Effects of nonlinear impulsive controls and seasonality on hantavirus infection

Abstract

Hemorrhagic fever with renal syndrome (HFRS) caused by hantavirus is prevalent across China and causes a significant number of deaths every year. This study aims to examine the transmission dynamics of hantavirus and to suggest effective control measures. We extend a periodic model of HFRS infection including house/field mice, contaminated environments, and the human population by introducing nonlinear pulses used to describe impulsive interventions. In our model, the systemic period determined by natural factors may be inconsistent with the periods of control strategies for the two kinds of mice. We prove that the model is uniformly and ultimately bounded and discuss the existence and uniqueness of the disease-free periodic solution. We calculate the basic reproduction number for the house/field mouse subsystem denoted by $R_{01}$/$R_{02}$. We then examine the threshold dynamics and analyze the conditions for global asymptotic stability of the disease-free periodic solution. Additionally, we determine that the HFRS infection uniformly persists in the human population when $max\{R_{01},R_{02}\}>1$. Further, the existence of nontrivial periodic solutions for subsystems is examined via bifurcation theory. In particular, we observe complicated dynamics in the proposed model with multiple periods and nonlinear pulses. By fitting data on HFRS cases, we estimate the unknown parameters and predict the trend of HFRS infection in the human population. Numerical simulations show that enhancing the intensity and frequency of culling mice could curb the spread of hantavirus. Our findings suggest that improving the vaccination rate and decreasing the number of rodents, especially wild mice, are crucial in reducing HFRS infection.