Analysis and Control of an SEIQR Epidemic Model with Application to Ebola Disease Vaccination

A modified Susceptible - Exposed - Infected - Quarantined - Recovered (SEIQR) epidemic model with vaccination is considered to understand the transmission dynamics of Ebola disease.

The impact of vaccination as a control strategy is investigated in two cases: vaccination is a constant function of time and time - dependent vaccination. For the first case, the reproduction number R0 is derived and mathematical analysis reveals that the existence of equilibrium points and the qualitative properties of solutions of the resulting autonomous model are completely determined by R0. For the second case, we conduct an analysis that is based on optimal control theory to determine optimal application of vaccination control.

It is shown that the disease - free equilibrium is locally asymptotically stable if R0 < 1 and unstable if R0 > 1 . When  R0 > 1, the disease - free equilibrium loses its stability and an endemic equilibrium point that is locally asymptotically stable emerges as also verified by demonstrating the existence of forward bifurcation at R0 = 1 using the method by Castillo - Chavez and Song. Optimal control analysis shows that that vaccination effort is affected by the cost associated with it. Vaccination control of Ebola can be carried out at maximum rate from the onset of the outbreak if it is not costly.

Vaccination is an important intervention strategy in controlling Ebola outbreaks.