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.

Osteoporosis, a bone metabolic disease, is one of the major diseases occurring in aging population especially in postmenopausal women. A system of impulsive differential equations is developed in this paper in order to investigate the effects of parathyroid hormone and prolactin on bone-forming cells, namely, osteoblasts, and bone-resorbing cells, namely, osteoclasts, under the impulsive estrogen supplement. The theoretical analysis of the developed model is carried out so that we obtain the conditions on the system parameters in which the stability and permanence of the model can occur. Computer simulations are also provided to illustrate the theoretical predictions.