Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 12, Number 6 (2016), pp. 4959-4989 © Research India Publications http://www.ripublication.com/gjpam.htm Optimal Control Analysis of Cryptosporidiosis Disease S.T. Ogunlade African Institute for Mathematical Sciences, Senegal K.O. Okosun 1 , R.S. Lebelo, and M. Mukamuri Vaal University of Technology, Vanderbijlpark, South Africa. Abstract In Sub-Saharan Africa, HIV/AIDS and chronic parasitic diseases (such as try- panosomiasis, schistosomiasis, malaria, etc) have profound effect on the immune system and alter the host’s immune response to infections, thereby paving way for opportunistic parasitic infections (such as cryptosporidiosis, isosporiasis, mi- crosporidiosis, etc) to attack. Hence, mathematical models provide a quantitative and potentially valuable tool for this purpose. This paper therefore is to derive and analyze a deterministic model for the transmission of cryptosporidiosis dis- ease. The basic reproduction number, and the existence and stability of equilibria were investigated. Firstly, we analyzed the model and investigated its stability and bifurcation behaviour. In our findings, model exhibited a backward bifurcation phenomenon. This has epidemiological implication, which means that for effective eradication and control of the disease, bringing R0 less than unity was no longer sufficient, but rather, that R 0 <R 0c . Furthermore, we modified the model to incor- porate susceptible individuals with weakened immune system. We then analyzed the model and investigated its stability property, in order to determine the effect and impact of individuals with weakened immune systems in the disease transmission. From the sensitivity analysis, it was found that increase in the number of suscepti- ble individuals with weak immune system increases the basic reproduction number. AMS subject classification: Keywords: 1 Corresponding Author - E-mail: kazeemoare@gmail.com