Qualitative analysis and sensitivity based optimal control of pine wilt disease

Aziz Ullah Awan,Kazeem Oare Okosun,Takasar Hussain,Muhammad Ozair

doi:10.1186/s13662-018-1486-1

Abstract

We design a deterministic model of pine wilt affliction to analyze the transmission dynamics. We obtain the reproduction number in unequivocal form, and global dynamics of the ailment is totally controlled by this number. With a specific end goal to survey the adequacy of malady control measures, we give the affectability investigation of basic reproduction number R_{0} and the endemic levels of diseased classes regarding epidemiological parameters. From the aftereffects of the sensitivity analysis, we adjust the model to evaluate the effect of three control measures: exploitation of the tainted pines, preventive control to limit vector host contacts, and bug spray control to the vectors. Optimal analysis and numerical simulations of the model show that limited and appropriate utilization of control measures may extensively diminish the number of infected pines in a viable way.

Highlights

Vector-borne illnesses are the maladies that outcome from disease transmitted by the nibble of infected arthropod species, for example, mosquitoes, fleas, ticks, and bugs
Many occurrences of vector-borne ailments are known for plants, for instance, coconut palm disease in palms and pine wilt illness in pine trees [1]
Pine wilt disease is a deadly ailment since it slays the infected tree within a few months

Summary

Introduction

Vector-borne illnesses are the maladies that outcome from disease transmitted by the nibble of infected arthropod species, for example, mosquitoes, fleas, ticks, and bugs. Monochamus alternatus, pine sawyer beetle, serves as a vector for this parasite, and it spreads the nematode to pine trees [2] It was first observed in 1905 in Japan. We formulate a mathematical model based on ordinary differential equations This model describes the infectious disease of pine trees through pine sawyer beetles. The transmission rate of the nematode through infected vectors is denoted by δ2, and β2 denotes the average number of contacts per day when adult beetles oviposit. The susceptible pine trees are exploiting at the rate μh, the infected pine trees are isolating and felling at the rate σ , and μv is the death rate of vector population Under these assumptions, the mathematical model can be described as the following system of ordinary differential equations: dSh = dt h – β1δ1ShIv – β2δ2ηShIv – μhSh, dIh dt.

This leads to

Iv v μv

Ih v Ivμv

Sensitivity Index