Mathematical modeling of begomovirus dynamics in tomato fields using whitefly and fungal biocontrol
Year: 2025
Type: article
Abstract: Tomato cultivation in Burkina Faso and elsewhere constitutes a source of income for farmers. Tomato is a very important fruit for a good complete diet, unfortunately low productivity is caused by various factors including climate change, fungal plant diseases linked to pathogens and spread by insect pests. Every year farmers suffer huge losses due to the tomato yellow virus (begomovirus), which is transmitted by insect vectors Bemisia Tabaci. However, we analyze these insect management problems using mathematical models. In this paper we developed a mathematical model of tomato yellow leaf curve virus (TYLCV) disease in the tomato plantation with the growth rate of insects vectors following the logistic function, taking into account the two latent stages of the vegetative phase and the generative phase of tomato plants. We determined the value of the basic reproduction number \(\mathcal{R}_0\) of the model from the dominant eigenvalue of the next generation matrix. In practice the basic reproduction number represent the number of new cases generated by an infectious individual during its infection phase . But in theory we use the basic reproduction number to analyze the stability of the equilibrium states of the model. This parameter is used to evaluated the speed of spread of the virus in the population. The results illustrates that when \(\mathcal{R}_0 < 1\), the disease-free equilibrium point is asymptotically globally stable and the model has an endemic equilibrium point which is asymptotically globally stable when \(\mathcal{R}_0 >1\). We have also provided numerical simulation examples describing the population of the model that was developed. The numerical simulation results illustrate that for a use of Verticillium lecanii at a dose greater than \(10\%\) the population of tomato plants latent, infected in the vegetative and in the generative phase will experience extinction, just like the susceptible and infected population of Bemisia Tabaci. In the last part of our work, we also calculated the sensitivity indices of certain parameters that are very sensitive to the variation in the value of the basic reproduction number. These findings provide a scientific basis for optimizing biocontrol strategies in tomato farming.
Institution: Nazi Boni University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
SDG: Zero hunger
Open Access status: diamond
OpenAlex ID: W4410849130