Abstract
An HIV/AIDS epidemic model with general nonlinear incidence rate and treatment is formulated. The basic reproductive number Re_{0} is obtained by use of the method of the next generating matrix. By carrying out an analysis of the model, we study the stability of the disease-free equilibrium and the unique endemic equilibrium by using the geometric approach for ordinary differential equations. Numerical simulations are given to show the effectiveness of the main results.
Highlights
The human immuno-deficiency virus (HIV) infection, which can lead to acquired immuno-deficiency syndrome (AIDS), has become an important infectious disease in both the developed and the developing nations
Yusuf and Benyah [ ] presented a deterministic model for controlling the spread of the disease, and the results show that the optimal way to mitigate the spread of the disease is for susceptible individuals to consistently practise safe sex as much as possible, while the ARV treatment should be initiated for patients as soon as they progress to the pre
They study the effect of treatment on the transmission dynamics of the HIV/AIDS epidemic model
Summary
The human immuno-deficiency virus (HIV) infection, which can lead to acquired immuno-deficiency syndrome (AIDS), has become an important infectious disease in both the developed and the developing nations. Muldowney [ ] proposed a way to prove the asymptotical stability of periodic orbits through estimating the right derivative of the Lyapunov function, and the global asymptotical stability of the epidemic equilibrium was proved by using a Poincaré-Bendixson property and a general criterion for the orbital stability of periodic orbits concerned with higher-dimensional nonlinear autonomous systems as well as the theory of competitive system of differential equations This geometric method is used in [ , ] to resolve the global asymptotical stability of the epidemic equilibrium for an SEIR with bilinear and nonlinear incidence rates. Motivated by the above work, in this paper, we consider an HIV/AIDS epidemic model with nonlinear incidence rate Sg(I) and treatment. K is the rate at individuals with HIV receiving treatment, that is, the proportion of the infection class I receiving treatment per unit time.
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