Optimal distribution strategy of a prevention tool in a heterogeneous population

Response to infectious disease epidemics requires an optimal distribution strategy for tools of primary prevention (vaccines or prophylaxis for instance) with the aim of protecting those susceptible from acquiring the infection. We propose various distribution scenarios based on different epidemic phases and the goal one wants to reach: outbreak prevention (before the disease actually becomes an epidemic), containment (when the outbreak already occurred but stochastic fluctuations may still lead to the extinction of the disease), mitigation (once the endemic state is well established, one needs to adapt the strategy in order to eliminate the disease). Through the introduction of both a mean field and a stochastic view of an epidemiological model of a disease spread coupled with a prevention strategy, this research provides some insights into an adaptive approach. By analyzing various epidemiological indicators, it was possible to devise a strategy that takes into account the specific phase of the epidemic. The results indicate that a risk-based strategy, which prioritizes individuals with a higher number of contacts, does not always yield optimal results.