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Math Biosci Eng. 2013 Oct-Dec;10(5-6):1615-34. doi: 10.3934/mbe.2013.10.1615.

Optimal strategies of social distancing and vaccination against seasonal influenza.

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Department of Mathematics, University of Tulsa, Tulsa, OK 74104, United States.


Optimal control strategies for controlling seasonal influenza transmission in the US are of high interest, because of the significant epidemiological and economic burden of influenza. To evaluate optimal strategies of vaccination and social distancing, we used an age-structured dynamic model of seasonal influenza. We applied optimal control theory to identify the best way of reducing morbidity and mortality at a minimal cost. In combination with the Pontryagins maximum principle, we calculated time-dependent optimal policies of vaccination and social distancing to minimize the epidemiological and economic burden associated with seasonal influenza. We computed optimal age-specific intervention strategies and analyze them under various costs of interventions and disease transmissibility. Our results show that combined strategies have a stronger impact on the reduction of the final epidemic size. Our results also suggest that the optimal vaccination can be achieved by allocating most vaccines to preschool-age children (age under five) followed by young adults (age 20-39) and school age children (age 6-19). We find that the optimal vaccination rates for all age groups are highest at the beginning of the outbreak, requiring intense effort at the early phase of an epidemic. On the other hand, optimal social distancing of clinical cases tends to last the entire duration of an outbreak, and its intensity is relatively equal for all age groups. Furthermore, with higher transmissibility of the influenza virus (i.e. higher R0), the optimal control strategy needs to include more efforts to increase vaccination rates rather than efforts to encourage social distancing. Taken together, public health agencies need to consider both the transmissibility of the virus and ways to encourage early vaccination as well as voluntary social distancing of symptomatic cases in order to determine optimal intervention strategies against seasonal influenza.

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