Modeling the transmission dynamics of yellow fever with optimal control

In this presentation, a model for yellow fever transmission dynamics in a human-mosquito setting is constructed and analyzed. The model incorporates vertical transmission within mosquito population. Threshold quantities (such as the basic offspring and the type reproduction numbers) and their interpretations for the models are presented. Analysis of the mosquito-only component shows that the reduced model has a mosquito-extinction equilibrium, which is globally-asymptotically stable whenever the basic offspring number is less than unity. Optimal control theory is applied to the model to characterize the controls parameters. Using Pontryagin's maximum principle and modified forward-backward sweep technique, the necessary conditions for existence of solutions to the optimal control problem is determined. The effect of various control strategies (bed nets, adulticides and vaccination) were assess via numerical simulations.