The Attracting Basins and the Assessment of the Transmission Coefficients for Hiv and M. Tuberculosis Infections Among Women Inmates

It has been observed that in many cases one infection can partially protect against another infection or it may lead to a co-infection. For instance, the interaction between infections with different strains, like dengue and malaria or tuberculosis and lepra, induces cross immunity. On the other hand, individuals infected with HIV are much more susceptible to other infections, for instance, tuberculosis. We propose a compartmental model to describe the transmission of AIDS and tuberculosis in a closed community as an example of one infection activating the other one. When studying the dynamics of the interactions we obtain basins of attraction where one infection prevails over the other one and where both infections coalesce. Furthermore, we are taking into account an adaptation of the model in order to assess the transmission coefficients for HIV and Mycobacterium tuberculosis infections among women inmates.