Mathematical analysis of COVID-19 by using SIR model with convex incidence rate

Din, Rahim Ud; Algehyne, Ebrahem A.

doi:10.1016/j.rinp.2021.103970

Cited by 46 publications

(33 citation statements)

References 20 publications

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“…In Section 4.5, we will consider the use of some secondary parameters to overcome this issue. 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 3, 6, 3, 8, 10, 10, 17, 16,24,19,21,20,27,22,37,20,29,16,34,35,29,26,35,34,31,32,32,30,28,30,27,21,27,23,35,34,26,23,25,20,25,16,18,16,20,20,11,15,16,9,12,9,9,19,12,9,6,13,15,…”

Section: Data and Parameter Estimationmentioning

confidence: 99%

“…The qualitative analysis of a system of ODE of the SIR type model can shed light on the characteristic features of the evolution of the variables, such as susceptible, infected, and recovered. Such a study is developed in [12] for a SIR model, in which the proportion of deaths caused by disease is not a variable and, having as additional parameters, the protection rate and the isolation rate; these parameters being non-estimable; due to the lack of data, the model is exploited with plausible given values for the parameters. The models proposed in [13] consider, besides the usual subpopulations in a SEIR type model ".…”

Section: Introductionmentioning

confidence: 99%

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The Multi-Compartment SI(RD) Model with Regime Switching: An Application to COVID-19 Pandemic

et al. 2021

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We study—with existence and unicity results—a variant of the SIR model for an infectious disease incorporating both the possibility of a death outcome—in a short period of time—and a regime switch that can account for the mitigation measures used to control the spreading of the infections, such as a total lockdown. This model is parametrised by three parameters: the basic reproduction number, the mortality rate of the infected, and the duration of the disease. We discuss a particular example of application to Portuguese COVID-19 data in two short periods just after the start of the epidemic in 4 March 2020, with the first two cases dated that day. We propose a simple and effective method for the estimation of the main parameters of the disease, namely, the basic reproduction number and the mortality rate of the infected. We correct these estimated values to take into account the asymptomatic non-diagnosed members of the population. We compare the outcome of the model in the cases of the existence, or not, of a regime switch, and under three different scenarios, with a remarkable agreement between model and data deaths in the case of our basis scenario. In a final short remark, we deal with the existence of symmetries for the proposed model.

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Section: Data and Parameter Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Multi-Compartment SI(RD) Model with Regime Switching: An Application to COVID-19 Pandemic

et al. 2021

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“…A system-theoretic approach is pursued in [33], where the resulting parameters are analyzed regarding the sensitivity and conditional local asymptotic stability of the equilibria is mathematically proven. In [34], the global stability is calculated using a Lyapunov function construction while the local stability is determined using a Jacobian. In [35], an interval predictor in combination with the SEIR model is proposed to predict the virus propagation in eight different countries.…”

Section: Literature Reviewmentioning

confidence: 99%

“…In fact, condition (31) alone is able to achieve the overall convergence if E and S converge faster than I does. Condition (34), on the other hand, is sufficient in case S is the slowest compartment to converge. The third condition (36) about S d is sufficient if both I and S converge faster than E. If E is the slowest compartment to converge, that is, in case I = 0 and S = S d , Equation (36) states the condition for convergence of the remaining compartment E. Depending on which state converges the slowest, in a mathematical sense it is enough to employ only one of the three sufficient conditions, but using all three (if possible) obviously speeds up convergence to our real-life goal.…”

Section: Analysis and Control Of The Advanced Speiqrd Modelmentioning

confidence: 99%

Extension of SEIR Compartmental Models for Constructive Lyapunov Control of COVID-19 and Analysis in Terms of Practical Stability

2021

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Due to the worldwide outbreak of COVID-19, many strategies and models have been put forward by researchers who intend to control the current situation with the given means. In particular, compartmental models are being used to model and analyze the COVID-19 dynamics of different considered populations as Susceptible, Exposed, Infected and Recovered compartments (SEIR). This study derives control-oriented compartmental models of the pandemic, together with constructive control laws based on the Lyapunov theory. The paper presents the derivation of new vaccination and quarantining strategies, found using compartmental models and design methods from the field of Lyapunov theory. The Lyapunov theory offers the possibility to track desired trajectories, guaranteeing the stability of the controlled system. Computer simulations aid to demonstrate the efficacy of the results. Stabilizing control laws are obtained and analyzed for multiple variants of the model. The stability, constructivity, and feasibility are proven for each Lyapunov-like function. Obtaining the proof of practical stability for the controlled system, several interesting system properties such as herd immunity are shown. On the basis of a generalized SEIR model and an extended variant with additional Protected and Quarantined compartments, control strategies are conceived by using two fundamental system inputs, vaccination and quarantine, whose influence on the system is a crucial part of the model. Simulation results prove that Lyapunov-based approaches yield effective control of the disease transmission.

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“…I denote infected population, who have fully developed the symptoms of COVID-19 and can spread the virus through contact with the susceptible population. The populations section who has fully recovered after the treatment and they have no symptoms of disease (free from the disease) is denoted by R. To respect was presented a discussed by different authors, among them, Yadava and Verma [4], Savioli et al [5], Carcione et al [6], Lopez and Rodo [7], Din and Algehyne [8], Cintra and Fontinele [9].…”

Section: Mathematical Modelingmentioning

confidence: 99%

Numerical Simulation of the Influence of Vaccines on Covid-19 Control: A Warning for Its Spread and Control

Pariona¹,

Pelotoni²

2021

IJSMR

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The goal of this study was to apply a modified susceptible-exposed-infectious-recovered (SEIR) compartmental mathematical model for prediction of COVID-19 epidemic dynamics, for the high and low pandemic case, which occurred during the year 2021 at State de Paraná Brazil and these results were compared. For this procedure, the model parameters using officially reported of State de Paraná Brazil were calibrate. As result the S (susceptible population) and E (exposed population) parameters decay as a function of time, being a very drastic drop for S and a slow decrease to E in high pandemic, however, the I (infected population) parameter rises and decays as a function of time, but, in a high pandemic, the tendency is to grow, nevertheless, the R (recovered population) parameter rises as a function of time, in low pandemics this parameter has a much higher growth behavior than in high pandemics, as expected. So, the numerical simulation is consistent with reality. This result is coherent with what is happening in the scenario in the different cities of the countries of the world. Among the advantages of the implemented model, it should be noted that despite the simplicity of the hypotheses, the adjustments obtained were quite accurate and the projections made do not differ much from those other more complex models. Our results could also provide useful suggestions for the prevention and control of the COVID-19 outbreaks in different countries and locations.

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Mathematical analysis of COVID-19 by using SIR model with convex incidence rate

Cited by 46 publications

References 20 publications

The Multi-Compartment SI(RD) Model with Regime Switching: An Application to COVID-19 Pandemic

The Multi-Compartment SI(RD) Model with Regime Switching: An Application to COVID-19 Pandemic

Extension of SEIR Compartmental Models for Constructive Lyapunov Control of COVID-19 and Analysis in Terms of Practical Stability

Numerical Simulation of the Influence of Vaccines on Covid-19 Control: A Warning for Its Spread and Control

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