Modeling the Transmission Dynamics of Hantavirus with Environmental Viral Persistence
S. Musa *
Department of Mathematics, Sule Lamido University Kafin Hausa, Jigawa, Nigeria.
I.C. Nwokike
Department of Mathematics, Federal University of Technology, Owerri, Nigeria and Centre of Excellence in Sustainable Procurement, Environmental & Social Standards, Federal University of Technology, Owerri, Nigeria.
W.I. Osuji
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
B.N. Okechukwu
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
K. Koko
Department of Mathematics and Statistics, Air Force Institute of Technology, Kaduna, Nigeria.
B. N. Anukam
Department of Chemistry, Federal University of Technology, Owerri, Nigeria.
O. C. Ezea
Department of Biology, Federal University of Technology, Owerri, Nigeria.
N. C. Umelo-Ibemere
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
J. C. Gideon
Department of Mechanical Engineering, Air Force Institute of Technology, Kaduna, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Hantavirus is a zoonotic infection maintained principally in rodent reservoirs, and human exposure occurs mainly through environments contaminated with infectious viral particles. This study formulates and analyses a deterministic compartmental model for hantavirus transmission involving susceptible and infected rodents, susceptible, exposed, infectious and recovered humans, and an environmental viral reservoir. The model includes logistic rodent growth, direct rodent-to-rodent transmission, indirect environmental transmission, viral shedding from infected classes and natural viral clearance. Fundamental qualitative properties of the system are established, including existence, uniqueness, positivity and boundedness of solutions within a feasible region. The disease-free equilibrium is obtained, and the basic reproduction number is derived using the next-generation matrix method. Stability analysis shows that the disease-free equilibrium is locally and globally asymptotically stable when R0 < 1, whereas disease persistence is associated with R0 > 1 and the existence of a biologically feasible endemic equilibrium. Local stability conditions for the endemic equilibrium are characterised through the Jacobian matrix and the Routh-Hurwitz criterion. The analysis indicates that environmental viral persistence provides an indirect pathway that can sustain transmission between infected rodents, susceptible rodents and humans. These findings suggest that reducing rodent infection, limiting environmental contamination and increasing viral clearance may help move the system below the epidemic threshold. The model offers a mathematically tractable framework for interpreting hantavirus persistence and for guiding future extensions involving seasonality, spatial structure, stochasticity and data-driven parameterisation.
Keywords: Hantavirus, environmental viral persistence, rodent reservoirs, zoonotic disease, mathematical epidemiology, basic reproduction number, stability analysis, endemic equilibrium