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 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].
The vertebrate immune system is capable of strong, focused adaptive responses that depend on T-cell specificity in recognizing antigenic sequences of a pathogen. Recognition tolerance and antigenic convergence cause cross-immune reactions that extend prompt, specific responses to rather similar pathogens. This suggests that reaching herd-immunity might be facilitated during successive epidemic outbreaks (e.g., SARS-CoV-2 waves with different variants). Qualitative studies play down this possibility because cross-immune protection is seldom sterilizing. We use minimal quantitative models to study how cross-immunity affects epidemic dynamics over short and long timescales. In the short scale, we investigate models of sterilizing and attenuating immunity, finding equivalences between both mechanisms—thus suggesting a key role of attenuating protection in achieving herd immunity. Our models render maps in epidemic-parameter space that discern threatening variants depending on acquired cross-immunity levels. We illustrate this application with SARS-CoV-2 data, including protection due to vaccination rates across countries. In the long-time scale, we model sterilizing cross-immunity between rolling pathogens to characterize statistical properties of successful strains. We find that sustained cross-immune protection alters the regions of epidemic-parameter space where large outbreaks happen. Our results suggest an optimistic revision concerning prospects for herd protection based on cross-immunity, including for the SARS-CoV-2 pandemics.
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