Mathematical Approach to Investigate Stress due to Control Measures to Curb COVID-19

Abstract

COVID-19 is a world pandemic that has affected and continues to affect the social lives of people. Due to its social and economic impact, different countries imposed preventive measures that are aimed at reducing the transmission of the disease. Such control measures include physical distancing, quarantine, hand-washing, travel and boarder restrictions, lockdown, and the use of hand sanitizers. Quarantine, out of the aforementioned control measures, is considered to be more stressful for people to manage. When people are stressed, their body immunity becomes weak, which leads to multiplying of coronavirus within the body. Therefore, a mathematical model consisting of six compartments, Susceptible-Exposed-Quarantine-Infectious-Hospitalized-Recovered (SEQIHR) was developed, aimed at showing the impact of stress on the transmission of COVID-19 disease. From the model formulated, the positivity, bounded region, existence, uniqueness of the solution, the model existence of free and endemic equilibrium points, and local and global stability were theoretically proved. The basic reproduction number ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:msub> <a:mrow> <a:mi>R</a:mi> </a:mrow> <a:mrow> <a:mn>0</a:mn> </a:mrow> </a:msub> </a:math> ) was derived by using the next-generation matrix method, which shows that, when <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:msub> <c:mrow> <c:mi>R</c:mi> </c:mrow> <c:mrow> <c:mn>0</c:mn> </c:mrow> </c:msub> <c:mo>&lt;</c:mo> <c:mn>1</c:mn> </c:math> , the disease-free equilibrium is globally asymptotically stable whereas when <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M3"> <e:msub> <e:mrow> <e:mi>R</e:mi> </e:mrow> <e:mrow> <e:mn>0</e:mn> </e:mrow> </e:msub> <e:mo>&gt;</e:mo> <e:mn>1</e:mn> </e:math> the endemic equilibrium is globally asymptotically stable. Moreover, the Partial Rank Correlation Coefficient (PRCC) method was used to study the correlation between model parameters and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" id="M4"> <g:msub> <g:mrow> <g:mi>R</g:mi> </g:mrow> <g:mrow> <g:mn>0</g:mn> </g:mrow> </g:msub> </g:math> . Numerically, the SEQIHR model was solved by using the Rung-Kutta fourth-order method, while the least square method was used for parameter identifiability. Furthermore, graphical presentation revealed that when the mental health of an individual is good, the body immunity becomes strong and hence minimizes the infection. Conclusively, the control parameters have a significant impact in reducing the transmission of COVID-19.