HIV and HBV infections are viral infections with the same route of transmission through sexual intercourse with an infected person and mother-to-child transmission among other means of transmission. Over the decades, these mono infections have led to the deaths of millions of people around the world despite increased access to prevention, diagnosis, treatment, and care. Yet, there have been no conclusive findings in the hunt for HIV/AIDS cure or vaccine. However, the hepatitis B vaccine is available, though not easily acces sible. Consequently, HIV and HBV co-infection is equally a major global health burden that has attracted limited research interest. The interactions and synergistic relationship between these viruses are not well understood and documented. The co-infection presents complex transmission dynamics within a population. Few mathematical models of HIV and HBV co-infection are available that include risk factors and control measures. The effect of variability in predicting infection outcomes is also not captured in deterministic models. In addition, optimality conditions in co-infection models are not explored. This study sought to model HIV and HBV co-infection with optimal control interventions. This study set out to develop and examine a deterministic model of HIV-HBV co-infection, for mulate an optimal control problem for the deterministic model and determine the optimal controls and finally convert the deterministic model into a stochastic model that accounts for variability and uncertainties in infection outcomes. The deterministic model formu lation is based on SI and SIRS epidemic model framework. The theories of calculus are applied to analyze the deterministic model based on reproduction numbers. The thresh old parameter; the basic and control reproduction number is obtained using the Jacobian NGM and survival function approaches. Co-infection-free and endemic equilibrium points are determined and it’s local and global stability analysis established using Routh-Hurwitz criterion and Metzler matrix method respectively. The local sensitivity analysis of the model parameters on R0 and A0 are determined by use of forward normalized sensitivity index method. Using Pontryagin’s Maximum Principle, an optimal control problem is for mulated. The stochastic model is developed by extending the deterministic model using SDEs. The three models are implemented using MATLAB solver based on Runge-Kutta and Euler-Maruyama numerical schemes. The normalized sensitivity analysis of model parameters showed that co-infection transmission rate, β4 and recruitment rate, π con tribute the highest to R0 and A0. Numerical simulations of deterministic model revealed that the combined effect of clinical and non-clinical control interventions led to the re duction in infection rates with time. The effect of HIV and HBV viral loads on infection progression pointed out that the progression is faster at high levels of viral loads. Further, numerical results of optimal controls exhibited a gradual decrease in co-infection of HIV HBV. The sample paths of SDEs showed variations in infection outcomes due to random noise transmission. Thus, this study recommends that focus should be directed towards reducing co-infection rate and vertical transmission to mitigate the co-infection, while re inforcing policies relating to both clinical and non-clinical control interventions at optimal conditions