Research Article | | Peer-Reviewed

### Mathematical Modelling for Rice Blast Re-Infection

Received: 1 September 2023     Accepted: 8 November 2023     Published: 21 April 2024
Abstract

Rice is the thirdly most valued cereal crops in Kenya after maize and wheat. The demand for rice in Kenya has increased greatly over the last few years while production has still remained low. This is because rice production is affected by serious constraints especially rice diseases of which the most threatening is rice blast. Rice blast infection and re-infection can occur in different stages of rice growth and therefore need to be controlled. This study aims to developed a mathematical model for rice blast re-infection. The model employs a system of nonlinear ordinary differential equations which is analysed in details for its stability properties. Basic reproduction number Ro for rice blast re-infection was found to be less than one. Numerical simulation of the model is done using Mathematica, and graphical profile of the main variables are depicted. We conclude that rice blast re-infection reduces rice yield and necessary remedy are needed.

 Published in American Journal of Applied Mathematics (Volume 12, Issue 2) DOI 10.11648/j.ajam.20241202.12 Page(s) 37-49 Creative Commons This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. Copyright Copyright © The Author(s), 2024. Published by Science Publishing Group
Keywords

Mathematical Modeling, Basic Reproduction Ratio, Rice Blast, Epidemiology Model, Epidemic Mode

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• APA Style

Obita, B. O., Okongo, M. O., Jimrise, O. O., Lunani, A. M. (2024). Mathematical Modelling for Rice Blast Re-Infection. American Journal of Applied Mathematics, 12(2), 37-49. https://doi.org/10.11648/j.ajam.20241202.12

ACS Style

Obita, B. O.; Okongo, M. O.; Jimrise, O. O.; Lunani, A. M. Mathematical Modelling for Rice Blast Re-Infection. Am. J. Appl. Math. 2024, 12(2), 37-49. doi: 10.11648/j.ajam.20241202.12

AMA Style

Obita BO, Okongo MO, Jimrise OO, Lunani AM. Mathematical Modelling for Rice Blast Re-Infection. Am J Appl Math. 2024;12(2):37-49. doi: 10.11648/j.ajam.20241202.12

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author = {Bonface Ouma Obita and Mark Onyango Okongo and Ochwach Onyango Jimrise and Alice Mulama Lunani},
title = {Mathematical Modelling for Rice Blast Re-Infection},
journal = {American Journal of Applied Mathematics},
volume = {12},
number = {2},
pages = {37-49},
doi = {10.11648/j.ajam.20241202.12},
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abstract = {Rice is the thirdly most valued cereal crops in Kenya after maize and wheat. The demand for rice in Kenya has increased greatly over the last few years while production has still remained low. This is because rice production is affected by serious constraints especially rice diseases of which the most threatening is rice blast. Rice blast infection and re-infection can occur in different stages of rice growth and therefore need to be controlled. This study aims to developed a mathematical model for rice blast re-infection. The model employs a system of nonlinear ordinary differential equations which is analysed in details for its stability properties. Basic reproduction number Ro for rice blast re-infection was found to be less than one. Numerical simulation of the model is done using Mathematica, and graphical profile of the main variables are depicted. We conclude that rice blast re-infection reduces rice yield and necessary remedy are needed.},
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AB  - Rice is the thirdly most valued cereal crops in Kenya after maize and wheat. The demand for rice in Kenya has increased greatly over the last few years while production has still remained low. This is because rice production is affected by serious constraints especially rice diseases of which the most threatening is rice blast. Rice blast infection and re-infection can occur in different stages of rice growth and therefore need to be controlled. This study aims to developed a mathematical model for rice blast re-infection. The model employs a system of nonlinear ordinary differential equations which is analysed in details for its stability properties. Basic reproduction number Ro for rice blast re-infection was found to be less than one. Numerical simulation of the model is done using Mathematica, and graphical profile of the main variables are depicted. We conclude that rice blast re-infection reduces rice yield and necessary remedy are needed.
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Author Information
• Department of Physical Sciences, Faculty of Science, Engineering and Technology, Chuka University, Chuka, Kenya

• Department of Physical Sciences, Faculty of Science, Engineering and Technology, Chuka University, Chuka, Kenya

• Department of Physical Sciences, Faculty of Science, Engineering and Technology, Chuka University, Chuka, Kenya

• Department of Physical Sciences, Faculty of Science, Engineering and Technology, Chuka University, Chuka, Kenya

• Sections