Exploring optimal control strategies in seasonally varying flu-like epidemics

Abstract

The impact of optimal control strategies in the context of seasonally varying infectious disease transmission remains a wide open research area. We investigate optimal control strategies for flu-like epidemics using an SIR (susceptible-infectious-recovered) type epidemic model where the transmission rate varies seasonally Specifically, we explore optimal control strategies using time-dependent treatment and vaccination as control functions alone or in combination. Optimal strategies and associated epidemic outcomes are contrasted for epidemics with constant and seasonal transmission rates. Our results show that the epidemic outcomes assessed in terms of the timing and size of seasonal epidemics subject to optimal control strategies are highly sensitive to various parameters including R₀, the timing of the introduction of the initial number of infectious individuals into the population, the time at which interventions start, and the strength of the seasonal forcing that modulates the time-dependent transmission rate. Findings highlight the difficult challenge in predicting short-term epidemic impact in the context of seasonally varying infectious disease transmission with some interventions scenarios exhibiting larger epidemic size compared to scenarios without control interventions.

Keywords: Influenza transmission dynamics; Optimal control theory; Seasonally varying transmission rate; Vaccination and treatment strategies.