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 ( R 0 ) was derived by using the next-generation matrix method, which shows that, when R 0 < 1 , the disease-free equilibrium is globally asymptotically stable whereas when R 0 > 1 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 R 0 . 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.

Mathematical modeling of vaccination as a control measure of stress to fight COVID-19 infections

“…This study aims to add a vaccination compartment to the epidemic model [21] , and obtain a new deterministic model with vaccination compartment, . The new model aims to investigate the effects of vaccination in reducing stress among the population, which will help them to build strong immune systems.…”

Mathematical Modeling and Analysis of COVID-19 Infection: Application to the Kingdom of Saudi Arabia Data

“…For the application of mathematical modeling to smart phone and image processing, we refer the readers to visit [11][12][13]. To learn more about mathematical models used to research infectious illnesses, and in particular to comprehend the COVID-19's dynamics, visit [14][15][16][17][18][19][20][21][22][23]. For instance, the work in [14] has included the lockdown in modeling coronavirus infection.…”

“…Also, they provided graphical results for possible elimination of the disease in Ethiopia. Te mathematical model is designed to incorporate the stress and tension assumptions in the study given in [20]. In [24], the authors considered a fractional model to study COVID-19 with the impact of vaccination.…”

Application of piecewise fractional differential equation to COVID-19 infection dynamics

“…A mathematical study established the results for the coronavirus infection by considering the Ethiopian cases in [21] . The impact of stress due to coronavirus infection has been modeled mathematically and discussed their effects in [22] . The authors considered a modified model to analyze the disease dynamics of the coronavirus infection by taking the real cases from Saudi Arabia [23] .…”