Complex dynamics of a fractional-order SIR system in the context of COVID-19

Majee, Suvankar; Adak, Sayani; Jana, Soovoojeet; Mandal, Manotosh; Kar, Tapan Kumar

doi:10.1007/s12190-021-01681-z

Cited by 20 publications

(9 citation statements)

References 33 publications

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“…The dynamics of COVID-19 have been extensively studied since the beginning of the pandemic (see e.g., [1][2][3][4][5][6]). As with many natural systems, the dynamics of COVID-19 are complex with non-linear second order and higher effects playing a role in the dynamics of transmission and fatality [7][8][9][10]. In particular, factors such as age, race, population density, socioeconomic status, and income inequality are all associated with [11][12][13][14][15] COVID-19 mortality.…”

Section: Introductionmentioning

confidence: 99%

Race, employment, and the pandemic: An exploration of covariate explanations of COVID-19 case fatality rate variance

Griffin¹,

Block

Silverman

et al. 2023

PLoS ONE

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We derive a simple asymptotic approximation for the long-run case fatality rate of COVID-19 (alpha and delta variants) and show that these estimations are highly correlated to the interaction between US State median age and projected US unemployment rate (Adj. r2 = 60%). We contrast this to the high level of correlation between point (instantaneous) estimates of per state case fatality rates and the interaction of median age, population density and current unemployment rates (Adj. r2 = 50.2%). To determine whether this is caused by a “race effect,” we then analyze unemployment, race, median age and population density across US states and show that adding the interaction of African American population and unemployment explains 53.5% of the variance in COVID case fatality rates for the alpha and delta variants when considering instantaneous case fatality rate. Interestingly, when the asymptotic case fatality rate is used, the dependence on the African American population disappears, which is consistent with the fact that in the long-run COVID does not discriminate on race, but may discriminate on access to medical care which is highly correlated to employment in the US. The results provide further evidence of the impact inequality can have on case fatality rates in COVID-19 and the impact complex social, health and economic factors can have on patient survival.

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Section: Introductionmentioning

confidence: 99%

Race, employment, and the pandemic: An exploration of covariate explanations of COVID-19 case fatality rate variance

Griffin¹,

Block

Silverman

et al. 2023

PLoS ONE

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“…Our investigations of the Delta and Omicron epidemics in the California/Mexico region illustrate the complex interplay and the multiplicity of viral and structural factors that need to be considered to limit viral spread, even as vaccination is reducing disease burden. While our phylodynamic analysis provided insight into patterns of viral introductions into the region and migration across the border, future analysis using compartmental ordinary differential equation models could provide additional insight on how changes in transmission rates, vaccination rates and flow across the border could impact these and future SARS-CoV-2 variant epidemics in the border region [ 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 ]. Given the rapid observed diffusion of Delta, and then Omicron, as the infectiousness of successive variants increases, containment strategies would need to be increasingly extreme to reduce spread.…”

Section: Discussionmentioning

confidence: 99%

Comparative Dynamics of Delta and Omicron SARS-CoV-2 Variants across and between California and Mexico

Mehta

Smith

Boukadida

et al. 2022

Viruses

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Evolutionary analysis using viral sequence data can elucidate the epidemiology of transmission. Using publicly available SARS-CoV-2 sequence and epidemiological data, we developed discrete phylogeographic models to interrogate the emergence and dispersal of the Delta and Omicron variants in 2021 between and across California and Mexico. External introductions of Delta and Omicron in the region peaked in early July (2021-07-10 [95% CI: 2021-04-20, 2021-11-01]) and mid-December (2021-12-15 [95% CI: 2021-11-14, 2022-01-09]), respectively, 3 months and 2 weeks after first detection. These repeated introductions coincided with domestic migration events with no evidence of a unique transmission hub. The spread of Omicron was most consistent with gravity centric patterns within Mexico. While cross-border events accounted for only 5.1% [95% CI: 4.3–6] of all Delta migration events, they accounted for 20.6% [95% CI: 12.4–29] of Omicron movements, paralleling the increase in international travel observed in late 2021. Our investigations of the Delta and Omicron epidemics in the California/Mexico region illustrate the complex interplay and the multiplicity of viral and structural factors that need to be considered to limit viral spread, even as vaccination is reducing disease burden. Understanding viral transmission patterns may help intra-governmental responses to viral epidemics.

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“…This enhanced modeling capability allows for a more accurate portrayal of disease dynamics, contributing to improved understanding, diagnosis, and treatment strategies [28,29]. Fractional operators provide a more nuanced and realistic approach to modeling biological systems, offering more accurate predictions and insights for infectious diseases [30,31]. It is evident that fractional calculus is used in a variety of fields, including chemistry, economics, biology and physics [32,33].…”

Section: Introductionmentioning

confidence: 99%

Modeling the dynamical behavior of the interaction of T-cells and human immunodeficiency virus with saturated incidence

Boulaaras,

Jan,

Khan

et al. 2024

Commun. Theor. Phys.

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In the last forty years, the rise of HIV has undoubtedly become a major concern in the field of public health, imposing significant economic burdens on affected regions. Consequently, it becomes imperative to undertake comprehensive investigations into themechanisms governing the dissemination of HIV within the human body. In this work, we devise a mathematical model that elucidates the intricate interplay between CD4+ Tcells and viruses of HIV, employing the principles of fractional calculus. The productionrate of CD4+ T-cells, like other immune cells depends on factors like age, health status, and the presence of infections or diseases. Therefore, we incorporate a variable source term in the dynamics of HIV infection with saturated incidence rate to enhance the precision of our findings. We introduce the fundamental concepts of fractional operators as a means of scrutinizing the proposed HIV model. To facilitate a deeper understanding of our system, we represent an iterative scheme that elucidates the trajectories of solution pathways of the system. We present the time series analysis of our model through numerical findings to conceptualize and understand the key factors of the system. In addition to this, we present the phase portrait and the oscillatory behavior of the systemwith the variation of different input parameters. These information can be utilized to predict the long-term behavior of the system, including whether it will converge to a steady state or exhibit periodic or chaotic oscillations.

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Complex dynamics of a fractional-order SIR system in the context of COVID-19

Cited by 20 publications

References 33 publications

Race, employment, and the pandemic: An exploration of covariate explanations of COVID-19 case fatality rate variance

Race, employment, and the pandemic: An exploration of covariate explanations of COVID-19 case fatality rate variance

Comparative Dynamics of Delta and Omicron SARS-CoV-2 Variants across and between California and Mexico

Modeling the dynamical behavior of the interaction of T-cells and human immunodeficiency virus with saturated incidence

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