Mathematical Modeling of the Transmission Dynamics of Covid-19 with Quarantine and Hospitality Treatment

Abstract

This study presents a COVID-19 epidemic disease model that has been tailored to fit the specific circumstances of world. The Nigerian population has been partitioned into seven subpopulations in this model system. These subpopulations include the Susceptible class, Exposed class, Symptomatic Infected class, Asymptomatically Infected class, Quarantined individuals, Hospitalised individuals, and Recovered individuals. The model was augmented with control measures parameters, specifically those related to hospitalisation and quarantine. The disease-free equilibrium and endemic equilibrium points were derived. The determination of the basic reproduction number was achieved through the utilisation of the novel generation matrix. Additionally, an analysis of the local and global stability was conducted, revealing that the system is both locally and globally asymptotically stable at the aforementioned point of R0<1 for the DFE. We did numerical simulations using (Maple 17) software. The results showed the importance of the control measures and social distancing through graph.

Introduction

I. INTRODUCTION

A novel coronavirus known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2; formerly 2019-nCoV), which was first discovered during an outbreak of respiratory illness cases in Wuhan City, Hubei Province, China, is known as coronavirus disease 2019 (COVID-19). Since December 2019, there have been a large number of unexplained cases of pneumonia in Wuhan, China, with cough, dyspnoea, fatigue, and fever as the primary symptoms (Adedayo et al. 2022).

Infection with the new coronavirus pandemic, COVID-19, is characterised by respiratory symptoms, fever, coughing, shortness of breath, and dyspnoea. The new coronavirus SARS-CoV-2 is a novel strain of coronaviruses that have not yet been discovered in humans. In more severe cases, this illness may result in mortality, renal failure, severe acute respiratory syndrome, pneumonia, and other complications (WHO, 2019).

Chinese health officials in Wuhan City reported the first incidence of the new coronavirus severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in December 2019. The Middle East respiratory syndrome and severe acute respiratory syndrome are two diseases that can be brought on by the coronavirus family of viruses (Mayo, 2020). The COVID-19 infection has a wide clinical spectrum, ranging from minimal symptoms to severe pneumonia. In one study, 40–50% of COVID-19 patients did not exhibit any symptoms (Verity et al., 2020). Other patients experienced fever, body aches, nausea, or diarrhoea typically 2 to 14 days after virus exposure (CDC, 2020). Only 14% of all infections during COVID-19's initial phase in China (10–23 January 2020) were confirmed.

On February 6, 2020, there were a total of 31,161 confirmed cases, including 636 fatalities, on the Chinese mainland; 22,112 confirmed cases, including 618 fatalities; and 11,618 confirmed cases, including 478 fatalities; in Hubei province. Numerous interventions and the spread of COVID-19 have had a tremendously detrimental effect on people's daily lives and societal norms. Different levels of closures and traffic restrictions have been implemented in cities throughout China's Hubei Province (Chan et al.2020).

In China, Europe, America, and Africa, the coronavirus disease 2019 (COVID-19) has caused high morbidity and mortality rates, resulting in unprecedented public health crises around the globe. The World Health Organisation (WHO) classified COVID-19 a global pandemic on March 11, 2020.

A new coronavirus known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the cause of COVID-19. After SARS-CoV in 2002 and the Middle East respiratory syndrome coronavirus (MERSCoV) in 2012, SARS-CoV-2 is regarded as the third zoonotic human coronavirus to emerge in the twenty-first century.

Nigeria, a West African nation of around 207 million people, reported its first COVID-19 case on February 27, 2020 (NCDC, 2020), and as of March 30, 2020 (22:00 WAT), 131 people had contracted the virus. Eight recoveries in all and two fatalities. The state of Lagos in Nigeria has the most infected residents, followed by Abuja, the nation's capital.  Currently, the country's major cities are under lockdown (Mbah F, 2020), and entry flights from nations with more than 1000 cases are prohibited (Mbah F, 2020).

In actuality, there are a lot of pressing concerns regarding COVID-19's proliferation. How many people will contract the illness tomorrow?

