tetano
Editor, Senior Moderator
Infect Dis Model. 2019 Dec 14;5:61-90. doi: 10.1016/j.idm.2019.12.003. eCollection 2020. [h=1]Qualitative analysis of a stochastic SEITR epidemic model with multiple stages of infection and treatment.[/h]
Otunuga OM[SUP]1[/SUP], Ogunsolu MO[SUP]2[/SUP].
[h=3]Author information[/h]
[h=3]Abstract[/h] 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 [FONT=MathJax_Math]R[/FONT][FONT=MathJax_Math]T[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Math]n[/FONT] and [FONT=MathJax_Math]R[/FONT][FONT=MathJax_Math]T[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Math]n[/FONT] 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.
[h=4]KEYWORDS:[/h] Infection; Recovery; Reproduction number; Stability; Stochastic epidemic model; Susceptible; Treatment
PMID: 31930182 PMCID: PMC6948245 DOI: 10.1016/j.idm.2019.12.003
Free full text
Otunuga OM[SUP]1[/SUP], Ogunsolu MO[SUP]2[/SUP].
[h=3]Author information[/h]
[h=3]Abstract[/h] 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 [FONT=MathJax_Math]R[/FONT][FONT=MathJax_Math]T[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Math]n[/FONT] and [FONT=MathJax_Math]R[/FONT][FONT=MathJax_Math]T[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Math]n[/FONT] 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.
[h=4]KEYWORDS:[/h] Infection; Recovery; Reproduction number; Stability; Stochastic epidemic model; Susceptible; Treatment
PMID: 31930182 PMCID: PMC6948245 DOI: 10.1016/j.idm.2019.12.003
Free full text