Effects of Fogging and Mosquito Repellent on the Probability of Disease Extinction for Dengue Fever

Abstract

A Continuous-Time Markov Chain model is constructed based on the a deterministic model of dengue fever transmission including mosquito fogging and the use of repellent. The basic reproduction number (R0) for the corresponding deterministic model is obtained. This number indicates the possible occurrence of an endemic at the early stages of the infection period. A multitype branching process is used to approximate the Markov chain. The construction of offspring probability generating functions related to the infected states is used to calculate the probability of disease extinction and the probability of an outbreak (P0). Sensitivity analysis is shown for variation of control parameters and for indices of the basic reproduction number. These results allow for a better understanding of the relation of the basic reproduction number with other indicators of disease transmission.