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HIV/AIDS model for assessing the effects of prophylactic sterilizing vaccines, condoms and treatment with amelioration. (English) Zbl 1116.92042

Summary: An HIV/AIDS vaccination model for heterosexual transmission with explicit incubation period is presented as a system of delay differential equations. The model considers prophylactic vaccination of sexually immature (pre- and early-adolescents) and mature susceptibles in a community. We start by formulating and analyzing an HIV/AIDS vaccination model that we extend to incorporate condom use based on efficacy and compliance. Further, we extend HIV/AIDS vaccination model with condom use by incorporating treatment which allows AIDS patients to undergo amelioration.
The thresholds and equilibria for the models are determined, and the stabilities analyzed. The basic reproductive numbers for the models are computed and compared to assess the possible community benefits of using prophylactic vaccines, condoms and treatment with amelioration of AIDS patients. We conclude from the study that vaccination and condom use can reduce the basic reproductive number \(({\mathcal R}_0)\) to values below unity but treatment with amelioration intended to lengthen the lives of AIDS patients may result in more numbers of HIV infections and fail to reduce \({\mathcal R}_0\) to values less than unity as intended for disease control.

MSC:

92C60 Medical epidemiology
34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K20 Stability theory of functional-differential equations
92C50 Medical applications (general)
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