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 the interactive webpage https://mybinder.org/v2/gh/IkerAtienza/SIYRD/main?urlpath=\%2Fvoila\%2Frender\%2FSimulator.ipynb

The authors are indebted to A. Vespignani for support with the use of their data. Grants PID2020-113284GB-C21 (I.A., S.M.) and BADS (PID2019-109320GB-100, S.A.) funded by MCIN/AEI/10.13039/501100011033. The Spanish MICINN has also funded the “Severo Ochoa” Centers of Excellence to CNB, SEV 2017-0712, and the special grant PIE 2020-20E079 (CNB) entitled “Development of protection strategies against SARS-CoV-2”.

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