When will the infection rate reach its turning point? How many people will contract the disease during the busiest time? Can the COVID-19 be adequately controlled by current interventions?  What mathematical tools are at our disposal to help us resolve these issues? Since the COVID-19 is a brand-new coronavirus that was only identified in December 2019, there is still a lack of information about the outbreak, and medical interventions like clinical trials are still in a challenging exploratory phase (Chan et al., 2020).

There are still issues to be resolved regarding the effectiveness of the current emergency response, how to allocate medical resources more scientifically in the future, and other issues because it has been challenging to directly apply epidemic data to mathematical models that are already in use.  One of the infectious viruses in the globe is COVID-19. The World Health Organisation (WHO) estimates that there are at least 26 million COVID-19 infections worldwide and at least one million deaths, 30% of which occur in Africa, are recorded every few months. Understanding how a virus spreads, how to prevent it from happening, and how to forecast when an outbreak will occur are all crucial. In developing nations, the spread of several vector-borne viruses has also increased due to population expansion. The majority of COVID-19 mathematical modelling took asymptomatic infected and interacting peoples into account when predicting how the virus would spread, however in this research, tracing and partial Recovery will be taken into account.

VI. DISCUSSION OF RESULTS

Figure 1: is the graph of Susceptible Individuals Against Time for Different Contact Rate. It is observed that the population susceptible individual decreases as the rate of the Contact Rate increases.

Figure 2: is the graph of Exposed Individuals Against Time for Different Contact Rate. It is observed that the population of Exposed individuals increases as the Contact Rate increases.

Figure 3: is the graph of Infectious Symptomatic Against Time for Different Transmission rate after incubation period and transferred to symptomatic infected class. It is observed that the population Infectious Symptomatic individuals increase as the transmission rate after incubation period and transferred to symptomatic infected class increase.

Figure 4: is the graph of Quarantined Individuals Against Time at Different Hospitality rate of quarantined individuals and transferred to hospitality class. It is observed that the population of the quarantined individuals increases as the hospitality rate of quarantined individuals and transferred to hospitality class increases.

Figure 5: is the graph of Hospitality Individuals Against Time at Different Hospitality rate of quarantined individuals and transferred to hospitality class in Humans. It is observed that the population of the hospitality individuals decreases as the hospitality rate of quarantined individuals and transferred to hospitality class in humans increases.

Figure 6: is the graph of Infectious Asymptomatic Individuals Against Time at Different Transmission rate after incubation period and transferred to asymptomatic infected class. It is observed that the population of the infectious asymptomatic individuals increases as the transmission rate after incubation period and transferred to asymptomatic infected class rates increases.

Figure 7: is the graph of Recovered Individuals Against Time at Different Recovery rate of symptomatic infected individuals and transferred to recovery class. It is observed that the population of the recovery individuals increases as the recovery rate of symptomatic infected individuals and transferred to recovery class rates increases.

Conclusion

In this research paper, a mathematical model for the transmission dynamic of COVID-19 with quarantine and hospitality treatment in Nigeria was developed and analyzed in this study. The Disease Free State (DFE) was analyzed for stability and it revealed that it is stable. The Reproduction number was analyzed and the result shows the stability of the disease, which implies that the disease would be wiped out if vaccination is used as a control parameter. COVID-19 eradication needs systematic thinking, effective hospital isolation, and effective COVID-19 drug and vaccination. The desired eradication deadline based on our models can determine the demand of the three weapons against COVID-19 virus. It is recommended that the model shows that the spread of COVID-19 infection depends largely on the contact rate, hence the NCDC and Hospitals should emphasize on the improvement in early detection of COVID-19 infection cases by developing strategies to improve the rate of testing so that transmission rate can be minimized. The Government should improve on sensitization measures in order to make individuals fully aware of the virus potency and also encourage them to be generally available for testing, infectious individuals should be isolated and treated immediately. And It is recommended that the government strictly enforces the use of hand sanitizers, nose masks and adherence to social distancing. This would enable the reduction to the exposure of the populace to the virus and turn reduces the overcrowding of the isolation centres and Hospitals.

References

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Copyright

Copyright © 2023 Adedayo O.A, Sunday L. A., Ugwu U.C, Akande S. A., Muhammed, I., Job. O.S., Adebayo, O.J. , Tiamiyu. A.T.. 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.