Mathematical model for the biocontrol of vector-borne viral diseases in solanaceous vegetable plants

Table of Contents

CHAPTER ONE: INTRODUCTION

1.1 Background of the Study

1.2 Statement of the Problem

1.3 Aim and Objectives of the Study

1.4 Scope of the Study

1.5 Justification of the Study

1.6 Definitions of Basic Concepts/Terms

CHAPTER TWO: LITERATURE REVIEW

2.1 The Concept of Biological Control

2.2 Biological Control of Pests

2.3 Modelling of Interactions within Biological Spheres

2.4 Stability of Biological Systems

2.5 The Basic Reproduction Number and Disease Control

2.6 Sensitivity Analysis of Biological Models

2.7 Reviewed Literatures on Mathematical Models of Plants Diseases

CHAPTER THREE: METHODOLOGY

3.1 Introduction

3.2 The existing model

3.3 The Modified Model

3.4 Method of Model Analysis

CHAPTER FOUR: RESULTS

4.1 Introduction

4.2 Analytical Analysis of the modified model

4.2 Sensitivity Analysis

4.3 Analysis of Sub Model for Interspecific Competition

4.4 Analysis of Sub Model for Intra Specific Competition

4.5 Analysis of Predator – Prey Sub Model

4.6 Stability Analysis of the Predator – Prey Sub Model

CHAPTER FIVE: NUMERICAL SIMULATION AND DISCUSSION

5.1 Introduction

5.2 The Numerical Values used for Simulation

5.3 Numerical Simulation on the Modified Model

5.4 Discussion of the Results

CHAPTER SIX: SUMMARY, CONCLUSION AND RECOMMENDATIONS

6.1 Summary

6.2 Conclusion

6.3 Recommendations

6.4 Contribution to Knowledge

Objectives & Core Topics

This thesis aims to develop and analyze a mathematical model for the biological control of vector-borne viral diseases in solanaceous vegetable plants by introducing lady beetles as predatory agents. The research evaluates disease stability, sensitivity, and ecological interactions to establish an effective control strategy.

• Mathematical modeling of plant disease propagation using ordinary differential equations (ODEs).
• Evaluation of biological control efficacy using predatory lady beetles.
• Stability analysis of disease-free (DFE) and disease-endemic (DEE) equilibria.
• Sensitivity analysis of the basic reproduction number (R0) to prioritize control parameters.
• Numerical simulation for practical farmland application and pest eradication strategies.

Extract from the Book

Summary of Chapters

CHAPTER ONE: INTRODUCTION: Outlines the significance of solanaceous plants, the impact of pests on food security, and defines the research scope and objectives for applying mathematical modeling in agriculture.

CHAPTER TWO: LITERATURE REVIEW: Examines biological control concepts, pathogen population dynamics, and mathematical modeling methodologies used in ecological and epidemiological research.

CHAPTER THREE: METHODOLOGY: Presents the existing models and introduces the modifications needed to accurately represent the interaction between vectors, plants, and predators.

CHAPTER FOUR: RESULTS: Provides the analytical derivation of the model, including stability proofs of equilibrium points and the calculation of the basic reproduction number.

CHAPTER FIVE: NUMERICAL SIMULATION AND DISCUSSION: Details the simulations performed in MATLAB and discusses how predation and competition influence vector eradication.

CHAPTER SIX: SUMMARY, CONCLUSION AND RECOMMENDATIONS: Synthesizes the core findings, confirms that biological control is a viable strategy, and offers recommendations for agricultural practitioners.

Keywords

Biological Control, Mathematical Modeling, Solanaceous Plants, Vector-Borne Diseases, Aphids, Thrips, Whiteflies, Lady Beetles, Basic Reproduction Number, Sensitivity Analysis, Stability Theory, Predator-Prey Interaction, Integrated Pest Management, Equilibrium Points, Population Dynamics.

Frequently Asked Questions

What is the core focus of this research?

The research focuses on creating a mathematical model to assess the effectiveness of using lady beetles as biological control agents for managing vector-borne viral diseases in solanaceous vegetables.

What are the primary fields of study involved?

The work combines applied mathematics, mathematical epidemiology, and agricultural ecology to analyze pest-plant interactions.

What is the main objective of the proposed model?

The objective is to derive a threshold (R0) and test the stability of a system of equations that includes different species of vectors and predators to determine the optimal conditions for pest eradication.

Which mathematical tools are used?

The study employs ordinary differential equations (ODEs), Lyapunov stability analysis, linearization methods, the next-generation matrix methodology, and numerical simulations using MATLAB.

How is the effectiveness of the control agent measured?

Effectiveness is measured by the basic reproduction number and the rate of reduction in infected plant populations observed through numerical simulation.

Are there specific vectors covered?

Yes, the study specifically examines three vector types: aphids, thrips, and whiteflies.

How does the predation rate influence the results?

The study concludes that a predation rate greater than 0.6 is required for successful biocontrol and the subsequent eradication of the pest population within 4–6 weeks.

What led to the modification of the existing model?

The existing model from literature was found to have flaws regarding biting rate definitions (plants do not bite) and an incorrect application of a disease-induced death rate parameter.