State feedback impulsive therapy to SIS model of animal infectious diseases

Abstract

h i g h l i g h t s• A state feedback impulsive model is constructed to analyze the treatment of animal epidemics.• The existence of order-1 periodic solution to an impulsive system is proved.• The stability of the order-1 periodic solution is proved with a novel method. a b s t r a c tControlling animal infectious diseases and its related infra microbes is of great significance to public health, since a lot of infectious diseases originate from animal epidemics and they often threaten human health. A state feedback impulsive model is constructed to depict the transmission and treatment of animal epidemics. Basing on the impulsive model, the existence of order-1 periodic solution and its stability are proved with a novel method. The theoretical results indicate that the impulsive treatment triggered by the number of infectious is an efficient approach to control animal infectious disease from breakout. Numerical simulation is presented to support the theoretical conclusion in the end.

Study on Predator-Prey System with Impulsive Release of Predator Population in Polluted Water

“…Mathematically, impulsive state feedback control of dynamic systems can accurately describe these behaviors. In recent years, great progress has been made in the study of impulsive state feedback control [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In [2], the basic theory of impulsive semicontinuous dynamical systems and the existence and stability of periodic solutions of impulsive semicontinuous dynamical systems are introduced.…”

“…In [2], the basic theory of impulsive semicontinuous dynamical systems and the existence and stability of periodic solutions of impulsive semicontinuous dynamical systems are introduced. In [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], impulsive state feedback controlled dynamic systems were applied in different fields such as vegetation protection, algal fish systems, rare animal protection, and cyber security. Through state feedback pulse control, the interaction between various groups in the aquatic ecosystem can also be adjusted, which helps to maintain the balance and stability of the system.…”

Dynamic Analysis of a Phytoplankton-Fish Model with the Impulsive Feedback Control Depending on the Fish Density and Its Changing Rate

“…Jiang et al obtained the order-1 periodic solutions using the Poincaré map [18,19], and Chen developed the idea of successor functions to study the mathematical models with pulse state feedback control [20]. Due to its importance in applications, in recent years, systems of impulsive differential equations have attracted more and more attention and been applied to different areas from population dynamics to chemical regulator systems [21][22][23][24][25][26][27][28]. Due to the challenges in analysing these models, most of existing models only considered the population size without considering the population growth rate when proposing a control strategy [29,30].…”