Numerical simulation of a deterministic model of HIV transmission between major cities in Kenya is carried out. The model considered two closed patches connected by the commuter movements of truck drivers being the agents of HIV transmission. The transmission kernel being the function of distance between the patches is ignored. The numerical algorithms are applied in the solution of a nonlinear firstorder differential equations. The algorithms are implemented with the aid of MATLAB solver which has an in- built mechanism of Runge Kutta method of fourth order. Numerical simulation indicated the population dynamics of the patches, effect of migration on female sex workers and model reproduction number. The findings of the study were that the migration of the truck drivers between two closed patches contributed significantly to the spread of HIV. In this regard, it was recommended that, stakeholders should target the truck driving population and towns along the transport corridors to mitigate the growing HIV infections and integrate the truck drivers in the national health strategy.