Because the latent period and the infectious period of tuberculosis TB are very long, it is not reasonable to consider the time as constant. So this paper formulates a mathematical model that divides the latent period and the infectious period into n-stages. For a general n-stage stage progression SP model with bilinear incidence, we analyze its dynamic behavior. First, we give the basic reprod...

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 we consider switched systems composed of LTI non Hurwitz dynamics and we deal with the problem of computing an appropriate switching law such that the controlled system is globally asymptotically stable. We first present a method to design a feedback control law that minimizes a linear quadratic performance index when an infinite number of switches is allowed and at least one dyna...

We conduct rigorous stability analysis for the well-known cholera model proposed by Codeço [7]. Using theory of monotone dynamical systems, we prove that the endemic equilibrium, when it exists, of the model is globally asymptotically stable, implying the persistence of the disease in the absence of interventions. We then modify Codeço’s model by incorporating various control strategies, and st...

The asymptotic behavior of the principal eigenvalue for general linear cooperative elliptic systems with small diffusion rates is determined. As an application, we show that if a cooperative system of ordinary differential equations has a unique positive equilibrium which is globally asymptotically stable, then the corresponding reaction-diffusion system with either the Neumann boundary conditi...

This paper examines the propagation behavior of computer virus under human intervention. A dynamical model describing the spread of computer virus, under which a susceptible computer can become recovered directly and an infected computer can become susceptible directly, is proposed. Through a qualitative analysis of this model, it is found that the virus-free equilibrium is globally asymptotica...

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)...

We extend a recent investigation by Meehan et al. (2017) [1] regarding the global stability properties of the general Kermack-McKendrick model to the multi-strain case. We demonstrate that the basic reproduction number of each strain R0j represents a sharp threshold parameter such that when R0j ≤ 1 for all j each strain dies out and the infection-free equilibrium is globally asymptotically stab...

The global dynamics of discrete competitive model of Lotka-Volterra type with two species is considered. Earlier works have shown that the unique positive equilibrium is globally attractive under the assumption that the intrinsic growth rates of the two competitive species are less than 1 ln 2, and further the unique positive equilibrium is globally asymptotically stable under the stronger cond...

The main goal of this paper is to investigate the periodic character, invariant intervals, oscillation and global stability and other new results of all positive solutions of the equation$$x_{n+1}=frac{alpha+beta x_{n}}{A + Bx_{n}+ Cx_{n-k}},~~ n=0,1,2,ldots,$$where the parameters $alpha$, $beta$, $A$, $B$ and $C$ are positive, and the initial conditions $x_{-k},x_{-k+1},ldots,x_{-1},x_{0}$ are...