Optimal vaccination strategies in the control of an infectious disease: a SEIRV model for administration of two vaccines

Abstract

In this paper, we study the optimal control for an SEIR model adapted to the vaccination strategy of susceptible individuals. There are factors associated with a vaccination campaign that make this strategy not only a public health issue but also an economic one. In this case, optimal control is important as it minimizes implementation costs. We consider the availability of two vaccines with different efficacy levels, and the control indicates when each vaccine should be used. The optimal strategy specifies in all cases how vaccine purchases should be distributed. For similar efficacy values, we perform a sensitivity analysis on parameters that depend on the intrinsic characteristics of the vaccines. Additionally, we investigate the behavior of the number of infections under the optimal vaccination strategy.

Figures (18)

• Figure 1: Compartment diagram of the model.
• Figure 2: The optimal controls for use of vaccines with effectiveness of $91\%$ and $51\%$ for different vaccination campaigns lengths.
• Figure 3: The optimal controls for use of vaccines with effectiveness of $74\%$ and $51\%$ for different vaccination campaigns lengths.
• Figure 4: The optimal controls for use of vaccines with effectiveness of $67\%$ and $51\%$ for different vaccination campaigns lengths.
• Figure 5: Behavior of rate transmission for vaccinated people.