Impact of human behavior on the perpetuation of thelife cycle: A mathematical approach.

Abstract

This study presents, as a proof-of-concept, a mathematical model describing the transmission dynamics of cystic echinococcosis. This neglected zoonosis is caused by the larval stage of Echinococcus granulosus s.l. involving dogs and sheep as definitive hosts and sheep as intermediate hosts. The model incorporates the dual role of humans as final hosts and as active participants in the parasite's transmission cycle through practices such as feeding dogs with infected viscera. A system of nine ordinary differential equations represents human subpopulations (children and adults) and the concentration of viable parasite eggs. The basic reproductive number ($ R_0 $) was computed via the next-generation matrix approach, and bifurcation analysis indicated a forward bifurcation at $ R_{0} = 1, $ confirming that $ R_{0} < 1 $ ensures disease control. Global sensitivity analysis using Sobol indices identified the infestation rate ($ \beta $) and adult transmission rate ($ \beta_{AG} $) as the most influential parameters, explaining 35.9% and 29.9% of $ R_0 $ variance, respectively. These findings highlight that interventions reducing $ \beta $ and $ \beta_{AG} $ may effectively decrease human infection rates.