Finite-time contraction stability of a stochastic reaction-diffusion dengue model with impulse and Markov switching

Abstract

From the perspective of prevention and treatment of dengue, it is important to minimize the number of infections within a limited time frame. That is, the study of finite time contraction stability (FTCS) of dengue system is a meaningful topic. This article proposes a dengue epidemic model with reaction-diffusion, impulse and Markov switching. By constructing an equivalent system, the well-posedness of the positive solution is proved. The main result is that sufficient conditions to guarantee the finite time contraction stability of the dengue model are acquired based on the average pulse interval method and the bounded pulse interval method. Furthermore, the numerical findings indicate the influences of impulse, control strategies and noise intensity on the FTCS.

Keywords

• reaction-diffusion
• finite-time contraction stability
• bounded pulse interval method
• markov switching
• average pulse interval method