## Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Mathematical Modelling of HIV/AIDS in a sex-structured population: Effect of Case Detection and Treatment}
Mini Ghosh

It is observed that in a developing country like India, female population is hesitant to approach medical practitioner even if they are sick. Most of the time they approach doctors only when it becomes intolerable.  So the rate of screening and the rate of treatment vary from male to female. Keeping this fact in view, a nonlinear two-sex model for HIV/AIDS is proposed and analyzed by incorporating case detection and treatment. The model is formulated by considering transmission of disease by heterosexual contact only.  The epidemic threshold and equilibria for the model are determined, local stability and global stability of both disease-free equilibrium(DFE) and endemic equilibrium(EE) are discussed. The disease-free equilibrium is shown to be locally and globally stable when the basic reproductive number $\mathcal{R}_0$ is less than unity. We also proved that the endemic equilibrium is locally and globally asymptotically stable under some restriction on parameters. Numerical simulation are performed to support the analytical findings. It is found that the total HIV infectives at equilibrium level can be lowered by increasing the rate of screening and treatment for women.