ABSTRACT
COVID-19, since its
discovery in 2019, has posed a major health problem in the world. It is caused
by the SARS-CoV-2 virus and is transmitted via infected respiratory droplets
and contaminated surfaces. There is an urgent need to understand the
transmission characteristics of the virus in response to social interventions.
This is important to evaluate the overall impact of such programs in the
management of the disease. We seek to develop a mathematical model that
characterizes the transmission dynamics of COVID-19. The model analyzes the
impact of preventive practices on the spread of SARS-CoV-2 by incorporating
human behavior in modeling disease prevalence depending on contact rates for
direct and indirect transmissions and infectious host shedding. The model is
also applied to reported data from Wuhan and the state of Tennessee. Our
results imply that applying strategically created awareness programs to a geological
setting can eradicate COVID-19.
TABLE OF CONTENTS
CHAPTER ONE
INTRODUCTION
1.1 BACKGROUND
1.2
PROBLEM STATEMENT
1.3
OBJECTIVES
1.4 THESIS LAY OUT
CHAPTER TWO
LITERATURE REVIEW
2.1 THE SEIR MODEL
CHAPTER THREE
FORMULATION OF MODEL AND ANALYSIS
3.1 MODEL ANALYSIS
CHAPTER FOUR
EQUILIBRIUM
ANALYSIS
CHAPTER FIVE
NUMERICAL
SIMULATIONS AND RESULTS
CHAPTER SIX
CONCLUSION
6.1 RECOMMENDATIONS
REFERENCES
CHAPTER
ONE
INTRODUCTION
1.1 BACKGROUND
At present, the
world faces a pandemic brought about by the SARS-CoV-2 virus. The severe acute
respiratory syndrome coronavirus 2 (SARS-CoV-2), a spike protein virus is the
causative agent of the widespread coronavirus disease. It is known to belong to
a broad family of viruses known as the coronaviruses. The first severe illness
caused by a coronavirus is the 2003 Severe Acute Respiratory Syndrome (SARS)
pandemic which started in China. A second flare-up was the Middle East
Respiratory Syndrome (MERS) which was discovered in 2012 in Saudi Arabia
[1].The coronavirus disease 2019 was first declared a Public Health Emergency
of International Concerns by the World Health Organization on January 30, 2020
[2] and finally a pandemic on March 11, 2020 [1] since the disease was
determined to be a public health risk to all nations through the international
spread of diseases. The disease is mostly transmitted through contact with
infected respiratory droplets from coughs, sneezes and speech[3, 4]. Further
research has shown that the disease could be transmitted via airborne
transmission [5]. Contact with contaminated surfaces is also a known risk of
infection. Some confirmed symptoms of COVID-19 known to appear after 2-14 days of
exposure are coughs, fever, windedness, muscle pain, loss of smell, diarrhea
sore throat, fatigue and running nose.
As at
January 11, 2021 there were 680,908 new infected cases recorded worldwide with 222,921 cases in the USA, 4,255
cases in the state of Tennessee and 134 cases in China [6, 7]. A total of
11,416 deaths were recorded worldwide [6]. The American continent currently has
over 40million confirmed cases with the USA leading all other countries in this
region and the world with about 25million confirmed cases. While there seem to
be a rapidly increasing number confirmed cases, there are also several
intervention programs created to combat the current characteristics of the
disease. These programs include the current vaccination programs which begun in
the last quarter of 2020 [8] , use of disinfectants, social distancing, public
health education, use of nose masks and other protective shields, isolation of
infected/exposed persons, funding of COVID-19 projects etc.
Awareness programs
as defined in this project comprises all actions and measures aimed at the
prevention and treatment of COVID-19. These range from individual behavioral
change to organizational and worldwide interventions. Social distancing is one
of the most utilized COVID-19 preventive strategies. It is observed by limiting
face-to-face interactions by remaining in any event 6 feet from others and
maintaining a strategic distance from swarmed places. This intervention has
resulted in the lockdown of several countries and the closing of organizations
such as schools, churches and businesses. Though these interventions appear to
be drastic as they have negative impact on productivity, virtual alternatives
for social gatherings, meet-ups and workplaces have been discovered. Thus,
resulting in the booming economies of the virtual networking industry.
