Abstract
Different strains of influenza viruses spread in human populations during every epidemic season. As the size of an infected population increases, the virus can mutate itself and grow in strength. The traditional epidemic SIR model does not capture virus mutations and, hence, the model is not sufficient to study epidemics where the virus mutates at the same time as it spreads. In this work, we establish a novel framework to study the epidemic process with mutations of influenza viruses, which couples the SIR model with replicator dynamics used for describing virus mutations. We formulated an optimal control problem to study the optimal strategies for medical treatment and quarantine decisions. We obtained structural results for the optimal strategies and used numerical examples to corroborate our results.
Highlights
An epidemic of infectious disease occurs when a virus population undergoes genetic mutations or new species of viruses are introduced into the host population, and host immunity to that change in the virus population is suddenly reduced below a certain threshold
Different from past works, this paper considers a coupled system framework composed of the SIR epidemic model and the evolutionary dynamic model for virus mutations
We studied an epidemic model that takes into account the evolutionary dynamics of virus mutations
Summary
An epidemic of infectious disease occurs when a virus population undergoes genetic mutations or new species of viruses are introduced into the host population, and host immunity to that change in the virus population is suddenly reduced below a certain threshold. There exist methods of prevention that reduce the sickness rate to protect populations, and medical measures (pharmacological products, quarantine policies, etc.) that reduce the number of the infected in the population Another aspect of the influenza epidemic is that different strains of influenza viruses can spread in the population during each epidemic season. We formulated the SIR model under the mechanism of a virus mutation that affects a human population and considered the minimization of treatment costs and the number of infected in both subpopulations to reduce the speed of epidemics. This complex problem is formulated as an optimal-control problem, and the virus mutation is described by replicator dynamics.
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