Oseloka, Okey (Professer)Tigabie, Ayalnesh2019-04-302023-11-092019-04-302023-11-092017-08-05http://10.90.10.223:4000/handle/123456789/18169In this paper, I build epidemiological model to investigate the dynamics of spread of dengue fever in human population. I study the demographic factors that influence equilibrium prevalence, and perform a sensitivity analysis on the basic reproduction number. Among several intervention measures, the effects of two potential control methods for dengue fever are estimated: introducing educate and treat the population. A stochastic model for transmission of dengue fever is also built to explore the effect of some demographic factors and review a number of compartmental models in epidemiology which leads to a nonlinear system of ordinary differential equations. I focus an SEIRS epidemic models with and without education and treatment. A threshold parameter R0 is identified which governs the spread of diseases,and this parameter is known as the basic reproductive number. The models have at least two equilibria, an endemic equilibrium and the disease-free equilibrium. We demonstrate that the disease will die out, if the basic reproductive number R0 < 1. This is the case of a disease-free state, with no infection in the population. Otherwise the disease may become endemic if the basic reproductive number R0 is bigger than unity. Furthermore, stability analysis for both endemic and disease-free steady states are investigated and we also give some numerical simulations. The second part of this dissertation deals with optimal education and treatment by drug strategy in epidemiology. We use optimal control technique on education and treatment to minimize the impact of the disease. Hereby we mean minimizing the spread of the disease in the population, while also minimizing the effort on education and treatment roll-out. We do this optimization for the cases of SEIRS models, and show how optimal strategies can be obtained which minimize the damage caused by the dengue fever disease. Finally, we describe the numerical simulations using the fourth-order Runge-Kutta method. Computational Science program, AAU i Dengue Fever Application of Optimal ControlenBasic Reproductive NumberDisease-Free EquilibriumEndemic EquilibriumEpidemiologyNumerical SimulationPopulation ModelOptimizationStability AnalysisComputationalThesis