Impact of human behavior on the perpetuation of the <i>Echinococcus granulosus</i> life cycle: A mathematical approach

Richard Lagos; Andrei González-Galeano; Jaleydi Cárdenas-Poblador; Álvaro Mella-Parra; María Esther Leyva-Borges; Richard Lagos; Andrei González-Galeano; Jaleydi Cárdenas-Poblador; Álvaro Mella-Parra; María Esther Leyva-Borges

doi:10.3934/mbe.2026030

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 3: 776-798. doi: 10.3934/mbe.2026030

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Impact of human behavior on the perpetuation of the Echinococcus granulosus life cycle: A mathematical approach

1.
Departamento de Matemática y Física, Facultad de Ciencias, Universidad de Magallanes, Punta Arenas P.O. Box 113-D, Chile
2.
Centro de Ciencias Matemáticas, UNAM, Morelia, México
3.
Departamento de Matemáticas, Universidad El Bosque, Bogotá, Colombia
4.
Dynamical Systems Research Group, Departamento de Matemáticas y Física, Facultad de Ciencias Básicas e Ingeniería, Universidad de los Llanos, Villavicencio, Colombia
5.
Centro de Investigación en Matemáticas A.C., Guanajuato, México

Received: 25 November 2025 Revised: 22 January 2026 Accepted: 30 January 2026 Published: 06 February 2026

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.
- compartmental model,
- hydatidosis,
- neglected tropical disease,
- Sobol indices,
- zoonosis
Citation: Richard Lagos, Andrei González-Galeano, Jaleydi Cárdenas-Poblador, Álvaro Mella-Parra, María Esther Leyva-Borges. Impact of human behavior on the perpetuation of the Echinococcus granulosus life cycle: A mathematical approach[J]. Mathematical Biosciences and Engineering, 2026, 23(3): 776-798. doi: 10.3934/mbe.2026030

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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.

References

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