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Modelling and Optimal Control of Insect Transmitted Plant Disease
Current Issue
Volume 8, 2020
Issue 1 (March)
Pages: 1-9   |   Vol. 8, No. 1, March 2020   |   Follow on         
Paper in PDF Downloads: 65   Since Apr. 23, 2020 Views: 758   Since Apr. 23, 2020
Alex Xavery Matofali, Department of Mathematics, Informatics and Computational Sciences, Sokoine University of Agriculture (SUA), Morogoro, Tanzania.
Insect-vectored diseases pose one of the greatest threats to plants on a global scale. At present, few effective control strategies have been developed to prevent the transmission of insect-transmitted diseases. These strategies largely rely on the use of chemical insecticides which have negative impacts on the environments and human health. In this study, a mathematical model is formulated and analysed to study the optimal control of the insects transmitted plants diseases. The model is sub-divided into two sub-populations namely the plant population and the insect population. The plant population is divided into two classes, namely; susceptible plants and infected plants and vector (insect) population comprises susceptible vector and infected vector. The optimal control model is formulated and analysed to minimize the transmission of disease from an infected vector (insect) to susceptible plant. Optimal control method using Pontryagin’s Maximum Principle was applied to determine the necessary conditions for the optimal control of the impact of plant inoculation. It is concluded that, if the plants are controlled then more plants will be produced compared with plants without control.
Modelling, Optimal, Insects, Transmission, Disease
Abdullatif NS, Wake GC, Regliuski T, and Philip AG, 2014. Modelling Induced resistance to plant. Journal of theoretical biology 347, 144-150.
Augusto FB, Del Valle SY, Blayneh KW, Ngonghala CN, Goncalves MJ, Li N, Zhao R, Gong H, 2013. The impact of bed net use on malaria prevalence. Journal of Theoretical biological B20 (2013) 58-65.
Castillo-Chavez C and Song B, 2004, Dynamical Models of Tuberculosis and their Applications. Mathematical Biosciences and Engineering. 1 (2): 361-404.
Chan MS and Jeger MJ, 1994. An analytical model of plant virus disease dynamics with roguing and replanting. Journal appl. Ecology 31, 413-427.
Cheryl B, Lori L, and David Z, 2002. The economics of controlling Insect Transmitted Plant Diseases. Oxford University Press, American journal of agricultural Economics Vol. 84, No 2, pp 279-291.
Cunniffe NJ, Gilligan CA, Lavanjeira FF, Neri M, and Erik R, 2014. Cost-Effective control of Plant disease when Epidemiological knowledge is Incomplete: Modelling Bahia Bark scaling of Citrus. PLOS| Computational biology.
Diekmann, O., Heesterbeek, J. A. P., & Metz, J. A. J., 1990. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology. 28, 365–382.
Driessche P and Watmough J, 2002. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Bio-Sciences. 180: 29-48.
Fishman S, and Marcus R, 1984. A model for spread of plant disease with Periodic removals. J. math. Biol. 21, 149-158.
Gray S, and Banerjee N, 1999. Mechanisms of arthropod transmission of plant and animal virus. Microbiol. Mol. Biol. Rev. 1999, 63, 128-148.
Jeger MJ, Holt J, Bosch F, and Madden LV, 2004. Epidemiology of insect-transmitted plant viruses: modelling disease dynamics and control interventions. Physiol. Entomol. 9, 291–304.
Joshi R, 2002. Optimal control of an HIV immunology model. Optim. Con. Appl. Methods 23, 199–213.
Muilerman H, 2011. New revolutionary regulation enters in force... but will Europe abandon its bad old habits.
Meng X, Zhong T, Song Y, and li Z, 2010. The dynamics of plant disease models with continuous and Impulsive cultural control strategies. Journal of theoretical Biology 266, 29-40.
Nakazawa T, Urano S, Yamanaka T, 2012. Model analysis for plant disease dynamics co-mediated by herbirory and Herbivore-Borne phytopathogens. Biodiversity Division, National Institute for Agro Environmental sciences, Kannondai, Tsukuba, japan.
Okosun KO, Makinde OD and Takaidza I, 2012. Analysis of recruitment and industrial human resources management for optimal productivity in the presence of the HIV/AIDS epidemics. J Biol Phys. 39: 99-121.
Pscheidt, J. W., & Hartman, J. R., 2011. Plant Disease. Agriculture and Natural Resources Publications. Publication Number PPA-46.
Pontryagin LS, Boltyanskii VG, Gamkrelidze RV. and Mishchenko EF, 1962. The mathematical theory of optimal processes. Wiley, New York.
Shi R, Zhao H, and Tang S, 2014. Global dynamic analysis of a vector-borne plant Disease model. Springer.
Walters D, Walsh D, Newton A, and Lyon G, 2005. Inducing resistance for plant disease control: maximizing the efficacy of resistance elicitors. Phy topathology, 95, 1368-1373.
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