Pest insect is one of the major pests that cause damage and loss in agriculture around the world. This threat also comes with other complex problems such as environmental hazards by the indiscriminate pesticide and the rapid development of insects due to the environmental change. Therefore, more environmentally friendly and sustainable control methods need to be implemented. This paper discusses a generic model to describe plant-insect interaction and focuses on the interaction between non-vector pest insect and plant. The model consists of a set of non-linear ordinary differential equations representing insect-plant predator-prey interaction with the addition of two controls, namely green insecticide and mating disruption. An optimal control approach was exploited to solve the control problem and find a set of control strategies that regulate the system optimally. The simulations were conducted for three strategies and four scenarios describing possibilities in the real-world application. Our results suggest that all strategies managed to prevent agriculture loss. A cost-effectiveness analysis was conducted to examine the cost and benefit of applying each strategy.

In the framework of integrated pest management, biological control through the use of living organisms plays important roles in suppressing pest populations. In this paper, the complex interaction between plants and pest insects is examined under the intervention of natural enemies releases coupled with sterile insects technique. A set of nonlinear ordinary differential equations is developed in terms of optimal control model considering characteristics of populations involved. Optimal control measures are sought in such a way they minimize the pest density simultaneously with the control efforts. Three different strategies relating to the release rate of sterile insects and predators as natural enemies, namely, constant, proportional, and saturating proportional release rates, are examined for the attainability of control objective. The necessary optimality conditions of the control problem are derived by using Pontryagin maximum principle, and the forward–backward sweep method is then implemented to numerically calculate the optimal solution. It is shown that, in an environment consisting of rice plants and brown planthoppers as pests, the releases of sterile planthoppers and ladybeetles as natural enemies can deteriorate the pest density and thus increase the plant biomass. The release of sterile insects with proportional rate and the release of natural enemies with constant rate are found to be the most cost-effective strategy in controlling pest insects. This strategy successfully decreases the pest population about 35 percent, and thus increases the plant density by 13 percent during control implementation.

Pest and plant diseases cause damages and economic losses, threatening food security and ecosystem services. Thus, proper pest management is indispensable to mitigate the risk of losses. The risk of environmental hazards induced by toxic chemicals alongside the rapid development of chemical resistance by insects entails more resilient, sustainable, and ecologically sound approaches to chemical methods of control. This study evaluates the application of three dynamical measures of controls, namely, green insecticide, mating disruption, and the removal of infected plants, in controlling pest insects. A model was built to describe the interaction between plants and insects as well as the circulation of the pathogen. Optimal control measures are sought in such a way they maximize the healthy plant density jointly with the pests’ density under the lowest possible control efforts. Our simulation study shows that all strategies succeed in controlling the insects. However, a cost-effectiveness analysis suggests that a strategy with two measures of green insecticide and plant removal is the most cost-effective, followed by one which applies all control measures. The best strategy projects the decrease of potential loss from 65.36% to 6.12%.

Conventional pesticide application is the most common method in dealing with pests. However, the application of conventional pesticide has a considerable drawback to the environment and the agricultural sector in the long run. Therefore, a more environmentally friendly pest control method is needed. Mating disruption is one of the alternative methods available. This paper discusses the characteristics and the optimal implementation of a mating disruption using optimal control approach. A generic insect life cycle model is examined and modified to add mating disruption as a dynamic control method. 4th order Runge-Kutta method and forward-backwards sweep method was used to numerically solve the control problem. An illustrative comparison between the implementation of constant control and dynamic control was also given for a variety of scenarios. From the simulations, it was found that mating disruption generates a large amount of benefit when it is fully effective. When it has imperfect effectiveness in disrupting the mating process, mating disruption will generate significantly less benefit. The optimal control approach reduces the application cost significantly while still preserving the benefit.

The SARS-CoV-2 outbreak that started in China created COVID-19 pandemic all around the world. This pandemic is declared as a world health crisis by the World Health Organization in 2020. In response to this pandemic, many countries have been conducting various measures to manage the spread of the disease employing lockdown, contacts tracing, and massive testing. As the vaccine and medicine for this virus are under development, the governments all around the world can only apply non-curative measures. With many considerations, especially in the economic sector, governments seem hesitant to apply extensive control measures and this results in a considerable financial loss. In this paper, a generic mathematical model with thirteen compartments is developed, of which it is equipped with five control measures namely quarantine, active carrier identification, recovered individual identification, past infection identification, and medical treatment. We employ the COVID-19 outbreak in Jakarta as a study case to evaluate a series of control scenarios. Optimal control approach is used to find the best control strategy in managing the pandemic. It is suggested that adding the efforts on testing policy and medical treatment 40 days after the first confirmed infection is the most cost-effective strategy with the number of death decreased as much as 60:21 percent of the death cases under initial control strategy.