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Mathematics & Economics
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# Estimation of the probability of reinfection with COVID-19 coronavirus by the SEIRUS model (Research Paper Sample)

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With the sensitivity of the Polymerase Chain Reaction (PCR) test used to detect the presence of the virus in the human host, the global health community has been able to record a great number of recovered populations. Therefore, the objective of this study was to evaluate the probability of reinfection in the recovered class and the model equations which exhibit the disease-free equilibrium (E_0 ) state for COVID-19 coronavirus. The model differential equation was evaluated for the disease-free equilibrium for the case of reinfection as well as the existence and stability criteria for the disease using the model proportions. This evaluation shows that the criteria for a locally or globally asymptotic stability with a basic reproductive number R_0=0 are satisfied. Hence, there is a chance of no secondary reinfections from the recovered population as the rate of incidence of the recovered population vanishes, that is, B=0. With a total of about 900,000 infected cases worldwide, numerical simulations for this study 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. As shown by the results, the proportion of the 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 and most significant for this study is the rate of reinfection by the recovered population which will decline to zero over time as the virus is cleared clinically from the system of the recovered class.

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Estimation of the probability of reinfection with COVID-19 coronavirus by the SEIRUS model
Victor Alexander Okhuese
Email: alexandervictor16@yahoo.com
Affiliation: Department of Mathematics, Nasarawa State University, Keffi – Nigeria
Abstract
With sensitivity of the Polymerase Chain Reaction (PCR) test used to detect the presence of the virus in the human host, the global health community has been able to record a great number of recovered population. Therefore, the objective of this study was to evaluate the probability of reinfection in the recovered class and the model equations which exhibits the disease-free equilibrium E0 state for COVID-19 coronavirus. The model differential equation was evaluated for the disease-free equilibrium for the case of reinfection as well as existence and stability criteria for the disease using the model proportions. This evaluation shows that the criteria for a locally or globally asymptotic stability with a basic reproductive number R0=0 is satisfied. Hence, there is a chance of no secondary reinfections from the recovered population as the rate of incidence of the recovered population vanishes, that is, B=0. With a total of about 900,000 infected cases worldwide, numerical simulations for this study was 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.

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