Mathematical modeling and optimal control of PVY transmission dynamics in potatoes farm with mixed-cropping system

Abstract

Currently, there is a growing interest in studying mixed-cropping farming system (planting the host potato mixed with a non-host crop plant) as an alternate, environmentally friendly control strategy of vector-borne plant viruses as widespread use of chemical controls have many drawbacks. PVY is an aphid-borne virus and one of the most damaging diseases affect ing potato production worldwide. Mixed-cropping can reduce the vector-mediated spread of PVY, the non-host plant interferes with the virus transmission processes in many ways. Math ematical modeling can assist in creating and describing effects of mixed-cropping using rep resentative parameters and analyzing the dynamical properties of the epidemic. Therefore, in this dissertation, to asses various effects of mixed-cropping on the transmission dynamics of PVY in potatoes crop, we formulating and analyzing mathematical models where the host and a non-host plants exist in the field. Analytic results show that the transmission rate is considerably affected and these effects depend on the quality and density of the non-host plant used in attracting vectors. These effects are expressed by the basic reproduction num ber which affects the existence and stability of the endemic equilibrium. Also, an extension to optimal control models where considered that aims to study the impacts of using insecti cide, mineral oil and their mixture, use of certified seed and roguing of infected host plants and alternate host-weeds. Results show that mixed-cropping is better than chemical con trols in reducing the spread of PVY. Results show that combination of mixed-cropping and chemical controls is the best, however, the disease can be eliminated by effective use of the mixed-cropping strategy alone. Finally, for a model with time-delay, we found that the sys tem hardly exhibits a delay-induced Hopf bifurcation being influenced by the mixed-cropping situation.