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# Susceptible-Exposed-Infectious- Recovered-Undetectable-Susceptible (SEIRUS) Model Predictions of the Spread of COVID-19 Pandemic (Research Paper Sample)

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The model equations which exhibits the disease-free equilibrium (E_0 )state for COVID-19 coronavirus does not exist and hence does not satisfy the criteria for a locally or globally asymptotic stability when the basic reproductive number R_0=1 for and endemic situation. This implies that the COVID-19 coronavirus does not have a curative vaccine yet and precautionary measures are advised through quarantine and observatory procedures. The basic reproductive number was found to be R_0<1and hence shows that there is a chance of decline of secondary infections when the ratio between the incidence rate in the population and the total number of infected population quarantined with observatory procedure.
Furthermore, numerical simulations were carried to complement the analytical results in investigating the effect of the implementation of quarantine and observatory procedures has on the projection of the further spread of the virus globally. Result shows that the proportion of infected population in the absence of curative vaccination will continue to grow globally meanwhile the recovery rate will continue slowly which therefore means that the ratio of infection to recovery rate will determine the death rate that is recorded globally.
Therefore, the effort to evaluate the disease equilibrium shows that unless there is a dedicated effort from individual population, government, health organizations, policy makers and stakeholders, the world would hardly be reed of the COVID-19 coronavirus and further spread is eminent and the rate of infection will continue to increase despite the increased rate of recovery until a curative vaccine is developed.

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APPLICATION OF AN AGE-STRUCTURED DETERMINISTIC ENDEMIC MODEL FOR DISEASE CONTROL IN NIGERIA
VICTOR ALEXANDER OKHUESE1* AND ODUWOLE HENRY KEHINDE2
1Department of Mathematics, Nasarawa State University, Keffi, Nigeria
2Department of Mathematics, Nasarawa State University, Keffi, Nigeria
Copyright © 2020 the authors. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: This paper focuses on the development and analysis of the endemic model for disease control in an aged-structured population in Nigeria. Upon the model framework development, the model equations were transformed into proportions with rate of change of the different compartments forming the model, thereby reducing the model equations from twelve to ten homogenous ordinary differential equations. The model exhibits two equilibria, the endemic state and the disease-free equilibrium state while successfully achieving a Reproductive Number R0=0.
The deterministic endemic susceptible-exposed-infected-removed-undetectable=untransmissible-susceptible (SEIRUS) model is analyzed for the existence and stability of the disease-free equilibrium state. We established that a disease-free equilibrium state exists and is locally asymptotically stable when the basic reproduction number 0≤R0<1. Furthermore, numerical simulations were carried to complement the analytical results in investigating the effect treatment rate and the net transmission rate on recovery for both juvenile and adult sub-population in an age-structured population.
Keywords: susceptible, exposed, latent, infectious, removed, recovery, undetectable.

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