This research presents a mathematical model for the bacterial wilt of brinjal, employing differential equations to explore the interactions between host plants, bacterial infection and its disease dynamics. This study addresses varying initial conditions to represent different densities of susceptible and infected populations. The key properties of the model, including the feasibility and boundedness of solutions, are thoroughly analyzed. This research establishes the existence and uniqueness of solutions and identifies the steady state, notably the infection-free and endemic equilibrium. The next-generation method calculates the reproduction number for both the vegetative and generative states. Additionally, a sensitivity analysis is conducted to pinpoint critical parameters influencing the spread of infection. The highlights of the study are the local stability of the equilibrium points and the sensitivity of the bacterial brinjal wilt in the vegetative state. The sensitive parameters are α and μ1, and in the generative state, the positive parameters are <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10343_2025_1118_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha ,\mu _{2},\pi\)</EquationSource> </InlineEquation> and ρ1, and the reproduction number expressed as the secondary infections <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10343_2025_1118_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(R_{0}< 1\)</EquationSource> </InlineEquation> the disease reduces, and if <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10343_2025_1118_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(R_{0}> 1\)</EquationSource> </InlineEquation> spreads the disease. For numerical simulations, MATLAB was used to validate the model’s predictions and enhance the understanding of disease dynamics in brinjal cultivation.

Predicting and Controlling Bacterial Wilt in Brinjal: A Mathematical Model Approach

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发表日期：

2025年4月25日

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C. Pooja,
A. Sabarmathi

摘要

This research presents a mathematical model for the bacterial wilt of brinjal, employing differential equations to explore the interactions between host plants, bacterial infection and its disease dynamics. This study addresses varying initial conditions to represent different densities of susceptible and infected populations. The key properties of the model, including the feasibility and boundedness of solutions, are thoroughly analyzed. This research establishes the existence and uniqueness of solutions and identifies the steady state, notably the infection-free and endemic equilibrium. The next-generation method calculates the reproduction number for both the vegetative and generative states. Additionally, a sensitivity analysis is conducted to pinpoint critical parameters influencing the spread of infection. The highlights of the study are the local stability of the equilibrium points and the sensitivity of the bacterial brinjal wilt in the vegetative state. The sensitive parameters are α and μ₁, and in the generative state, the positive parameters are \(\alpha ,\mu _{2},\pi\) and ρ₁, and the reproduction number expressed as the secondary infections \(R_{0}< 1\) the disease reduces, and if \(R_{0}> 1\) spreads the disease. For numerical simulations, MATLAB was used to validate the model’s predictions and enhance the understanding of disease dynamics in brinjal cultivation.