Stability Analysis of a Rodent-Human Hantavirus Model with Immune Response
I. C. Nwokike *
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
G. O. Nwafor
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
N. C. Umelo-Ibemere
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
I. D. Ajana
Griggs Specialist Hospital, Lekki, Lagos, Nigeria.
O. C. Ezea
Department of Biology, Federal University of Technology, Owerri, Nigeria.
B. N. Anukam
Department of Chemistry, Federal University of Technology, Owerri, Nigeria.
I. C. Obinwanne
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
C. Nwutara
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
T. W. Owolabi
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
B. N. Okechukwu
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this study, a deterministic mathematical model for the transmission dynamics of hantavirus incorporating immune response dynamics is formulated and analyzed. The model consists of susceptible and infected rodent populations together with susceptible, exposed, infectious, and recovered human compartments. An immune response compartment is introduced to describe immune activation and immune-mediated clearance of infection in humans. The proposed framework captures rodent-mediated transmission, disease progression, recovery, disease-induced mortality, and host immune interactions. The positivity and boundedness of solutions is proved, which yields that the system is biologically and mathematically well-posed in a feasible invariant region. The existence of the disease-free equilibrium is proved and the basic reproduction number is determined by the next-generation matrix method. We prove that the disease-free equilibrium is locally and globally asymptotically stable if R0 < 1, while a unique endemic equilibrium point exists if R0 > 1. It is found that the rodent ecology plays a primary role in hantavirus persistence, while the role of immune response is important for infection clearance and recovery in infected rodents. In particular, for strong immune stimulation and immune clearance rates, the infection burden is reduced, leading to disease suppression, while weak immune action can cause persistent infection and prolonged epidemic outbreaks. This work emphasizes the epidemiological role of incorporating the immune response in hantavirus transmission models, and gives insight into the integrated intervention strategies involving rodent population management, exposure reduction and immune protection enhancement for effective disease management.
Keywords: Mathematical modeling, disease transmission dynamics, hantavirus, immune response dynamics, rodent populations