Abstract
Pre-emptive vaccination is regarded as one of the most protective measures to control influenza outbreak. There are mainly two types of influenza viruses—influenza A and B with several subtypes—that are commonly found to circulate among humans. The traditional trivalent (TIV) flu vaccine targets two strains of influenza A and one strain of influenza B. The quadrivalent (QIV) vaccine targets one extra B virus strain that ensures better protection against influenza; however, the use of QIV vaccine can be costly, hence impose an extra financial burden to society. This scenario might create a dilemma in choosing vaccine types at the individual level. This article endeavours to explain such a dilemma through the framework of a vaccination game, where individuals can opt for one of the three options: choose either of QIV or TIV vaccine or none. Our approach presumes a mean-field framework of a vaccination game in an infinite and well-mixed population, entangling the disease spreading process of influenza with the coevolution of two types of vaccination decision-making processes taking place before an epidemic season. We conduct a series of numerical simulations as an attempt to illustrate different scenarios. The framework has been validated by the so-called multi-agent simulation (MAS) approach.
Highlights
Pre-emptive vaccination is regarded as one of the most protective measures to control influenza outbreak
Individuals who commit to vaccination can benefit themselves as well as their surroundings; people who do not vaccinate, expose themselves to the risk of infection that may cause illness and more financial burden compared to the vaccination cost, or they may become free riders, benefiting from ‘herd immunity’ that can be attained from the situation when a larger portion of the population is vaccinated
Let us first briefly discuss the relative dynamics of infections due to influenza A and B viruses for different transmission rates and degree of initial infections in a single season without considering game aspect
Summary
We entangle the simultaneous spreading of two influenza viruses (A and B) and the evolution of vaccination (QIV or TIV or none) decision by constructing a repetitive sequence of a two-stage process in an infinite and well-mixed population. As influenza vaccines are not 100% perfect, we consider imperfect vaccinations in our disease modelling, where both vaccines are presumed to provide the same level of efficiency against A virus but different efficacies against B virus The inclusion of these parameters allows us to consider some individuals from vaccinated groups who fail to get immunity from vaccination (QIV or TIV) and still face the risk of infection like susceptible. Using table 1, we estimate the average social payoff π ; average payoff for QIV vaccinees ( πVQ ), TIV vaccinees ( πVT ) and non-vaccinators ( π NV ) as follows: Individuals assess their payoffs after an epidemic season and decide whether to imitate others’ strategy or stay with their previous season’s strategy. We solve equations (2.8) and (2.9) numerically, allowing the system to reach the steady state as, t → ∞
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