Sensitivity and Threshold Analysis of the Basic Reproduction Number in a Lassa Fever Model

Abstract

This paper presents a comprehensive sensitivity and threshold analysis of the basic reproduction number (R₀) for a deterministic model describing the transmission dynamics of Lassa fever between human and rodent populations. The next-generation matrix approach is employed to derive an explicit expression for R₀, which quantifies the average number of secondary infections generated by a single infectious individual in a fully susceptible population. Analytical differentiation of R₀ with respect to each model parameter yields normalized forward-sensitivity indices that measure the relative contribution of epidemiological and demographic parameters to disease transmission. The results indicate that transmission rates between humans and rodents (βHV and βVH) and population recruitment rates (ΛH and ΛV) exert the most positive influence on R₀, while the recovery rate (γH) and natural mortality of rodents (μV) produce the strongest negative effects. Threshold analysis further reveals that when R₀ < 1, the disease-free equilibrium is locally asymptotically stable, whereas for R₀ > 1, an endemic equilibrium emerges. These findings highlight that targeted interventions such as enhancing recovery through medical treatment and reducing human rodent contact are the most effective strategies for lowering R₀ below unity and achieving disease eradication.