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

Nkamba L., Manga T., Ntaganda J. M., Abboubakar H., Kamgang J. C., Castelli L. Mathematical model to assess vaccination and effective contact rate impact in the spread of tuberculosis, Open Journal of Modelling and Simulation, Vol. 5, No. 01 (2017).DOI: 10.4236/ojmsi.2017.51008

Abstract: 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 vaccinated 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 vac Rvac > 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.

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