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.

We propose a new epidemic model to study the coinfection dynamics of COVID-19 and bacterial pneumonia, which is the first model in the literature used to describe mathematically the interaction of these two diseases while considering two infection ways for pneumonia: community-acquired and hospital-acquired transmission. We show that the existence and local stability of equilibria depend on three different parameters, which are interpreted as the basic reproduction numbers of COVID-19, bacterial pneumonia, and bacterial population in the hospital. Numerical simulations are performed to complement our theoretical analysis, and we show that both diseases can persist if the basic reproduction number of COVID-19 is greater than one.

In this work, we further the investigation of an SEIRS model to study the dynamics of the Coronavirus Disease 2019 pandemic. We derive the basic reproduction number R0 and study the local stability of the disease-free and endemic states. Since the condition R0 < 1 for our model does not determine if the disease will die out, we consider the backward bifurcation and Hopf bifurcation to understand the dynamics of the disease at the occurrence of a second wave and the kind of treatment measures needed to curtail it. Our results show that the limited availability of medical resources favours the emergence of complex dynamics that complicates the control of the outbreak.

In this study, we propose and analyse an extended SEIARD model with vaccination. We compute the control reproduction number $\mathcal{R}_c$ of our model and study the stability of equilibria. We show that the set of disease-free equilibria is locally asymptotically stable when $\mathcal{R}_c<1$ and unstable when $\mathcal{R}_c>1$, and we provide a sufficient condition for its global stability. Furthermore, we perform numerical simulations using the reported data of COVID-19 infections and vaccination in Mexico to study the impact of different vaccination, transmission and efficacy rates on the dynamics of the disease.

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