Estimated Numerical Results and Simulation of the Plant Disease Model Incorporating 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
Numerical simulations facilitate in the study of the behaviour of systems whose mathematical models are too complex to obtain analytical solutions. In this paper, we used assumed values of the model parameters and variable to simulate a non-linear deterministic model for plant vector borne diseases developed by Murwayi in [1]. Available models incorperate one climate change parameters at a time but our model includes the three temperature, precipitate and wind at ago. The non linear deterministic model included the climate change parameters with temperature and precipitation that influence the biting rate as (a) while wind as an agent of movement of the insect vector, emmigration and immigration is incorperatedin the model as (±θ). We obtained the basic reproductive number R0 and carried out the normalized sensitivity analysis to obtain the positive and negative numerical sensitivity indices to determine the parameters that have the greatest and lowest impact on the basic reproductive number R0 of the model. We used Matlab ODE 45 in built solver to simulate the dynamics of the model.
Keywords: Basic reproduction number, numerical sensitivity analysis and simulation point.