Optimal individual strategies for influenza vaccines with imperfect efficacy and durability of protection

Francesco Salvarani (1, 2) , Gabriel Turinici (3, 1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Dipartimento di matematica F. Casorati
3 IUF - Institut universitaire de France

We analyze a model of agent based vaccination campaign against influenza with imperfect vaccine efficacy and durability of protection. We prove the existence of a Nash equilibrium by Kakutani's fixed point theorem in the context of non-persistent immunity. Subsequently, we propose and test a novel numerical method to find the equilibrium. Various issues of the model are then discussed, such as the dependence of the optimal policy with respect to the imperfections of the vaccine, as well as the best vaccination timing. The numerical results show that, under specific circumstances, some counter-intuitive behaviors are optimal, such as, for example, an increase of the fraction of vaccinated individuals when the efficacy of the vaccine is decreasing up to a threshold. The possibility of finding optimal strategies at the individual level can help public health decision makers in designing efficient vaccination campaigns and policies.

Mots clés: vaccination persistence; SIR model; Mean Field Games; vaccination efficacy; individual vaccination; vaccination games; vaccination; Nash equilibrium.

Domaines: Analyse numérique [math.NA]

Francesco Salvarani, Gabriel Turinici. Optimal individual strategies for influenza vaccines with imperfect efficacy and durability of protection. Mathematical Biosciences and Engineering, 2018, 15 (3), ⟨10.3934/mbe.2018028⟩. ⟨hal-01302557v3⟩