Global Stability of a SVEIR Epidemic Model: Application to Poliomyelitis Transmission Dynamics

The lack of treatment for poliomyelitis doing that only means of preventing is immunization with live oral polio vaccine (OPV) or/and inactivated polio vaccine (IPV). Poliomyelitis is a very contagious viral infection caused by poliovirus. Children are principally attacked. In this paper, we assess the impact of vaccination in the control of spread of poliomyelitis via a deterministic SVEIR (Susceptible-Vaccinated- Latent-Infectious-Removed) model of infectious disease transmission, where vacci- nated individuals are also susceptible, although to a lesser degree. Using Lyapunov- Lasalle methods, we prove the global asymptotic stability of the unique endemic equilibrium whenever Rvac > 1 . Numerical simulations, using poliomyelitis data from Cameroon, are conducted to approve analytic results and to show the importance of vaccinate coverage in the control of disease spread.