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Dynamics and optimal control of a non-linear epidemic model with relapse and cure

Author

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  • Lahrouz, A.
  • El Mahjour, H.
  • Settati, A.
  • Bernoussi, A.

Abstract

In this work, we introduce the basic reproduction number R0 for a general epidemic model with graded cure, relapse and nonlinear incidence rate in a non-constant population size. We established that the disease free-equilibrium state Ef is globally asymptotically exponentially stable if R0<1 and globally asymptotically stable if R0=1. If R0>1, we proved that the system model has at least one endemic state Ee. Then, by means of an appropriate Lyapunov function, we showed that Ee is unique and globally asymptotically stable under some acceptable biological conditions. On the other hand, we use two types of control to reduce the number of infectious individuals. The optimality system is formulated and solved numerically using a Gauss–Seidel-like implicit finite-difference method.

Suggested Citation

  • Lahrouz, A. & El Mahjour, H. & Settati, A. & Bernoussi, A., 2018. "Dynamics and optimal control of a non-linear epidemic model with relapse and cure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 299-317.
    • Handle: RePEc:eee:phsmap:v:496:y:2018:i:c:p:299-317
    DOI: 10.1016/j.physa.2018.01.007
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    References listed on IDEAS

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    Cited by:

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