Vaccinations is another ongoing major preventive strategy. Presently,
86,452,579 doses of the various vaccines have been administered worldwide with
US administering about 32% of the doses.[9] Below are the vaccines currently
available with their efficiencies and approvals discussed.
• The
Pfizer/BioNtech vaccine is one of the popular administered vaccines known for
its high efficiency against the SARS CoV-2 virus which is 95%. It was approved
for emergency use in USA, UK, Canada and the EU in December 2020. Storage and
transportation of the vaccine requires a temperature of -70oC.[10]
• Moderna-
this vaccine like the Pfizer vaccine has a high efficacy rate of 94.1% as they
both use a new vaccine approach involving a messenger RNA. It has been approved
for use in the USA, Canada, UK and the EU. Vaccine can be stored at 2-8oC. [9]
• AstraZeneca/Oxford
vaccine was approved in India on January 2, 2021 and the UK on Dec 30, 2020 for
emergency use. With clinical trial size of 65,000 people, results show that the
vaccine is 70% effective at preventing laboratory confirmed COVID-19.[8, 11]
• The
Novavax vaccine trials currently show 89.3% efficacy against the SARS CoV-2
virus.
Initial trial phases were conducted in South Africa and the
UK whiles further trials are been conducted in the USA and Mexico. This vaccine
is yet to receive approvals as it is in its trial stage. [9]
• The
Johnson & Johnson vaccine is the easiest to store and transport as it
requires standard refrigeration out of the leading vaccines. The single-dose
vaccine’s efficacy rate has currently dropped from 72% in the United States to
66% in Latin America and 57% in South Africa, where a profoundly infectious
variation is driving most cases. The vaccine is yet to receive approvals as it
is presently in its trial stage. [12]
• Sinovac
Biotech vaccine is the least effective vaccine with trial-based efficacy rate
of
50.38% in Brazil. Though it has a
low efficacy rate, it has been approved in Indonesia and Turkey where is known
to have higher efficacy rates of 65.3% and 91.25% respectively. Vaccination
requires two doses whiles storage and transportation can be done in standard
refrigeration conditions. [9, 11]
• Sinopharm-
it was approved in China on Dec 31st, 2020 for general use. Clinical trials
conducted on the vaccine shows 79% efficiency. It is currently been
administered in Morocco, China, Hungary and the United Arab Emirates.[9, 11]
• The
CanSino Biologics’ vaccine utilizes an innocuous cold virus to transfer its
genetic payload. Only a shot of the vaccine is required. Though its efficacy is
yet to be determined due to delay in clinical trials, it was cleared in June
29, 2020 for China military use as it was the first COVID-19 vaccine to enter
clinical trials.[9]
Notable side effects of these
vaccines are pain at the injection site, tiredness, headache, fever and chills.
1.4
PROBLEM STATEMENT
The 2019
coronavirus disease is a current health problem which was first discovered in
Wuhan, China. Due to its high mortality and infection rates, and the lack of
potent treatment available, it has claimed over 2.6million lives with over
118million infected cases worldwide.
Since its emergence, there has
been a rise on intervention programs created with the aim of mitigating its
transmission. However the extent of impact of these intervention programs is
unknown. To date, there is no mathematical model that predicts the efficiency
of these programs. So, the impact of the awareness programs is hard to analyze
especially on a global scale. Thus, there is an urgent need for a
fit-for-purpose model to probe into the impact of these awareness programs.
1.5
OBJECTIVES
The study was designed to achieve the following;
• To
formulate a mathematical model that measures the impact of current awareness
programs created in efforts of minimizing the spread of COVID-19.
• Analyze
the stability of the model developed at the Disease-Free Equilibrium and
Endemic Equilibrium.
• To
develop a model to accurately predict the spread of COVID-19.
• Investigate
and predict the transmission dynamics of COVID-19 in Wuhan, China and the state
of Tennessee.
1.4 THESIS
LAY OUT
Chapter
one of the study gives a detailed background of the study, the problem
statement, objectives, and thesis lay out. In Chapter 2, we shall put a
pertinent related literature on COVID-19 and the SEIR models. These include
publications, journals and seminars. Chapter 3 discusses the model description,
model analysis and equilibrium analysis of the model. Chapter 4 is devoted to
numerical simulations and results. Chapter 5, the final chapter presents the
discussion of the results, conclusions, and recommendations for further
studies.
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