Dynamics of plant disease models with continuous and pulse farming awareness control

Abstract

<p style='text-indent:20px;'>How to develop the mathematical model of plant disease transmission and consider the effect of saturated farming awareness strategies on plant disease control is of great practical significance. To do this, the plant disease transmission models with continuous and pulse farming awareness control strategy have been proposed in the present paper. For the model with continuous control strategies, the threshold values for the existence and stability of multiple equilibria have been given, and the effect of farming awareness on disease persistence is discussed; For the model with nonlinear impulsive control tactics, the existence and stability of the plant disease-free periodic solutions are investigated and the threshold condition is given, further we get the conditions for the permanence of the system and obtain the sufficient conditions under which the positive periodic solution exists by bifurcation theory. Numerical simulations reveal that people's farming awareness, especially global awareness, plays an important role in controlling and eradicating the plant disease. Moreover, the nonlinear impulsive control could result in the complex dynamic behavior, including period doubling, chaos and multiple attractors, which makes it difficult to design a successful plant disease control strategy.</p>