Game dynamic model of optimal budget allocation under individual vaccination choice.

Communicable diseases are leading cause of child mortality in developing and under-developed countries. Public health ministries in states and country allocate a considerable amount of budget every year for vaccination campaigns to control infections. Even third-party agencies such as Gates Foundation, UNDP, GAVI, World Bank, WHO also allocate huge funds to under-developed and developing countries for vaccination programs and disease eliminations. However, economic constraints and current disease prevalence are not enough driving factors for optimal decisions in budget allocations for vaccinations and controlling the disease. In a population under voluntary vaccination campaign, high vaccine coverage cannot be taken for granted, as individuals' free-riding behaviour plays a significant role in achieving the herd immunity level coverage. Individual-level vaccine exemptions and ignoring this important component by the policymakers are key determinants for failure of disease elimination program these days in many under-developed and developing countries. We integrate evolutionary game theory and compartmental model of disease transmission to analyze how individual vaccination choice influence the budget allocations and vice-versa. Our model illustrates that individuals' perceived risk plays an important role in optimal budget allocations to minimize infections. Analyses of our model indicate that the optimal distribution of third-party funds may be very different than usual, especially in multiple populations with contrasting demographic and economic profiles. These findings are certainly useful to public health policymakers and may help to quantify certain parameters in budget allocations to control vaccine-preventable diseases.