A Mathematical Model of COVID-19 Pandemic: A Case Study of Bangkok, Thailand
Pakwan Riyapan, Sherif Eneye Shuaib, Arthit Intarasit
Abstract
In this study, we propose a new mathematical model and analyze it to understand the transmission dynamics of the COVID-19 pandemic in Bangkok, Thailand. It is divided into seven compartmental classes, namely, susceptible <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mfenced open="(" close=")"> <a:mrow> <a:mi>S</a:mi> </a:mrow> </a:mfenced> <a:mo>,</a:mo> </a:math> exposed <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M2"> <e:mfenced open="(" close=")"> <e:mrow> <e:mi>E</e:mi> </e:mrow> </e:mfenced> <e:mo>,</e:mo> </e:math> symptomatically infected <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" id="M3"> <i:mfenced open="(" close=")"> <i:mrow> <i:msub> <i:mrow> <i:mi>I</i:mi> </i:mrow> <i:mrow> <i:mi>s</i:mi> </i:mrow> </i:msub> </i:mrow> </i:mfenced> <i:mo>,</i:mo> </i:math> asymptomatically infected <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" id="M4"> <m:mfenced open="(" close=")"> <m:mrow> <m:msub> <m:mrow> <m:mi>I</m:mi> </m:mrow> <m:mrow> <m:mi>a</m:mi> </m:mrow> </m:msub> </m:mrow> </m:mfenced> <m:mo>,</m:mo> </m:math> quarantined <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" id="M5"> <q:mfenced open="(" close=")"> <q:mrow> <q:mi>Q</q:mi> </q:mrow> </q:mfenced> <q:mo>,</q:mo> </q:math> recovered <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" id="M6"> <u:mfenced open="(" close=")"> <u:mrow> <u:mi>R</u:mi> </u:mrow> </u:mfenced> <u:mo>,</u:mo> </u:math> and death <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" id="M7"> <y:mfenced open="(" close=")"> <y:mrow> <y:mi>D</y:mi> </y:mrow> </y:mfenced> </y:math> , respectively. The next-generation matrix approach was used to compute the basic reproduction number denoted as <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" id="M8"> <cb:msub> <cb:mrow> <cb:mi>R</cb:mi> </cb:mrow> <cb:mrow> <cb:mtext>cvd</cb:mtext> <cb:mn>19</cb:mn> </cb:mrow> </cb:msub> </cb:math> of the proposed model. The results show that the disease-free equilibrium is globally asymptotically stable if <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" id="M9"> <eb:msub> <eb:mrow> <eb:mi>R</eb:mi> </eb:mrow> <eb:mrow> <eb:mtext>cvd</eb:mtext> <eb:mn>19</eb:mn> </eb:mrow> </eb:msub> <eb:mo><</eb:mo> <eb:mn>1</eb:mn> </eb:math> . On the other hand, the global asymptotic stability of the endemic equilibrium occurs if <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" id="M10"> <gb:msub> <gb:mrow> <gb:mi>R</gb:mi> </gb:mrow> <gb:mrow> <gb:mtext>cvd</gb:mtext> <gb:mn>19</gb:mn> </gb:mrow> </gb:msub> <gb:mo>></gb:mo> <gb:mn>1</gb:mn> </gb:math> . The mathematical analysis of the model is supported using numerical simulations. Moreover, the model’s analysis and numerical results prove that the consistent use of face masks would go on a long way in reducing the COVID-19 pandemic.