Modeling of vector‐borne disease with media impact on switching surface

Abstract

Human behavior has always been played a crucial role in spread of emerging infectious diseases. To make changes in human behavior toward epidemic is very important step for controlling the infectious diseases. In this regard, many efforts have been done so far by media to aware the human population during disease outbreak. To understand the impact of media on vector‐borne diseases, a vector‐host model has been proposed. The model incorporates the effect of media in transmission rate, which is depending on the case number and its rate of change. This transforms the model into two switching subsystems with the switching surface, which is the function of susceptible human and infected mosquito population. The qualitative analysis of the two subsystems has been performed. The basic reproduction number has been computed. The cross validation (CV) has been performed to evaluate the model performance for the weekly Zika cases of Costa Rica and Nicaragua, USA. By using k‐fold CV technique, the root‐mean‐square error (RMSE) has been computed to find the prediction accuracy of the model. Again, partial rank correlation coefficients (PRCCs) of the parameters associated with switching surface (Sq) have been computed that reveal the parameters associated with change in case numbers have more impact on Sq than the case numbers only. Also, the parameters associated with mosquitoes dynamics are drawing more effect on Sq than the parameters associated with human dynamics. Further, by numerical simulation, it is found that consideration of change in case numbers in transmission rate is more significant as it reduces the epidemic peak at the beginning of disease outbreak. However, the weights associated with mosquito dynamics is more important to consider as in absence of them, the infection level gets increased.