In this paper, we propose a determinist mathematical model for the co-circulating into two circulating recombinants forms (CRFs) Of HIV-disease in Mali. We divide the sexually active population within three compartmen...In this paper, we propose a determinist mathematical model for the co-circulating into two circulating recombinants forms (CRFs) Of HIV-disease in Mali. We divide the sexually active population within three compartments (susceptible, CRF-1 infected and CRF-2 or CRF-12 infected) and study the dynamical behavior of this model. Then, we define a basic reproduction number of the CRF-2 or CRF-12 infected individuals R0 and shown that the CRF-2 or CRF-12 infected-free equilibrium is locally-asymptotically stable if R0 1 (thus the CRF-2 or CRF-12 infected invade in the population). Fur-thermore, we prove that under certain conditions on the parameters of the model the controllability of CRF-2 or CRF-12 infected with regard to the CRF-1 infected. Numerical simulations are given to illustrate the results.展开更多
In this paper we introduce a classical SI model to capture the spread of an infectious disease within a population. More precisely, the spatial diffusion of HIV/AIDS in a population is modeled. For that, we assume tha...In this paper we introduce a classical SI model to capture the spread of an infectious disease within a population. More precisely, the spatial diffusion of HIV/AIDS in a population is modeled. For that, we assume that the spread is due to the anarchical comportment of infected individuals along a road, especially, “lorry drivers”. The question which consists of the control of the infection is also addressed. Infected individuals moving from a town to another one, the diffusion is then anisotropic with a main direction of propagation, namely the road direction. Using a semi-group argument and a maximum principle, the uniqueness of a solution to the problem is established. This solution is also estimated. We end this paper by considering some numerical experiments in the case of HIV/AIDS spread in Mali along a road connecting two towns.展开更多
文摘In this paper, we propose a determinist mathematical model for the co-circulating into two circulating recombinants forms (CRFs) Of HIV-disease in Mali. We divide the sexually active population within three compartments (susceptible, CRF-1 infected and CRF-2 or CRF-12 infected) and study the dynamical behavior of this model. Then, we define a basic reproduction number of the CRF-2 or CRF-12 infected individuals R0 and shown that the CRF-2 or CRF-12 infected-free equilibrium is locally-asymptotically stable if R0 1 (thus the CRF-2 or CRF-12 infected invade in the population). Fur-thermore, we prove that under certain conditions on the parameters of the model the controllability of CRF-2 or CRF-12 infected with regard to the CRF-1 infected. Numerical simulations are given to illustrate the results.
文摘In this paper we introduce a classical SI model to capture the spread of an infectious disease within a population. More precisely, the spatial diffusion of HIV/AIDS in a population is modeled. For that, we assume that the spread is due to the anarchical comportment of infected individuals along a road, especially, “lorry drivers”. The question which consists of the control of the infection is also addressed. Infected individuals moving from a town to another one, the diffusion is then anisotropic with a main direction of propagation, namely the road direction. Using a semi-group argument and a maximum principle, the uniqueness of a solution to the problem is established. This solution is also estimated. We end this paper by considering some numerical experiments in the case of HIV/AIDS spread in Mali along a road connecting two towns.
