This thesis treats the issue of Vector-Borne Virus Diseases (VBVDs) that are transmitted in solanaceous vegetable plants by incorporating three species of vectors (aphids, thrips and whiteflies). A mathematical model was developed that used lady beetles as biological control agents for controlling the spread of diseases in solanaceous vegetable plants through predation. The research adopted the linearization method.
This research is restricted to a biological control of VBVDs of solanaceous vegetable plants using compartmental modeling approach. The model is a system of first order nonlinear ODEs. Additionally, the study is limited to three solanaceous plants (i.e. tomato, pepper and eggplant). This is because solanaceous plants are among the world's most cultivated crops and given proper conditions and regular maintenance, they are relatively easy to grow. We focused on viral diseases that affect solanaceous vegetable plants especially Yellow Leaf Curl Virus (YLCV), Spotted Wilt Virus (SWV) and Cucumber Mosaic Virus (CMV).
It is a common knowledge that these plant viruses also require some sort of carrier, known as vectors to transmit the pathogen from plant to plant. Therefore, the study is demarcated to a class of aphids (green peach aphids), thrips (T. tabasi) and whiteflies (Bemisia tabasi) because these ones are reported as the common problem associated with solanaceous plants which can be controlled by natural predatory enemies - ladybugs (hippodamia convergens).
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
2.1 The Concept of Biological Control
Biological control is most commonly defined as the use of natural enemies to reduce the population size of pest species (McKimmie, 2000). It entails the suppression of damaging activities of one organism by one or more different organisms, often referred to as natural enemies (Coppel and Mertins, 2012). However, in terms of plant pathology, the definition of biological control refers to the purposeful utilization of introduced or resident living organisms, other than disease resistant host plants, to suppress the activities and populations of one or more plant pathogens (Pal and Gardener, 2006). Although not new to agricultural practice, modern efforts at biocontrol have taken place for about 100 years (Jackson and Chen-Charpentier, 2018). Biological control of pests has received great interest recently as an alternative to conventional pesticides. According to Naranjo, Ellsworth and Frisvold (2015), biological control is due to both environmental and economic concerns.
Biocontrol may be considered as a multi-trait phenomenon whose success depends on ability to compete for nutrients, adaptation to the changes in environmental conditions and above all protection of the host plant against pathogens (Stirling, 2011). In order to interact, plant beneficial organisms need to have some form of direct or indirect contact with the plant pathogens (Naranjo et al., 2015). The different types of interactions were named as mutualism, commensalism, neutralism, competition, parasitism and predation (Arthur and Mitchell, 1989). These terminologies originated in macro ecology but all of these types of interactions exist in the natural world (Coppel and Mertins, 2012). In plant science, the development of plant diseases involves both plants and microbes, the interactions that lead to biological control take place at different levels and rates (Pal and Gardener, 2006). Thus, biological control is a bio effect or-method of controlling pests (including insects, mites, weeds and plant diseases) using other living organisms (Jackson and Chen-Charpentier, 2018). It relies on predation, parasitism, herbivory, or other natural mechanisms, but typically also involves an active human management role.
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.
- Quote paper
- Timothy Ado Shamaki (Author), 2022, Mathematical model for the biocontrol of vector-borne viral diseases in solanaceous vegetable plants, Munich, GRIN Verlag, https://www.grin.com/document/1320768
