Dynamics of an SEIR epidemic model with nonlinear incidence and treatment rates

Upadhyay, Ranjit Kumar; Pal, Ashok; Kumari, Sangeeta; Roy, Parimita

doi:10.1007/s11071-019-04926-6

Cited by 78 publications

(38 citation statements)

References 53 publications

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“…Meanwhile, during the transmission of infectious diseases, susceptible people come into contact with infected people and are infected with a probability. A great deal of evidence shows that incidence rates are an important method for describing infectious diseases [ 9 – 11 ]. Bilinear incidence rate is often used in the modeling process of COVID-19 because of its high infectivity.…”

Section: Introductionmentioning

confidence: 99%

A fractional-order SEIHDR model for COVID-19 with inter-city networked coupling effects

Chen

et al. 2020

Nonlinear Dyn

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In the end of 2019, a new type of coronavirus first appeared in Wuhan. Through the real-data of COVID-19 from January 23 to March 18, 2020, this paper proposes a fractional SEIHDR model based on the coupling effect of inter-city networks. At the same time, the proposed model considers the mortality rates (exposure, infection and hospitalization) and the infectivity of individuals during the incubation period. By applying the least squares method and predictioncorrection method, the proposed system is fitted and predicted based on the real-data from January 23 to March 18 − m where m represents predict days. Compared with the integer system, the non-network fractional model has been verified and can better fit the data of Beijing, Shanghai, Wuhan and Huanggang. Compared with the no-network case, results show that the proposed system with inter-city network may not be able to better describe the spread of disease in China due to the lock and isolation measures, but this may have a significant impact on countries that has no closure measures. Meanwhile, the proposed model is more

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Section: Introductionmentioning

confidence: 99%

A fractional-order SEIHDR model for COVID-19 with inter-city networked coupling effects

Chen

et al. 2020

Nonlinear Dyn

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“…Values for α and ε were explored to understand their effects on the SEIR model as quarantine is lifted, Q(t) = 1 . Parameters α and ε, which correspond to β and γ in Upadhyay et al (2019), are the social awareness rate among susceptibles and the magnitude of interference within individuals in the infectious population, respectively. In practice, α and ε each represent a combination of behavioral factors (e.g., social distancing, wearing of masks, and handwashing) and disease-resistance factors (e.g., genetics, nutrition, exercise and overall health status) that disrupt disease transmission, with α and ε applying to S and I, respectively.…”

Section: Discussionmentioning

confidence: 99%

“…Recent studies (Zhou and Cui, 2011; Upadhyay et al, 2019) have developed models for epidemiology and virus dynamics with the Crowley-Martin incidence rate . Here, we combined the Q-SEIR epidemiology model with the Crowley-Martin incidence rate (non-linear).…”

Section: Methodsmentioning

confidence: 99%

Protection after Quarantine: Insights from a Q-SEIR Model with Nonlinear Incidence Rates Applied to COVID-19

Je²,

Castro

et al. 2020

Preprint

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Community quarantine has been resorted to by various governments to address the current COVID-19 pandemic; however, this is not the only non-therapeutic method of effectively controlling the spread of the infection. We study an SEIR model with nonlinear incidence rates, and introduce two parameters, α and ε, which mimics the effect of quarantine (Q). We compare this with the Q-SEIR model, recently developed, and demonstrate the control of COVID-19 without the stringent conditions of community quarantine. We analyzed the sensitivity and elasticity indices of the parameters with respect to the reproduction number. Results suggest that a control strategy that involves maximizing α and ε is likely to be successful, although quarantine is still more effective in limiting the spread of the virus. Release from quarantine depends on continuance and strict adherence to recommended social and health-promoting behaviors. Furthermore, maximizing α and ε is equivalent to a 50% successful quarantine in disease-free equilibrium (DFE). This model reduced the infectious in Quezon City by 3.45% and Iloilo Province by 3.88%; however, earlier peaking by nine and 17 days, respectively, when compared with the results of Q-SEIR.

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“…There is some debate about the role of pre-symptomatic transmission (occurring from exposed cases) and asymptomatic infected cases for coronavirus, which are not include in the present model [40] , [44] . Here, a compartmental epidemiological model is formulated, followed by the traditional SEIR model, to illustrate the spread and clinical progression of COVID-19 [11] , [39] , [50] , [69] . It is important to track the different clinical outcomes of infection, since they require different level of healthcare resources to care for and may be tested and isolated at different rates [4] , [26] , [48] , [63] .…”

Section: Introductionmentioning

confidence: 99%

COVID-19: Perturbation dynamics resulting chaos to stable with seasonality transmission

Batabyal

2021

Chaos, Solitons & Fractals

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The outbreak of coronavirus is spreading at an unprecedented rate to the human populations and taking several thousands of life all over the globe. In this paper, an extension of the well-known susceptible-exposed-infected-recovered (SEIR) family of compartmental model has been introduced with seasonality transmission of SARS-CoV-2. The stability analysis of the coronavirus depends on changing of its basic reproductive ratio. The progress rate of the virus in critical infected cases and the recovery rate have major roles to control this epidemic. Selecting the appropriate critical parameter from the Turing domain, the stability properties of existing patterns is obtained. The outcomes of theoretical studies, which are illustrated via Hopf bifurcation and Turing instabilities, yield the result of numerical simulations around the critical parameter to forecast on controlling this fatal disease. Globally existing solutions of the model has been studied by introducing Tikhonov regularization. The impact of social distancing, lockdown of the country, self-isolation, home quarantine and the wariness of global public health system have significant influence on the parameters of the model system that can alter the effect of recovery rates, mortality rates and active contaminated cases with the progression of time in the real world.

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Dynamics of an SEIR epidemic model with nonlinear incidence and treatment rates

Cited by 78 publications

References 53 publications

A fractional-order SEIHDR model for COVID-19 with inter-city networked coupling effects

A fractional-order SEIHDR model for COVID-19 with inter-city networked coupling effects

Protection after Quarantine: Insights from a Q-SEIR Model with Nonlinear Incidence Rates Applied to COVID-19

COVID-19: Perturbation dynamics resulting chaos to stable with seasonality transmission

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