A New Mathematical Model of COVID-19 with Quarantine and Vaccination

Abstract

A mathematical model revealing the transmission mechanism of COVID-19 is produced and theoretically examined, which has helped us address the disease dynamics and treatment measures, such as vaccination for susceptible patients. The mathematical model containing the whole population was partitioned into six different compartments, represented by the SVEIQR model. Important properties of the model, such as the nonnegativity of solutions and their boundedness, are established. Furthermore, we calculated the basic reproduction number, which is an important parameter in infection models. The disease-free equilibrium solution of the model was determined to be locally and globally asymptotically stable. When the basic reproduction number R0 is less than one, the disease-free equilibrium point is locally asymptotically stable. To discover the approximative solution to the model, a general numerical approach based on the Haar collocation technique was developed. Using some real data, the sensitivity analysis of R0 was shown. We simulated the approximate results for various values of the quarantine and vaccination populations using Matlab to show the transmission dynamics of the Coronavirus-19 disease through graphs. The validation of the results by the Simulink software and numerical methods shows that our model and adopted methodology are appropriate and accurate and could be used for further predictions for COVID-19.

On the Analytical Solution of the Sirv-Model for the Temporal Evolution of Epidemics for General Time-Dependent Recovery, Infection and Vaccination Rates

“…greater than unity at all times. As both rates are semi-positive the condition (30) for no extrema in the rate of new infections is fulfilled if either the vaccination rate v(t) > a(t) is greater than the infection rate and/or the recovery rate µ(t) > a(t) is greater than the infection rate. For large enough values of k and b, so that k(τ) + b(τ) > 1, we have thus shown in Equation ( 27) that no extrema of the rate of new infections j(τ) occur at any reduced time τ ≥ 0.…”

“…A number of numerical studies to quantify the effect of vaccination campaigns are available in the literature [28][29][30][31][32] using generalized SIRV-model equations with additional compartments. In these works, the time dependence of individual compartment quantities such as I(t) and R(t) have been derived, but these quantities are not regularly observed and monitored during pandemic waves.…”

A fractional-order mathematical model for malaria and COVID-19 co-infection dynamics

“…The dynamical model study is used to examine key parameters, forecast future trends, and assess control methods to offer conclusive information for decision-making [10] . In recent times, a variety of mathematical models have been developed to investigate the transmission dynamics of COVID-19; for examples, see [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] and the references listed therein. Malaria mathematical models are also thoroughly examined in [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] and references are mentioned.…”

Mathematical Modeling of SARS-CoV-2 Transmission between Minks and Humans Considering New Variants and Mink Culling

“…A considerable number of scientific works have appeared that assess the epidemiological characteristics of COVID-19 in order to reduce its burden on public health (e.g., [ 26 , 27 , 28 , 29 , 30 ]). Rasmussen et al [ 31 ] developed an SEIRS model that included deaths outside of hospitals, as well as independent assessments of cases with and without symptoms, with varied immune memories.…”