Abstract

ERDEM, Mustafa; SAFAN, Muntaser  and  CASTILLO-CHAVEZ, Carlos. A delay differential equations model for disease transmission dynamics. Rev. Mat [online]. 2020, vol.27, n.1, pp.49-71. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v27i1.39948.

A delay differential equations epidemic model of SIQR (Susceptible-Infective-Quarantined-Recovered) type, with arbitrarily distributed periods in the isolation or quarantine class, is proposed. Its essential mathematical features are analyzed. In addition, conditions that support the existence of periodic solutions via Hopf bifurcation are identified. Nonexponential waiting times in the quarantine/isolation class lead not only to oscillations but can also support stability switches.

Keywords : delay differential equation; integro-differential equation; epidemic model; quarantine; stability switch; oscillations; stage structure..

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