Vaccination Strategy and Optimal Control for Seasonal and H1N1 Influenza Outbreak

During the spring of 2009, a novel H1N1 influenza virus posed a serious threat worldwide. However, seasonal influenza is still a public health concern since each year in the United States it kills 36,000 people, causes more than 200,000 hospitalizations, and infects up to 20% of the population. In this paper, we explore what could happen if both a seasonal influenza and H1N1 outbreak were to coincide. First, a simple SAIR model is considered to study the dynamics of a single influenza strain. Then, a more complex two-strain model is constructed to examine the dynamics of two coexisting strains. In the two-strain model, we incorporate a seasonal flu vaccine to study the impact of vaccination on these dynamics. Optimal control theory is applied to both the single-strain model and the two-strain model with the goal of reducing the overall morbidity during an outbreak. Two controls are introduced to the systems: social distancing and treatment of H1N1 infected individuals. Introducing the seasonal vaccine significantly reduces the number of seasonal influenza cases, yet moderately increases the number of H1N1 infections. In the two-strain model, the application of optimal controls has a substantial impact on the H1N1 and seasonal influenza dynamics.