Mathematical modeling of leptospirosis: a dynamic regulated by environmental carrying capacity

Abstract

Leptospirosis is a public health problem whose main vectors are rodents. The main objective of this work is to study the dynamics of this zoonosis considering the interactions between rodents and humans. We assume that the rodent population presents a logistic growth unlike previous papers that consider exponential growth. We present a SI-SIR model for the dynamics of leptospirosis, also analyze the stability of its equilibriums and obtain an equation for the basic reproduction number,. In this case, it depends on rodents infection rate, birth rate and environmental carrying capacity, . We estimate a threshold for K which determines the extinction or persistence of the disease. Furthermore, we analyze the sensitivity of and we propose a way of quantifying the effect of different control measures on infection dynamics. Finally, we show numerical simulations in order to visualize our theoretical results.