Technical report: analysing the effects of the parameters in dynamical model in the spread of HIV / Muhammad Fahmi Ghazalli

Each year, the number of those who died from HIV are increasing. There are several factors that are identified as the major cause of spreading of HIV in a population. But, in this study, only consider two factors that are the unsafe sex and sharing of contaminated needles. Therefore, a dynamic mathematical model will be studied to find out about the spread of HIV in a population. Through the mathematical model, there are two variables were involved, namely the number of individuals carrying HIV and the number of individuals who are free from HIV. Next, made a search for equilibrium points of the model. As a result, there are two equilibrium points are obtained that are the free disease equilibrium point and the endemic equilibrium point. Through these solutions, know that the free disease equilibrium point has a trivial solution and the endemic equilibrium point has non-trivial solution. In addition, the stability of the both equilibrium points can be analyzed by using two methods that are the methods which involves the eigenvalues of the Jacobian matrix and the Routh-Hurwitz criteria. Thus, can determine the type of equilibrium points which involved namely node, focus and saddle point. Then, the equilibrium points can also be determined whether it will stable or unstable. To further this study, the relationship between the group infected by HIV and the group not infected by HIV are also discussed.