Addressing Various Strategies for Combating the Leaf-Roll Virus in Potato Plants

In this research, we introduced a mathematical simulation that describes the transmission dynamics of the potato leaf-roll virus (PLRV) and involves some control measures to eliminate the propagation of the PLRV disease. The proposed model consists of four ordinary differential equations divided into two categories: the host (potato plant) and the vector (Myzus persicae insect). We also split the potato plant into subgroups, such as susceptible and infected, as well as the vector. We examined the mathematical analysis for the models such as positivity, invariant region, existence, and uniqueness of the solution to prove the model’s well posedness. Furthermore, the reproduction number (Rc) is computed, and local stability criteria for the disease-free and endemic equilibrium points are determined. A sensitivity analysis is presented to determine which model parameter is more sensitive. The optimal control problem is constructed with three time-dependent control variables, represented by preventive control measures (u1) that reduce potato plants’ contact with vectors, quarantine control measures (u2), and a chemical control measure (u3) that reduces vectors of infection using insecticides. The appropriate employment of the mixed cropping strategy can reduce the spread of PLRV. We proposed different control strategies resulting from the intersection of the suggested controls to clarify the influences of these controls and to study the preferred strategy for eliminating the transmission of this disease. Numerical simulation is provided in the graphical representation to make it easier for the reader to understand the subject of this study.