In this paper, we propose an impulsive mathematical model of bone formation and resorption accounting for the number of active osteoclastic cells, bone resorbing cells, and the number of active osteoblastic cells, bone forming cells, based on the effects of parathyroid hormone and calcitonin with impulsive estrogen supplement. The model is then analyzed theoretically in terms of its stability, permanence and oscillatory behavior. The conditions on the model parameters, for which the desirable behaviors of the solution of the system can be expected, are derived. Numerical simulations are also carried out in order to support our theoretical predictions. The results indicate that the frequency and dosage of the estrogen supplements are important since the behavior of the solution of the system depends on the frequency and dosage of the estrogen supplements.

In this paper, a cellular automata model is developed in order to investigate the control of cassava mealybugs in a cassava field when the wasp Anagyrus lopezi is used as the biological control agent. The model is constructed based upon farmers’ usual practices of cassava planting in Thailand. However, the instructions on how to release the Anagyrus lopezi wasps in a cassava field are various. In this study, we developed a cellular automata model based upon farmers’ usual practices recommended by many organizations in Thailand such as the Department of Agriculture, Ministry of Agriculture and Cooperatives, Thailand, and the Thai Tapioca Development Institute. The effect of the life cycles of cassava mealybugs and the Anagyrus lopezi wasps is also taken into account. The available reported data from many sources are utilized so that parameter values in the model are obtained. Computer simulations of different tactics of biological control are carried out so that a guideline for controlling the spread of cassava mealybugs by the Anagyrus lopezi wasps is obtained.

Even though the effect of release frequency of green lacewings in controlling the spread of mealybugs in a cassava field was investigated by Promrak and Rattanakul in 2015, the effect of increased global temperature was not taken into account. In this work, cellular automata and Monte Carlo simulation are employed in order to study the effect of an increased global temperature on the life cycles of mealybugs and green lacewings which in turn effects the efficacy of the biological control of the spread of mealybugs. Computer simulations are carried out at different temperatures so that an efficient biological control of the spread of mealybugs in a cassava field is obtained.

In this work, a mathematical model is proposed to investigate the population dynamics of brown planthopper, which is a major insect pest of rice, and its natural enemies namely Cyrtorhinus Lividipennis and Lycosa Pseudoannulata. To analyse the model theoretically, the geometric singular perturbation method is employed. Conditions that differentiate dynamic behaviors exhibited by the model are derived. To illustrate our theoretical predictions, computer simulations are also presented showing that the dynamic behavior exhibited by the model correspond to the reported field observations.

Mealybug is an important pest of cassava plant in Thailand and tropical countries, leading to severe damage of crop yield. One of the most successful controls of mealybug spread is using its natural enemies such as green lacewings, where the development of mathematical models forecasting mealybug population dynamics improves implementation of biological control. In this work, the Sharpe–Lotka–McKendrick equation is extended and combined with an integro-differential equation to study population dynamics of mealybugs (prey) and released green lacewings (predator). Here, an age-dependent formula is employed for mealybug population. The solutions and the stability of the system are considered. The steady age distributions and their bifurcation diagrams are presented. Finally, the threshold of the rate of released green lacewings for mealybug extermination is investigated.