Global Analysis of an SEIRS Model for COVID-19 Capturing Saturated Incidence With Treatment Response (Preprint)
Authors: Oluyori David Adeyemi 
Published: July 2020

BACKGROUND

Sequel to [10], who studied the dynamics of COVID-19 using an SEIRUS model. We consider an SEIRS model capturing saturated incidence with treatment response. In this theoretical model, we assumed that the treatment response is proportional to the number of infected as long as the incidence cases are within the capacity of the healthcare system, after which the value becomes constant, when the number of confirmed cases exceed the carrying capacity of the available medical facilities. Thus, we obtain the reproduction number stating that when , the disease free equilibrium is globally asymptotically stable. Also, we studied the existence of the local and global stability of the disease free and endemic equilibria and found that the kind of treatment response and inhibitory measures deployed in tackling the COVID-19 pandemic determines whether the disease will die out or become endemic.

OBJECTIVE

To enlighten individuals and government on the effective response that works while trying to slow the spread of COVID-19 and avoid a pandemic situation

METHODS

Analytical Method through mathematical model

RESULTS

Recently, [10] considered an SEIRUS (Susceptible-Exposed-Infected-Recovered-Undetectable-Susceptible) model for COVID-19, where it was predicted that with strict adherence to the guidelines of the WHO on observatory and treatment procedures, the pandemic will soon die out. Based on the motivation from [10, 24, 27, 28 and 29], we present an SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) model with saturated incidence and treatment functions which prescribes inbihitory measures such as personal hygiene, wearing of face mask, travel/public gathering ban, partial or total lockdown etc and rapid responses such as public enlightenment, pool testing, increased medical facilities and trained medical personnel etc., as . potent means of slowing down the spread of COVID-19.

(PDF) Global Analysis of an SEIRS Model for COVID-19 Capturing Saturated Incidence with Treatment Response. Available from: https://www.researchgate.net/publication/341526868_Global_Analysis_of_an_SEIRS_Model_for_COVID-19_Capturing_Saturated_Incidence_with_Treatment_Response [accessed May 28 2020].

CONCLUSIONS

In this paper, we studied the global analysis of an SEIRS epidemic model capturing saturated incidence with treatment response. In the theoretical study of this model, we obtain the reproduction number which explains the dynamic behavior of the model showing that when ᡄ⡨㐇1, there is no positive equilibrium and the disease free equilibrium is globally asymptotically stable, that is the disease dies out and when ᡄ⡨㐈1, it becomes endemic. We also determine the existence of the local and global stability of the disease free and endemic equilibria and found that the efficiency of the treatment response such as contact tracing, quarantine, case search, pool testing, advanced medical technologies, increased trained personnels, funding medical research e.t.c and strict adherence to inhibitory measures such as personal hygiene, social distancing, stay at home orders etc deployed in tackling the COVID-19 pandemic determines whether the disease will die out or become endemic. So how long COVID-19 pandemic stays with us depends on how much we are willing to take responsibility as individuals and government.

(PDF) Global Analysis of an SEIRS Model for COVID-19 Capturing Saturated Incidence with Treatment Response. Available from: https://www.researchgate.net/publication/341526868_Global_Analysis_of_an_SEIRS_Model_for_COVID-19_Capturing_Saturated_Incidence_with_Treatment_Response [accessed May 28 2020].

CLINICALTRIAL

https://www.researchgate.net/publication/341526868_Global_Analysis_of_an_SEIRS_Model_for_COVID-19_Capturing_Saturated_Incidence_with_Treatment_Response

INTERNATIONAL REGISTERED REPORT

RR2-10.1101/2020.05.15.20103630