A review of fractional-order models for plant epidemiology

In the modern day, fractional operators are being utilized more and more to express problems and study the spread of epidemics, reflecting the growing interest in mathematical biology. Interventions pertaining to plant health and public health can benefit from the use of mathematical models to forecast the course of infectious illnesses, particularly those affecting plants. For the earth and all living beings, plants are extremely vital. Consequently, as it can offer valuable information on plant disease transmission, an understanding of plant disease dynamics is crucial. Among the most important maize diseases in the world are foliar diseases, which can be brought on by bacteria, viruses, or fungi. A mathematical model based on a hypothesis is expanded to include recovered plant species in order to observe the control effects of the early detection process. In the field, this strategy is now recognized as the conventional method. The importance of mathematical methods, especially fractional and integer calculus modeling, is emphasized by recent researchers when examining the dynamics of different disease models. Consequently, in order to monitor the continuous tracking of the disease’s spread caused by the infection, the constructed model is transformed into a fractional order model using the fractal-fractional operator. An investigation, both qualitative and quantitative, is carried out to determine whether the newly constructed fractional order system is stable. The boundedness and uniqueness of the model are examined, as they are essential properties to understand the complex dynamics and guarantee robust conclusions. By applying Lipschitz conditions and linear growth, the global derivative is verified for true positivity and utilized to calculate the rate of disease effects based on each sub-compartment. Assessing the overall impact of the disease’s spread and containment, the global stability of the system is examined through the application of Lyapunov’s first derivative functions. The work finds the requirements for a solution to the suggested disease model and calculates reproductive numbers under particular conditions using a computationally effective approach to tackle both model and simulation difficulties. In the context of fractal-fractional operators, fractional refers to the fractional ordered derivative operator, and fractal refers to the spatial distribution of the disease. To view the actual dynamics of infection-induced virus transmission and control for maize foliar with different sizes and continuous monitoring, we use combine operators. We model both the symptomatic and asymptomatic consequences of maize foliar disease using MATLAB code, providing insights into the underlying dynamics of disease propagation and the possible suppressive effects of early detection. This paper presents an innovative approach that incorporates memory into the model by employing an equal-dimensional fractal-fractional operator. This approach takes into account the dynamic effects of illnesses on society and offers insightful information for analysis, choice-making, and illness prevention.