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 |
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
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Download@article{10.11648/j.ajam.20241202.12,
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},
url = {https://doi.org/10.11648/j.ajam.20241202.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20241202.12},
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.},
year = {2024}
}
TY - JOUR T1 - Mathematical Modelling for Rice Blast Re-Infection AU - Bonface Ouma Obita AU - Mark Onyango Okongo AU - Ochwach Onyango Jimrise AU - Alice Mulama Lunani Y1 - 2024/04/21 PY - 2024 N1 - https://doi.org/10.11648/j.ajam.20241202.12 DO - 10.11648/j.ajam.20241202.12 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 37 EP - 49 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20241202.12 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. VL - 12 IS - 2 ER -
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
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