Dynamical study of an SIQR model with saturated incidence rate

Nirwani, Nidhi; Badshah, V. H.; Khandelwal, Rachana

doi:10.12988/nade.2016.51034

Cited by 3 publications

(2 citation statements)

References 8 publications

(7 reference statements)

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“…These diseases are typically toxic, which increases their activity in the proper circumstances, such as in the atmosphere, on the surface, within the water, and in the edible food. It is hard to estimate the natural fluctuations of disease having infections across the population, so qualitative and quantitative calculations may be valuable [3] .…”

Section: Introductionmentioning

confidence: 99%

Investigation of time-fractional SIQR Covid-19 mathematical model with fractal-fractional Mittage-Leffler kernel

Adnan¹,

Ali²,

Rahman³

et al. 2022

Alexandria Engineering Journal

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In this manuscript, we investigate a nonlinear SIQR pandemic model to study the behavior of covid-19 infectious diseases. The susceptible, infected, quarantine and recovered classes with fractal fractional Atangana-Baleanu-Caputo (ABC) derivative is studied. The non-integer order and fractal dimension in the proposed system lie between 0 and 1. The existence and uniqueness of the solution for the considered model are studied using fixed point theory, while Ulam-Hyers stability is applied to study the stability analysis of the proposed model. Further, the Adams-Bashforth numerical technique is applied to calculate an approximate solution of the model. It is observed that the analytical and numerical calculations for different fractional-order and fractal dimensions confirm better converging effects of the dynamics as compared to an integer order.

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Section: Introductionmentioning

confidence: 99%

Investigation of time-fractional SIQR Covid-19 mathematical model with fractal-fractional Mittage-Leffler kernel

Adnan¹,

Ali²,

Rahman³

et al. 2022

Alexandria Engineering Journal

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“…Afterwards Hethcote et al [11] analyzed six SIQS and SIQR models with bilinear, standard, or quarantine-adjusted incidence and found that a Hopf bifurcation might occur in the SIQR model with quarantine-adjusted incidence rate. Recently, Nirwani et al [12] considered a SIQR epidemic model with saturated incidence rate as follows:…”

Section: Introductionmentioning

confidence: 99%

Stationary Distribution and Extinction of a Stochastic SIQR Model with Saturated Incidence Rate

Zhang

Zhou

2019

Mathematical Problems in Engineering

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In this paper, we consider a stochastic SIQR epidemic model with saturated incidence rate. By constructing a proper Lyapunov function, we obtain the existence and uniqueness of positive solution for this SIQR model. Furthermore, we study the dynamical properties of this stochastic SIQR model; that is, (i) we establish the sufficient condition for the existence of ergodic stationary distribution of the model; (ii) we obtain the extinction of the disease under some conditions. At last, numerical simulations are introduced to illustrate our theoretical results.

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