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 analyze 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. 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 transmitted through direct interaction between infected and susceptible individuals, and any demographic structure, through a suitable estimation of parameter values. Two main conclusions stand out. First, the higher the fraction of reinfected individuals, the higher the likelihood that the disease becomes quasi-endemic. Second, optimal vaccine roll-out depends on demographic structure and disease fatality, so there is no unique vaccination protocol, valid for all countries, that minimizes the effects of a specific disease. Simulations of the general model can be carried out at this interactive webpage [1].

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.

Optimal protocols of vaccine administration to minimize the effects of infectiousdiseases depend on a number of variables that admit different degrees of control.Examples include the characteristics of the disease and how it impacts on differentgroups of individuals as a function of sex, age or socioeconomic status, its transmissionmode, or the demographic structure of the affected population. Here we introduce acompartmental model of infection propagation with vaccination and reinfection andanalyse the effect that variations on the rates of these two processes have on theprogression of the disease and on the number of fatalities. The population is split intotwo groups to highlight the overall effects on disease caused by different relationshipsbetween vaccine administration and various demographic structures. As a practicalexample, we study COVID-19 dynamics in various countries using real demographicdata. The model can be easily applied to any other disease and demographic structurethrough a suitable estimation of parameter values. Two main conclusions stand out.First, the higher the fraction of reinfected individuals, the higher the likelihood that thedisease becomes quasi-endemic. Second, optimal vaccine roll-out depends ondemographic structure and disease fatality, so there is no unique vaccination protocol,valid for all countries, that minimizes the effects of a specific disease. Simulations of thegeneral model can be carried out at this interactive webpage [1].

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