Global dynamics of Filippov‐type plant disease models with an interaction ratio threshold

Abstract

A Filippov‐type plant disease model is developed by introducing a interaction ratio threshold, the number of susceptible plants infected by per diseased plant, which determines whether control measures including replanting or roguing are carried out. The main purpose of this paper is to give a completely qualitative analysis of the model. By employing Poincaré maps, our analysis reveals rich dynamics including a global attractor bounded by a touching closed orbit, which is convergent in finite time from its outside, a global attractor bounded by two touching closed orbits and a pseudo‐saddle, and a globally asymptotically stable pseudo‐node. Moreover, we give biological implications of our results in implementing control strategies for plant diseases.

Study of Mathematical Modeling for Plant Disease Transmission: A Systematic Literature Review during 2012-2022

“…Only 3 out of 60 articles did not analyze the model contained mathematically. Analyzing the model aimed to check the solution positivity, solution boundedness, and equilibrium points with their local and global stability [26,28,55,56,83]. The analysis procedure conducted on the model in the nonautonomous system is different and more complicated than in the autonomous system.…”

Global dynamics of a non-smooth SIV system with uncertain effective vaccine protection rate

“…Next, based on the biological significance of infected and immune individuals, we need to prove the regularity and boundedness of the solution of system (3) [21][22][23][24].…”