Prevention of treatable infectious diseases: A game-theoretic approach

Abstract

We model outcomes of voluntary prevention using an imperfect vaccine, which confers protection only to a fraction of vaccinees for a limited duration. Our mathematical model combines a single-player game for the individual-level decision to get vaccinated, and a compartmental model for the epidemic dynamics. Mathematical analysis yields a characterization for the effective vaccination coverage, as a function of the relative cost of prevention versus treatment; note that cost may involve monetary as well as non-monetary aspects. Three behaviors are possible. First, the relative cost may be too high, so individuals do not get vaccinated. Second, the relative cost may be moderate, such that some individuals get vaccinated and voluntary vaccination alleviates the epidemic. In this case, the vaccination coverage grows steadily with decreasing relative cost of vaccination versus treatment. Unlike previous studies, we find a third case where relative cost is sufficiently low so epidemics may be averted through the use of prevention, even for an imperfect vaccine. However, we also found that disease elimination is only temporary-as no equilibrium exists for the individual strategy in this third case-and, with increasing perceived cost of vaccination versus treatment, the situation may be reversed toward the epidemic edge, where the effective reproductive number is 1. Thus, maintaining relative cost sufficiently low will be the main challenge to maintain disease elimination. Furthermore, our model offers insight on vaccine parameters, which are otherwise difficult to estimate. We apply our findings to the epidemiology of measles.

Can HIV epidemics among MSM be eliminated through participation in preexposure prophylaxis rollouts?

“…The situation is similar to that of vaccination prevention, which requires continuous vaccine coverage even though the disease is declared to be eliminated [47].…”

“…Otherwise, HIV can reemerge and reach again an endemic state of concern for public health. The situation is similar to that of vaccination prevention, which requires continuous vaccine coverage even though the disease is declared to be eliminated [47].…”

Impact of voluntary testing on infectious disease epidemiology: A game theoretic approach

“…Otherwise, diseases can reemerge and reach again an endemic state of concern for public health. The situation is similar to that of vaccination prevention, which requires continuous vaccine coverage even though the disease is declared to be eliminated [ 61 ]. In conclusion, perception of testing payoff and risk of infection are two key levers to increase the impact of test-and-treat strategies up to epidemic elimination and maintaining elimination in the context of less epidemic adversity.…”

Open-minded imitation can achieve near-optimal vaccination coverage

“…Other aspects that might be incorporated into more detailed versions of our model are restrictions of disease transmission and/or imitation to edges of contact networks, as has already been studied for the case of classical Fermi functions in [16] and a number of related papers; see [39] for a review. Similarly, one can study the effects of a mixture of rational decision-making and imitation [12,31], incentives [27,44,45], misperceptions of costs [4,9,10,32,38], altruism [34,36,46], peer pressure [23,42], presence of individuals who remain committed to vaccinating or not vaccinating without ever imitating others [19,28], the effects of other available control measures or treatment options [1,8,24,26,27,41], or variability of R 0 from season to season. One can also study the effects of our parameter α when imitation is based on comparison with the average cost of a larger sample of other individuals [18,23,25,27], or when weighted averages of costs over a number of previous seasons are being compared [43].…”

“…where the last line follows from (26). If V * < S(α, β) −1 and 0 < x(R V * 0 ) < 1, then by (32) and Proposition 6 we will have…”