On an SEIADR epidemic model with vaccination, treatment and dead-infectious corpses removal controls

This paper studies the non-negativity and stability properties of the solutions of a newly proposed SEIADR model with six subpopulations, namely, susceptible–exposed–symptomatic infectious–asymptomatic infectious–dead infectious corpses–recovered model, of potential interest in the characterization and control of the Ebola pandemic. Such an epidemic model incorporates asymptomatic and dead-infectious subpopulations to those of the typical SEIR models and, in parallel, three types of controls including feedback information and impulsive actions. In particular, the model incorporates feedback vaccination controls on the susceptible subpopulation and antiviral treatment controls on the symptomatic infectious subpopulations as well as infectious corpses removal. Those controls may incorporate constant, linear and impulsive terms and an additional quadratic feedback term in the treatment control law. The infectious corpses removal control is impulsive by nature. The practical implementation of that control consists in organization or brigades for lying bodies removal being active along short and intermittent periods of time. The positivity and the existence/non-existence of the endemic equilibrium point are investigated as well as the local stability properties around the equilibrium points and periodic steady-state solutions. The global stability is investigated via a Lyapunov function for the incremental systems about the equilibrium solution which is supported by an “ad hoc” designed time-varying Lyapunov equation.