Mathematical modeling and stability analysis of the COVID-19 with quarantine and isolation

Abstract

The present paper focuses on the modeling of the COVID-19 infection with the use of hospitalization, isolation and quarantine. Initially, we construct the model by spliting the entire population into different groups. We then rigorously analyze the model by presenting the necessary basic mathematical features including the feasible region and positivity of the problem solution. Further, we evaluate the model possible equilibria. The theoretical expression of the most important mathematical quantity of major public health interest called the basic reproduction number is presented. We are taking into account to study the disease free equilibrium by studying its local and global asymptotical analysis. We considering the cases of the COVID-19 infection of Pakistan population and find the parameters using the estimation with the help of nonlinear least square and have . Further, to determine the influence of the model parameters on disease dynamics we perform the sensitivity analysis. Simulations of the model are presented using estimated parameters and the impact of various non-pharmaceutical interventions on disease dynamics is shown with the help of graphical results. The graphical interpretation justify that the effective utilization of keeping the social-distancing, making the quarantine of people (or contact-tracing policy) and to make hospitalization of confirmed infected people that dramatically reduces the number of infected individuals (enhancing the quarantine or contact-tracing by 50% from its baseline reduces 84% in the predicted number of confirmed infected cases). Moreover, it is observed that without quarantine and hospitalization the scenario of the disease in Pakistan is very worse and the infected cases are raising rapidly. Therefore, the present study suggests that still, a proper and effective application of these non-pharmaceutical interventions are necessary to curtail or minimize the COVID-19 infection in Pakistan.

Discrete-time COVID-19 epidemic model with chaos, stability and bifurcation

“…For instance, Refs. [7] , [8] , [9] , [10] , [11] , [12] , [13] are quoted here few newly developed mathematical models regarding the COVID-19 pandemic. Refs.…”

“…Refs. [7] , [8] , [9] , [10] , [11] , [12] , [13] and more study show that various authors predict the case of this disease using mathematical models that represent systems of difference or differential equations. In addition, based on date analysis and mathematical analysis, authors have explored the effect of lockdown and medical resources on the COVID-19 transformation in Wuhan, China.…”

“… [11] have presented the graphical results which shows that human to human contact is the main cause of spread of the COVID-19 disease. For more recent studies regarding COVID-19 disease, we refer [12] , [13] and literature cited therein.…”

A Mathematical Evaluation of the Cost-Effectiveness of Self-Protection, Vaccination, and Disinfectant Spraying for COVID-19 Control

“…Using the Principle translates the COVID model (37) and its associated objective functional (38) into a problem of minimizing a Hamiltonian H, with respect to the controls u j ðtÞ, for j = 1 , 2, 3. The Hamiltonian for system (17) is given by; 2.…”

“…Their conclusion was based on the fact that the endemic equilibrium was globally asymptotically stable. Gu et al [17] proposed a mathematical model that primarily focused on isolation, quarantine, and hospitalization to study the transmission dynamics of the novel coronavirus epidemic. They exploited nonpharmaceutical intervention measures: social distancing, isolation, contact tracing, and quarantine to mitigate the spreading of the disease.…”