Mathematical Analysis of Plant Disease Dispersion Model that Incorporates wind Strength and Insect Vector at Equilibrium
A. L. M. Murwayi *
Department of Mathematics, Catholic University of Eastern Africa, P.O.Box 62157-00200, Nairobi, Kenya.
T. Onyango
Department of Industrial Mathematics, Technical University of Kenya, P.O.Box 52428-00200, Nairobi, Kenya.
B. Owour
Department of Natural Sciences, Catholic University of East Africa, P.O.Box 62157-00200, Nairobi, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Numerous plant diseases caused by pathogens like bacteria, viruses, fungi protozoa and pathogenic nematodes are propagated through media such as water, wind and other intermediary carries called vectors, and are therefore referred to as vector borne plant diseases.
Insect vector borne plant diseases are currently a major concern due to abundance of insects in the tropics which impacts negatively on food security, human health and world economies. Elimination or control of which can be achieved through understanding the process of propagation via Mathematical modeling. However existing models are linear and rarely incorporates climate change parameters to improve on their accuracy. Yields of plants can reduce significantly if they are infected by vectors borne diseases whose vectors have very short life span without necessarily inducing death to plants. Despite this, there is no reliable developed mathematical model to describe such dynamics.
This paper formulates and analyzes a dynamical nonlinear plant vector borne dispersion disease model that incorporates insect and plant population at equilibrium and wind as a parameter of climate change, to determine R0 , local and global stability in addition to sensitivity analysis of the basic reproduction number R0.
Keywords: Basic reproduction number, sensitivity analysis, disease free equilibrium point (DFEP), endemic equilibrium point (EEP), local and global stability