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Article

Modeling Foot-and-Mouth Disease Dynamics Among Livestock and Wild Ruminants: Integrating Community Viral Load and Environmental Transmission Pathways

by
Mukhethwa Chantel Kaletsane
1,
Azwindini Delinah Maphiri
1,* and
Rendani Netshikweta
2
1
Modelling Health and Environmental Linkages Research Group (MHELRG), Department of Mathematical and Computational Sciences, University of Venda, Private Bags X5050, Thohoyandou 0950, South Africa
2
Modelling Health and Environmental Linkages Research Group (MHELRG), Department of Mathematics and Applied Mathematics, University of Limpopo, Private Bag X1106, Sovenga, Mankweng 0727, South Africa
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(11), 1812; https://doi.org/10.3390/math14111812 (registering DOI)
Submission received: 4 February 2026 / Revised: 23 March 2026 / Accepted: 7 April 2026 / Published: 23 May 2026
(This article belongs to the Section E3: Mathematical Biology)

Abstract

Foot-and-mouth disease (FMD) is a highly transmissible viral infection of livestock that threatens food security and causes substantial economic losses in endemic regions. Despite its economic impact, the role of environmental viral load and wildlife reservoirs in sustaining FMD transmission remains poorly quantified. The aim of this study is to assess the extent to which community viral load sustains FMD persistence and to identify key transmission drivers in a coupled livestock–wildlife–environment system. A Susceptible–Exposed–Infected (SEI) model with a free-living virus compartment was analyzed via the basic reproduction number (R0) and solved numerically using a Nonstandard Finite Difference Method. Sensitivity analysis identified wild host population size, transmission rates, host recruitment, environmental viral decay, and viral load thresholds as major determinants of R0. Results indicate that higher transmission rates accelerate susceptible depletion and increase exposed and infected classes, with wildlife dominating environmental viral contributions. Community viral load is central to sustaining outbreaks and informs targeted control strategies.
Keywords: foot-and-mouth disease (FMD); mathematical modeling; wild animals; livestock; community viral load; Nonstandard Finite Difference method foot-and-mouth disease (FMD); mathematical modeling; wild animals; livestock; community viral load; Nonstandard Finite Difference method

Share and Cite

MDPI and ACS Style

Kaletsane, M.C.; Maphiri, A.D.; Netshikweta, R. Modeling Foot-and-Mouth Disease Dynamics Among Livestock and Wild Ruminants: Integrating Community Viral Load and Environmental Transmission Pathways. Mathematics 2026, 14, 1812. https://doi.org/10.3390/math14111812

AMA Style

Kaletsane MC, Maphiri AD, Netshikweta R. Modeling Foot-and-Mouth Disease Dynamics Among Livestock and Wild Ruminants: Integrating Community Viral Load and Environmental Transmission Pathways. Mathematics. 2026; 14(11):1812. https://doi.org/10.3390/math14111812

Chicago/Turabian Style

Kaletsane, Mukhethwa Chantel, Azwindini Delinah Maphiri, and Rendani Netshikweta. 2026. "Modeling Foot-and-Mouth Disease Dynamics Among Livestock and Wild Ruminants: Integrating Community Viral Load and Environmental Transmission Pathways" Mathematics 14, no. 11: 1812. https://doi.org/10.3390/math14111812

APA Style

Kaletsane, M. C., Maphiri, A. D., & Netshikweta, R. (2026). Modeling Foot-and-Mouth Disease Dynamics Among Livestock and Wild Ruminants: Integrating Community Viral Load and Environmental Transmission Pathways. Mathematics, 14(11), 1812. https://doi.org/10.3390/math14111812

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