Transmission Neural Networks (TransNNs) introduced by Gao and Caines (2022) connect virus spread models over networks and neural networks with tuneable activation functions. This paper presents the approximation technique and the underlying assumptions employed by TransNNs in relation to the corresponding Markovian Susceptible-Infected-Susceptible (SIS) model with 2^n states, where n is the number of nodes in the network. The underlying infection paths are assumed to be stochastic with heterogeneous and time-varying transmission probabilities. We obtain the conditional probability of infection in the stochastic 2^n-state SIS epidemic model corresponding to each state configuration under mild assumptions, which enables control solutions based on Markov decision processes (MDP). Finally, MDP control with 2^n-state SIS epidemic models and optimal control with TransNNs are compared in terms of mitigating virus spread over networks through vaccination, and it is shown that TranNNs enable the generation of control laws with significant computational savings, albeit with more conservative control actions.