Global stability analysis of an SEIR epidemic model with vertical transmission

Kaddar, Abdelilah; Elkhaiar, Soufiane; Eladnani, Fatiha

doi:10.1504/ijdsde.2017.086665

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Research In Applied Mathematics1

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2017

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“…As in [8], We assume that the incidence function ∶ ℝ 2 + ⟶ ℝ + is continuously differentiable in the interior of ℝ 2 + satisfying the following hypotheses. For the treatment function ∶ ℝ + ⟶ ℝ + we say that it is continuously differentiable and concave satisfying the following hypotheses:…”

Section: Research In Applied Mathematicsmentioning

confidence: 99%

Stability Analysis of an SEIR Model with Treatment

Elkhaiar

Kaddar

2017

Research in Applied Mathematics

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Abstract. We study the dynamics of a SEIR epidemic model with nonlinear treatment function, that takes into account the limited availability of resources in community. Under some conditions we prove the existence of two possible equilibria: the disease-free equilibrium and the endemic equilibrium. Using Lyapunov's method and Li's geometrical approach, We also show that the reproduction number 0 is a threshold parameter: the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is less than unity and the unique endemic equilibrium is globally asymptotically stable when the basic reproduction number is greater than this critical value. In the end, we give some concluding remarks concerning the role of treatment on the epidemic propagation.

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Section: Research In Applied Mathematicsmentioning

confidence: 99%