An Human Immunodeficiency Virus/Acquired Immuno-Deficiency Syndrome (HIV/AIDS) epidemic model for sexual transmission with asymptomatic and symptomatic phase is proposed as a system of differential equations. The threshold and steady state for the model are determined and stabilities of disease free steady state is investigated. We use the model and study the effect of public health education on the spread of HIV/AIDS as a single-strategy in HIV prevention. The education, including basic reproduction number R E for the model with public health education, is compared with the basic reproduction number R 0 for the HIV/AIDS in the absence of public health education. By comparing these two values, influence of public health education appears. According to property of R E , threshold proportion of educated adolescents, education rate for susceptible individuals and education efficacy is obtained.

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In this paper, we develop the operational approach to the Tau method to solve delay integro-differential equations (DIDEs). The differential and integral parts appearing in the equations are replaced by their operational Tau matrix representations. Some numerical results are given to demonstrate the superior performance of the method.

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Due to the prevalence of Human Immuno-deficiency Virus/Acquired Immuno-Deficiency Syndrome (HIV/AIDS) infection in society and the importance of preventing the spread of this disease, a mathematical model for sexual transmission of HIV/AIDS epidemic with asymptomatic and symptomatic phase and public health education is stated as a symmetric system of differential equations in order to reduce the spread of this infectious disease. It is demonstrated that public health education has a considerable effect on the prevalence of the disease. Moreover, the cost of education is very high and for this reason, a cost-optimal control is applied to provide the best possible combination of the parameters corresponding to education in controlling the spread of the disease by means of the Genetic Algorithm (GA) and Simulated Annealing (SA).