Analytical And Numerical Expression For The Infection Model Of Coffee Rust Disease

Abstract

Coffee rust disease is one of the major threats to the economy faced by many countries in which coffee production is their main occupation. The effective way to control the growth of coffee rust spore causing fungi Hemileia vastatrix is to use the bacteria Bacillus thuringiensis which maintains the soil health rather than using copper fungicides which harms humans as well as soil health. In this paper Mathematical Modeling of the Consumer population , the Resource population , the size of the population of coffee rust spores Hemileia vastatrix  H_{{i, j}} and the size of the population of bacteria Bacillus thuringiensis B_{{i, j}} ,where {i,j} denotes the position of the coffee tree in i^th row and j^th column of a plantation area, are considered.  The analytical solution of the system of differential equations has been derived using New Homotopy Perturbation Method (NHPM) & Homotopy Perturbation Method (HPM) and also compared with the numerical simulation satisfactorily. The solution thus obtained gives us a better understanding of the effect of various parameters over the coffee rust disease model.