Optimal Control Model for Vaccination Against H1N1 Flu

Pablo Amauri Carvalho Araujo e Souza, Claudia Mazza Dias, Edilson Fernandes de Arruda


This paper introduces a mathematical model to describe the dynamics of the spread of H1N1 flu in a human population. The model is comprised of a system of ordinary differential equations that involve susceptible, exposed, infected and recovered/immune individuals. The distinguishing feature in the proposed model with respect to other models in the literature is that it takes into account the possibility of infection due to immunity loss over time. The acquired immunity comes from self-recovery or via vaccination. Furthermore, the proposed model strives to find an optimal vaccination strategy by means of an optimal control problem and Pontryagin’s Maximum Principle.


Optimal control; Mathematical modeling; Pontryagin’s maximum principle; H1N1 flu; Vaccination

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DOI: http://dx.doi.org/10.5433/1679-0375.2020v41n1p105

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