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.
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.