Vaccination strategies in structured populations under partial immunity and reinfection

Optimal protocols of vaccine administration to minimize the effects of infectious diseases depend on a number of variables that admit different degrees of control. Examples include the characteristics of the disease and how it impacts on different groups of individuals as a function of sex, age or socioeconomic status, its transmission mode, or the demographic structure of the affected population. Here we introduce a compartmental model of infection propagation with vaccination and reinfection and analyse the effect that variations on the rates of these two processes have on the progression of the disease and on the number of fatalities. The population is split into two groups to highlight the overall effects on disease caused by different relationships between vaccine administration and various demographic structures. We show that optimal administration protocols depend on the vaccination rate, a variable severely conditioned by vaccine supply and acceptance. As a practical example, we study COVID-19 dynamics in various countries using real demographic data. The model can be easily applied to any other disease and demographic structure through a suitable estimation of parameter values. Simulations of the general model can be carried out at this interactive webpage [1]. Author summaryVaccination campaigns can have varying degrees of success in minimizing the effects of an infectious disease. It is often very difficult to assess a priori the importance and effect of different relevant factors. To gain insight into this problem, we present a model of infection propagation with vaccination and use it to study the effects of vaccination rate and population structure. We find that when the disease affects in different ways distinct population groups, the best vaccination strategy depends non-trivially on the rate at which vaccines can be administered. The application of our analysis to COVID-19 reveals that, in countries with aged populations, the best strategy is always to vaccinate first the elderly, while for youthful populations maximizing vaccination rate regardless of other considerations may save more lives.