Infection-free Equilibrium Point Research Articles

Visceral leishmania model

In this work we consider a mathematical model based on a system of ordinary differential equations describing the evolution of population of dogs infected by leishmania diseases. By analyzing the corresponding characteristic equations, the local stability of infection free equilibrium point and infection equilibrium point are discussed. It is shown that if the basic reproduction number R 0 is less than one, the infection free equilibrium is locally asymptotically stable, whereas if the basic reproduction number R 0 is great than one the infection equilibrium point is locally asymptotically stable, and the infection free equilibrium is unstable.

Dynamics analysis and simulation of a modified HIV infection model with a saturated infection rate.

This paper studies a modified human immunodeficiency virus (HIV) infection differential equation model with a saturated infection rate. It is proved that if the basic virus reproductive number R 0 of the model is less than one, then the infection-free equilibrium point of the model is globally asymptotically stable; if R 0 of the model is more than one, then the endemic infection equilibrium point of the model is globally asymptotically stable. Based on the clinical data from HIV drug resistance database of Stanford University, using the proposed model simulates the dynamics of the two groups of patients' anti-HIV infection treatment. The numerical simulation results are in agreement with the evolutions of the patients' HIV RNA levels. It can be assumed that if an HIV infected individual's basic virus reproductive number R 0 < 1 then this person will recover automatically; if an antiretroviral therapy makes an HIV infected individual's R 0 < 1, this person will be cured eventually; if an antiretroviral therapy fails to suppress an HIV infected individual's HIV RNA load to be of unpredictable level, the time that the patient's HIV RNA level has achieved the minimum value may be the starting time that drug resistance has appeared.

Modeling the propagation of mobile phone virus under complex network.

Mobile phone virus is a rogue program written to propagate from one phone to another, which can take control of a mobile device by exploiting its vulnerabilities. In this paper the propagation model of mobile phone virus is tackled to understand how particular factors can affect its propagation and design effective containment strategies to suppress mobile phone virus. Two different propagation models of mobile phone viruses under the complex network are proposed in this paper. One is intended to describe the propagation of user-tricking virus, and the other is to describe the propagation of the vulnerability-exploiting virus. Based on the traditional epidemic models, the characteristics of mobile phone viruses and the network topology structure are incorporated into our models. A detailed analysis is conducted to analyze the propagation models. Through analysis, the stable infection-free equilibrium point and the stability condition are derived. Finally, considering the network topology, the numerical and simulation experiments are carried out. Results indicate that both models are correct and suitable for describing the spread of two different mobile phone viruses, respectively.

Global stability of the virus dynamics model with Crowley-Martin functional response

In this paper, a virus dynamics model with Crowley-Martin functional response of the infec- tion rate is investigated. By analyzing the corresponding characteristic equations, the local stability of an infection-free equilibrium point and infection equilibrium point are discussed. By constructing suitable Lyapunov functions and using LaSalles invariance principle, the global stability also are established, it is proved that if the basic reproductive number, R0, is less than or equal to one, the infection-free equilib- rium point is globally asymptotically stable, if R0, is more than one, the infection equilibrium point is globally asymptotically stable.