Abstract
Many infectious diseases have seasonal outbreaks, which may be driven by cyclical environmental conditions (e.g., an annual rainy season) or human behavior (e.g., school calendars or seasonal migration). If a pathogen is only transmissible for a limited period of time each year, then seasonal outbreaks could infect fewer individuals than expected given the pathogen's in-season transmissibility. Influenza, with its short serial interval and long season, probably spreads throughout a population until a substantial fraction of susceptible individuals are infected. Dengue, with a long serial interval and shorter season, may be constrained by its short transmission season rather than the depletion of susceptibles. Using mathematical modeling, we show that mass vaccination is most efficient, in terms of infections prevented per vaccine administered, at high levels of coverage for pathogens that have relatively long epidemic seasons, like influenza, and at low levels of coverage for pathogens with short epidemic seasons, like dengue. Therefore, the length of a pathogen's epidemic season may need to be considered when evaluating the costs and benefits of vaccination programs.
Highlights
Mathematical models can be used to help understand the dynamics of infectious disease outbreaks [19, 21, 2]
We show that when epidemics are not interrupted by seasonality, the attack rate is a concave function of the vaccination coverage up to the critical vaccination fraction, i.e., the attack rate of the epidemic drops more and more rapidly with increasing coverage until the critical vaccination fraction is reached (Figure 1c)
Theorem 3.1—Assuming that the vaccine is fully protective, the final size of the noninterrupted epidemic simulated with the model described in Equations 1–4 is a decreasing concave function of the vaccination coverage up to the critical vaccination threshold and becomes zero afterwards
Summary
Mathematical models can be used to help understand the dynamics of infectious disease outbreaks [19, 21, 2]. With an estimate of the transmissibility of a pathogen, often summarized as R0, one can use models to gain insight into the relationship between the transmissibility of a disease, the fraction of a population it can infect, and the fraction of a population that needs to be vaccinated to prevent outbreaks [8, 2, 17, 31]. These relationships are less straightforward when a pathogen’s transmissibility is not constant over time. We hypothesize that the most efficient coverage level, defined as the number of infections averted per vaccination, can be affected by seasonal forcing
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