A Maize Foliar Disease Mathematical Model with Standard Incidence Rate

9th Annual Basic Science International Conference 2019

自然科学（总论）

Windarto^1 ; Fatmawati^1 ; Putri, Kamara Mustiko^1

Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Indonesia^1

关键词: Analytical results;    Asymptotically stable;    Basic reproductive ratio;    Bilinear incidence rates;    Disease-free equilibrium;    Endemic equilibrium;    Foliar disease;    Standard incidence rate;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/546/5/052085/pdf
DOI  :  10.1088/1757-899X/546/5/052085

学科分类：自然科学（综合）

来源: IOP

【 摘 要 】

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.