SVFRH: A Growth Stage-Based Compartmental Model for Predicting the Disease Incident in Tomato (Solanum lycopersicum)

The tomato is one of the most widely cultivated crops globally, yet it faces susceptibility to various diseases, resulting in substantial yield losses. Over decades, research has primarily focused on addressing these challenges through computer vision and deep learning techniques. In this work, we employ a comprehensive modelling approach that combines compartmental and logistic regression models to thoroughly address disease dynamics in tomato crops, with a particular focus on tomato early blight diseases. Our methodology employs the SVFRH (Susceptible, Vegetative, Flowering, Ripening and Harvesting) model to analyze disease dynamics across distinct plant growth stages. This stage-specific approach enables us to capture disease progression while considering the unique interactions between environmental factors, disease transmission, and plant development at each stage. By incorporating temporal and stage-specific modeling, we focus on understanding how disease spreads and evolves over time, with the aim of improving the precision of disease detection and developing effective control strategies. The accuracy of these models is ensured through rigorous assessments of key mathematical properties, such as positivity (to guarantee non-negative state variables) and boundedness (to ensure realistic limits on disease progression). The next-generation matrix method is then applied to calculate the basic reproduction number $\left ({{ R_{0} }}\right)$ . Numerical simulations validate the theoretical findings, and the outcomes indicate an increase in the number of vectors around the field with a decrease in tomato yield, emphasizing the epidemiological significance of these findings. The results demonstrate the model’s capacity to accurately predict disease incidents at each growth stage. An overall probability of disease incidents is calculated by combining the probabilities from each stage-specific model. The proposed model is capable of providing a dependable and efficient means of disease detection and prevention in tomato crops, enabling timely actions by farmers. Furthermore, this approach has the potential for generalization to other crops, promising improvements in crop health and yield within the realm of agriculture.