A Mathematical Model for Transmission of Hantavirus among Rodents and Its Effect on the Number of Infected Humans

Abstract

In this paper, we present a mathematical model for the transmission of hantavirus among rodents and its effect on the number of hantavirus-infected human population. We investigate the model and present a standard analysis in mathematical epidemiology, such as determining the equilibria of the system and their stability analysis, together with the relationship to the basic reproduction number. It is found that the endemic equilibrium exists and is locally asymptotically stable when the basic reproduction number is greater than one; otherwise, the disease-free equilibrium is stable. Later on, we also show that by constructing a suitable Lyapunov function, the endemic equilibrium is globally asymptotically stable whenever it exists. Based on the basic reproduction number, we present a critical level of intervention to control the spread of the disease to humans. We found a significant finding from the present model that if the basic reproduction number is greater than one, then it is impossible to completely eliminate hantavirus disease in the system by solely focusing on any intervention for humans, like vaccination and curative action, without paying any attention to interventions for rodent populations. However, we can still decrease the density of infected humans with those interventions. Hence, we suggest that a combination of several interventions is needed to obtain effective control in eliminating the hantavirus. This information is useful for further study in finding an optimal control strategy to reduce or eliminate the transmission of hantavirus to humans.