Author(s): Souﬁane Elkhaiar and Abdelilah Kaddar
We study the dynamics of a SEIR epidemic model with nonlinear treatment function,thattakesintoaccountthelimitedavailabilityofresourcesincommunity.Undersome conditionsweprovetheexistenceoftwopossibleequilibria:thedisease-freeequilibriumand the endemic equilibrium. Using Lyapunov’s method and Li’s geometrical approach, We also show that the reproduction number𝑅0is a threshold parameter: the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is less than unity and theuniqueendemicequilibriumisgloballyasymptoticallystablewhenthebasicreproduction number is greater than this critical value. In the end, we give some concluding remarks concerningtheroleoftreatmentontheepidemicpropagation.
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