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

Authors

Olusegun M. Otunuga, Marshall UniversityFollow
Mobolaji O. Ogunsolu

Document Type

Article

Publication Date

1-2020

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 R_T,n and ℛ_T,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.

Comments

The copy of record is available from the publisher at https://doi.org/10.1016/j.idm.2019.12.003.

Copyright © 2019 The Authors. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Recommended Citation

Otunuga, O. M. and Ogunsolu, M. O. (2020). Qualitative analysis of a stochastic SEITR epidemic model with multiple stages of infection and treatment. Infectious Disease Modelling, 5, 61-90. https://doi.org/10.1016/j.idm.2019.12.003.