Qualitative analysis of a stochastic SEITR epidemic model with multiple stages of infection and treatment

Olusegun Michael Otunuga, Mobolaji O. Ogunsolu

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We present a mathematical analysis of the transmission of certain diseases using a stochastic susceptible-exposed-infectious-treated-recovered (SEITR) model with multiple stages of infection and treatment and explore the effects of treatments and external fluctuations in the transmission, treatment and recovery rates. We assume external fluctuations are caused by variability in the number of contacts between infected and susceptible individuals. It is shown that the expected number of secondary infections produced (in the absence of noise) reduces as treatment is introduced into the population. By defining RT,n and RT,n as the basic deterministic and stochastic reproduction numbers, respectively, in stage n of infection and treatment, we show mathematically that as the intensity of the noise in the transmission, treatment and recovery rates increases, the number of secondary cases of infection increases. The global stability of the disease-free and endemic equilibrium for the deterministic and stochastic SEITR models is also presented. The work presented is demonstrated using parameter values relevant to the transmission dynamics of Influenza in the United States from October 1, 2018 through May 4, 2019 influenza seasons.

Original languageEnglish (US)
Pages (from-to)61-90
Number of pages30
JournalInfectious Disease Modelling
Volume5
DOIs
StatePublished - 2020
Externally publishedYes

Keywords

  • Infection
  • Recovery
  • Reproduction number
  • Stability
  • Stochastic epidemic model
  • Susceptible
  • Treatment

ASJC Scopus subject areas

  • Health Policy
  • Infectious Diseases
  • Applied Mathematics

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