A mathematical model of HIV/AIDS Spread in human population, the triangle transmission case.

There exist individuals that change their sexual behavior depending on the situation or at different stages in their life. A possibly common and transient example of situational sexuality is the person who self-identifies as heterosexual, but will sexually interact with a member of the same sex when lacking other opportunities. Less transient but also possibly common, a person who self-identifies as gay or lesbian (either at the time, or later) may sexually interact with a member of the opposite sex if a same-sex relationship seems unfeasible, Thompson 2008, [1]. HIV/AIDS transmission usually considers sexual contact in heterosexual and homosexual population separately, besides in sexual transmission the same format for men and women is assumed. Thus, Can the population be split in heterosexuals and homosexual and thus the group of bisexuals be ignored? Can the sexual transmission form be equal for men and women? What is the contribution of a bisexual group in the HIV transmission? and, How to consider sexual transmission in men and women according to sexual behavior? To try to answer these questions we proposed an original mathematical model considering bisexuals in the HIV transmission. Mathematical analysis undertaken and stationary points, stability analysis of disease free equilibrium and boundary equilibrium, the basic reproductive number is obtained and discussed through the next generation method; numerical simulations show that these casual contacts between bisexuals has less influence than homosexual case.