Optimal Control in Stochastic Model with Short Message Service to
HIV/AIDS patients under ARV
Abstract
In this paper, we treat an application of a optimal control problem to
the stochastic dynamic system in epidemic. We consider a HIV/AIDS
stochastic dynamic model with anti retro viral (ARV)-therapy. This model
is formulated and is analyzed previously in [11]. Our objective is
to minimize the newly infection cases. ARV-therapy is a curative measure
of HIV/AIDS patients. It presents until there the therapeutic effect
efficient, even in the cases of resistances. This treatment measure
associated to the preventive measures as HIV-Testing and Counseling
(HTC), i.e. test technology and education, sensitization campaign on
change sexual behavior among people that run the risk, especially, the
strategy of quick-alert by Short Message Service (SMS) to patients by
the care service, for to ensure that these take their treatment
effectively, are again the optimal strategies of the control that
permits to reduce the new cases of infection. Thus, we introduce three
additional variables in a stochastic dynamic proposed in [11] to act
on the proportions of HIV/AIDS patients under ARV by the optimal
strategies for the purpose to reduce the prevalence and the incidence. A
minimization problem of newly infection cases of HIV/AIDS is formulated
and solved analytically and numerically via Bellman’s principle. The
numerical results of this controlled dynamics are also described.