A MODEL FOR VECTOR-BORNE DISEASES: OPTIMAL TREATMENT AND PREVENTION Hee-Dae KWON 1 , Kebenesh W. Blayneh 2 and Yanzhao Cao 2 1) Department of Mathematics, Inha University, Incheon 402-751, KOREA 2) Florida A & M University, Department of Mathematics, FL, USA Corresponding Author : Hee-Dae KWON, hdkwon@inha.ac.kr ABSTRACT In this paper we study the dynamics of a vector-transmitted disease under two assumptions. We first look at time dependent prevention and treatment efforts where optimal control theory is applied. Using analytical and numerical techniques, it is shown that there are control efforts for treatment of hosts and prevention of host-vector contacts with minimal cost and side effects. Then we considered the autonomous counter part of the first mode and here we calculated an epidemiological parameter. Based on this parameter, we established conditions for the global stability of the disease-free equilibrium point of the model. The two general models are applied to get results on a malaria disease. Using this data several numerical results about the optimal control functions, the state variables and solutions of the autonomous version are given. INTRODUCTION Vector-borne diseases have been and are among the leading causes of death that they remain challenges for many countries in the world, claiming the lives of millions of people every year. The health as well as the socioeconomic impacts of emerging and re-emerging vector-borne diseases is significant. It affects workforce and resources, and hence, it hinders developments. Therefore, it is among the major concerns for several health organizations including, the World Health Organization, Center for Disease Control and National Health Institute. The geographic location and adaptation of vectors is vast and diverse. Vectors are found in areas ranging from tropical to temperate zones and at different landscapes. Although mosquitoes are commonly known vectors as a pathway for widely known diseases, others, like tsetes flies, blackflies, fleas, all blood-sucking vectors, constitute potential health hazard to mankind and sometimes to pets and livestock. While mosquitoes are common in swampy areas with vege- tation where moisture and shade are available and the temperature is warm, tsetes flies which enjoy the same environment are abundant in tropical Africa [2,3]. Accordingly the diseases that are transmitted by vectors are worldwide problems. For exam- ple, dengue fever is common in tropical climates including the southern part of the United States in the Texas and Florida regions. It is transmitted by mosquito Aedes aegypti while malaria which is carried by female Anopheles mosquito is prevalent mainly in Africa and some parts of Asia [7,9]. Similarly, sleeping sickness which is carried by tsetes flies among human beings, horses and cattle [3] is common in the sub Saharan countries of Africa. West Nile virus is also