Analytical analysis and bifurcation of pine wilt dynamical transmission with host vector and nonlinear incidence using sustainable fractional approach

Abstract

To study the dynamical system, it is necessary to formulate a mathematical model to comprehend the dynamics of the diseases that are prevalent around the world by using fractional calculus. A mathematical model is developed with the hypothesis created by adding control and asymptomatic variables to observe the rate of change of pine wilt and the ABC operator is used to turn the model into a fractional ordered model for continuous monitoring. The Boundedness and uniqueness of the developed model are investigated for bounded findings by using Banach space, which are the key properties of such an epidemic model. A newly developed system is examined both qualitatively and quantitatively to determine its stable position, and the verification of flip bifurcation has been made for developed systems. Derived reproductive numbers using the next-generation technique as well as the sensitivity of each involved parameter are verified. The Atangana–Toufik scheme is employed to find the solution for the developed system using different fractional values, which are advanced tools for reliable bounded solutions. Simulations have been made to see the real behavior and effects of pine wilt disease with control and asymptomatic battels in the community. Also, identify the real situation of the spread as well as the control of pine wilt after employing control and asymptomatic battels due to treatment. Such a type of investigation will be useful in investigating the spread of disease as well as helpful in developing control strategies based on our justified outcomes.