Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Dynamics of SEAIQR Model with Saturated Type Treatment: A Case Study of Spain COVID-19

Version 1 : Received: 12 May 2020 / Approved: 12 May 2020 / Online: 12 May 2020 (13:02:12 CEST)

How to cite: Ghosh, U.; Kamrujjaman, M.; Ghosh, J.K. Dynamics of SEAIQR Model with Saturated Type Treatment: A Case Study of Spain COVID-19. Preprints 2020, 2020050217 (doi: 10.20944/preprints202005.0217.v1). Ghosh, U.; Kamrujjaman, M.; Ghosh, J.K. Dynamics of SEAIQR Model with Saturated Type Treatment: A Case Study of Spain COVID-19. Preprints 2020, 2020050217 (doi: 10.20944/preprints202005.0217.v1).

## Abstract

Background: Outbreak of the Covid-19 is now an ongoing global health emergency. At the end of December 2019, the first infection was reported in Wuhan and the world did not pay attention to this extremely contaminated disease and plucked to react rapidly. The World is in an vulnerable state in disease spreading, facing a great loss of lives and socio-economic aspects also. That is why we have proposed a potential mathematical model with data analysis to predict and control the outcome of this pandemic. Methods: The model presented the epidemic dynamics of multiple compartments. We collected available online data of Spain. In primary step, we estimated the parameters using either the data analysis or reference papers. Then we did the data fitting analysis in comparison with the outcome of our mathematical results. The results of the system depended not only the parameters also on social consciousness. Results: It is found that disease progression in this model is determined by the basic reproductive ratio, $R_0$, the actual epidemic of $R_0$ and effective $R(t)$ of each day. If $R_0>1$, the number of latently infected individuals grows exponentially; endemic solution is stable while infection rate decays if $R_0<1$. The optimal control theory stated that vaccination and treatment strategies are highly effective for reducing both susceptible and infected population and to increase the recover rate high. In Spain, after state of alarm (quarantine) on 14 March 2020, reported cases increasing for 13 days only and from the 14th day, daily reported cases started to decline albeit with small fluctuation. Our proposed model approximates that the disease in Spain could be fully under control by after July 2020. Conclusion: Outbreak will be in control of health care system, reduce the death rate and will ensure social-economic stability.

## Subject Areas

SEAIQR model; stability analysis; COVID-19; optimal control; model validation

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