Mathematical modeling approach to the transmission dynamics of pine wilt disease with saturated incidence rate

Abstract

The present paper investigates the dynamics of pine wilt disease with saturated incidence rate. The proposed model is stable both locally and globally. The local stability of the disease-free equilibrium is determined by the basic reproduction [Formula: see text]. The disease-free equilibrium is stable locally and globally whenever [Formula: see text]. If [Formula: see text], then the endemic state is stable both locally and globally. Further, a brief discussion with conclusion on the numerical results of the proposed model is presented.

A fractional order pine wilt disease model with Caputo–Fabrizio derivative

“…In the present work, we extended the PWD model [12] to fractional order using the Caputo-Fabrizio fractional derivative. The model equilibria and basic reproduction number are explored.…”

“…Here, in this section, we extend the PWD model [12] to fractional order using a CF derivative of order τ ∈ [0, 1]. The classical integer order PWD model is formulated by the following nonlinear system of differential equations:…”

“…A mathematical model with variable population and suggested optimal control was developed in [11]. Most recently, in [12] the dynamics of PWD with saturated incidence rate was explored. All of the above PWD models are restricted to classical integer order differential equations.…”

“…Therefore, motivated by the above work, in this paper, we aim to extend the recently published PWD model [12]…”

Modelling the dynamics of Pine Wilt Disease with asymptomatic carriers and optimal control

“…Khan et al . 10 introduced a dynamical model of PWD and investigates the stability of the disease with saturated incidence rate. They classified the total host tree size into three states: susceptible, exposed and infected host pine trees, while the vector size was also classified into three similar states.…”