Numerical and Bifurcation Analysis with Sensitivity Assessment of a Deterministic Leptospirosis Hantavirus Co-Infection Model

Abstract

In this paper, a deterministic compartmental model is developed in order to study the dynamics of the transmission of leptospirosis and hantavirus co-infection with particular emphasis on the human population. The model includes compartments of susceptible individuals, singly infected classes, co-infected individuals, and recovered individuals, as well as important pathogen exposure and disease progression mechanisms. Analytical features of the proposed model are addressed, such as positivity, boundedness, the existence of equilibrium points, and bifurcation analysis. The next-generation matrix approach is used to obtain the dominant transmission threshold, denoted by, Rc 0 which determine the qualitative behavior of the system. The transmission-free equilibrium of the model is locally asymptotically stable when Rc 0 < 1 and unstable when Rc 0 > 1, indicating disease persistence in the population. In addition, bifurcation analysis is carried out to examine the system behavior near the critical threshold. The analysis confirm the occurrence of a backward transcritical bifurcation. The validity of the analytical results is confirmed through numerical simulations. In particular, the roles of transmission rates, recovery rates, and co-infection dynamics are studied in detail. Sensitivity analysis shows that parameters associated with infection transmission and recovery have the strongest influence on disease burden, with co-infection outcomes being especially responsive to changes in recovery rates. The results indicate that improving treatment efficiency and limiting transmission pathways can reduce both single infections and co-infection occurrences. Overall, this study highlights the importance of targeted control strategies for leptospirosis hantavirus co-infection and emphasizes the need for effective intervention measures to reduce public health risks.