The HIV/AIDS epidemic and the COVID-19 pandemic have ruined many people's lives. Antiretroviral therapy (ART) has controlled the HIV/AIDS epidemic and COVID-19 vaccine is expected to ease confusion caused by the pandemic. However, the supply of health-resource falls far short of the demand in resource-constrained countries; thus, decision-making about resource allocation should be discussed. Botswana, as a resource-constrained country with a high prevalence of HIV, needs to construct its own framework for ART allocation. We propose an equitable framework for ART and COVID-19 vaccine allocation in Botswana based upon the egalitarian principle, which provides each individual has an equal chance of receiving them. We use a spatial mathematical model of treatment accessibility with an equity objective function, and sequential quadratic programming is used to address the nonlinear programming model. Considering Botswana's current health infrastructure, our strategy brings the most equal health outcomes. However, the disparity of accessibility still exists between rural and urban areas even from our equitable strategy. We present proposals that can increase the accessibility of rural areas using sensitivity analysis. Our work can be applied to different contexts, especially in sub-Saharan Africa.