Open AccessAn SEIR epidemic model with constant latency time and infectious period
Author(s) -
Edoardo Beretta,
Dimitri Breda
Publication year - 2011
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2011.8.931
Subject(s) - epidemic model , mathematics , stability theory , constant (computer programming) , polynomial , saturation (graph theory) , basic reproduction number , combinatorics , mathematical analysis , physics , computer science , demography , quantum mechanics , nonlinear system , population , sociology , programming language
We present a two delays SEIR epidemic model with a saturation incidence rate. One delay is the time taken by the infected individuals to become infectious (i.e. capable to infect a susceptible individual), the second delay is the time taken by an infectious individual to be removed from the infection. By iterative schemes and the comparison principle, we provide global attractivity results for both the equilibria, i.e. the disease-free equilibrium E0 and the positive equilibrium E+, which exists iff the basic reproduction number R0 is larger than one. If R0 > 1 we also provide a permanence result for the model solutions. Finally we prove that the two delays are harmless in the sense that, by the analysis of the characteristic equations, which result to be polynomial trascendental equations with polynomial coefficients dependent upon both delays, we confirm all the standard properties of an epidemic model: E0 is locally asymptotically stable for R and unstable for R0 > 1 , while if R0 > 1 then E+ is always asymptotically stable.