Game dynamic model of social distancing while cost of infection varies with epidemic burden

'Social distancing' during an infectious disease outbreak can play a major role in controlling the spread of the disease. Individuals' interests in isolating themselves however, are constrained by the inherent costs in it. Rational decision making requires comparing the cost of social distancing with the cost of being infected such as availability of the vaccines, drugs, and treatment facilities that may depend on the current epidemic burden in the community. To understanding these, we develop a differential population game model of social distancing integrating with a simple SIR model describing the disease process. Using several type of cost functions of infections, we compute the Nash equilibrium strategies under variable efficiencies of social distancing. We also derive the closed form of the analytical solution of the utility functions under a special case. Depending on the efficiency of social distancing and the functional dependence of the cost of infections, we have shown that individuals behave very rationally to isolate themselves. This information may be useful in designing the public health policies during an epidemic outbreak.