Modeling and optimal control of Ebola virus disease in the presence of quarantine and treatment

The non linear mathematical model for the dynamics of Ebola virus diseases is formulated. The model has five classes namely susceptible human, exposed human, infected human, treated human and recovered human. Invariant region and positivity solution of the model are determined. Local stability analyses of disease free equilibrium analysis is determined using Routh-Hurwitz criteria, whereby it is found to be locally stable of the reproduction number is less than one. The mathematical model is found to exhibit forward bifurcation at the point where the reproduction number is equal to one. Numerical sensitity analysis of parameters is carried out access the sensitivity of each parameter to the reproduction number. Two control measures, u1(l) control measure due to quarantine of exposed and infected individuals) and u2(l) (control measure due to efficacy of treatment drug, used for treating Ebola virus disease Ebola victim) were added to the Ebola virus disease model. The mode with control variables is aalysed in order to determine the optimal control. Numerical simulation for the model in the absence and in the presence of control measures is carried out. The results show that in the presence of optimal control the Ebola virus disease can be eliminated in the society.