Open AccessA Maize Foliar Disease Mathematical Model with Standard Incidence Rate
Author(s) -
Windarto Windarto,
Fatmawati Fatmawati,
Kamara Mustiko Putri
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/546/5/052085
Subject(s) - basic reproduction number , stability theory , mathematics , incidence (geometry) , mathematical economics , statistics , physics , demography , nonlinear system , population , geometry , quantum mechanics , sociology
In this paper, we present a mathematical model of maize foliar disease with standard incidence rate. The present model is an improvement model from Collins and Duffy, where Collins and Duffy consider a mathematical model with the bilinear incidence rate. The present model has two equilibria namely the disease-free equilibrium and endemic equilibrium. We find that the disease-free equilibrium is asymptotically stable whenever the basic reproductive ratio is less than one. On the other hand, the endemic equilibrium will exist and be asymptotically stable whenever the basic reproductive ratio is greater than one. Furthermore, we perform numerical simulations to confirm the analytical results.