Optimal control analysis of a mathematical model for guava nutrients in an integrated farming with cost-effectiveness

Because of its high nutritional value and easy availability, guava fruit has become more popular as a crop in tropical regions in recent decades. Unfortunately, its cultivation faces multifaceted challenges, with increasing the guava borer due to global warming posing a significant threat to crop yield, while the cost of pesticides adds to the economic burden on farmers. To overcome this difficulty, an integrated cultivation method has been devised to simultaneously cultivate guava and tuberose flowers for the purpose of biological pest management, while also earning money through the sale of the flowers to support the integrated agricultural plan. The present mathematical modeling study has focused on the optimal control problem using the strategy of spraying pesticides and flower harvesting, to achieve the highest possible profit. Characterization of the proposed optimal control was then carried out using Pontryagin’s maximum principle, where the objective of our farming would be higher when optimal management of our strategies would be provided compared to other scenarios. To find the most efficient and least expensive approach, cost-effectiveness analysis has been performed. According to the findings, an optimal strategy for harvesting flowers is the most economical and efficient way to increase the amount of earnings from this integrated farming. However, the results of this study can help the farmers in developing beneficial strategies to gain maximum profit by reducing the cost.