Effectivity of the vaccination strategy for a fractional-order discrete-time SIC epidemic model

Abstract

Indirect disease transmission is modeled via a fractional-order discretetime Susceptible-Infected-Contaminant (SIC) model vaccination as a control strategy. Two control actions are considered, giving rise to two different models: the vaccine efficacy model and the vaccination impact model. In the first model, the effectiveness of the vaccine is analyzed by introducing a new parameter, while in the second model, the impact of the vaccine is studied incorporating a new variable into the model. Both models are studied giving population thresholds to ensure the eradication of the disease. In addition, a sensitivity analysis of the Basic Reproduction Number has been carried out with respect to the effectiveness of the vaccine, the fractional order, the vaccinated population rate and the exposure rate. This analysis has been undertaken to study its effect on the dynamics of the models. Finally, the obtained results are illustrated and discussed with a simulation example related to the evolution of the disease in a pig farm.

Keywords

• epidemic process
• discrete fractional-order
• indirect transmission
• vaccination
• sensitivity analysis