-strain models. We first present a basic model that incorporates fast and slow progression, effective chemoprophylaxis and therapeutic treatment. The system exhibits the traditional behavior. We prove that if the basic reproduction ratio R0 ≤ 1, then the disease free equilibrium is globally asymptotically stable on the no...

This paper studies the dynamics of a network-based SIRS epidemic model with vaccination and a nonmonotone incidence rate. This type of nonlinear incidence can be used to describe the psychological or inhibitory effect from the behavioral change of the susceptible individuals when the number of infective individuals on heterogeneous networks is getting larger. Using the analytical method, epidem...

We propose a general class of multistage epidemiological models that allow possible deterioration and amelioration between any two infected stages. The models can describe disease progression through multiple latent or infectious stages as in the case of HIV and tuberculosis. Amelioration is incorporated into the models to account for the effects of antiretroviral or antibiotic treatment. The m...

We analyze a mathematical model for infectious diseases that progress through distinct stages within infected hosts. An example of such a disease is AIDS, which results from HIV infection. For a general n-stage stage-progression (SP) model with bilinear incidences, we prove that the global dynamics are completely determined by the basic reproduction number R0: If R(0) =/< 1; then the disease-fr...

We consider an SIR model with variable size population and formulate an optimal control problem subject to the model with vaccination and treatment as controls. Our aim is to find the optimal combination of vaccination and treatment strategies that will minimize the cost of the two control measures as well as the number of infectives. Our model analyses show that the disease free equilibrium is...