Modeling and stability analysis of the spread of novel coronavirus disease COVID-19

2021 ◽  
pp. 2150035
Author(s):  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
D. Abraham Vianny ◽  
Mary Jacintha ◽  
Fatma Bozkurt Yousef
Keyword(s):  
Fractional Order ◽  
Disease Transmission ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Basic Reproductive Number ◽  
Phase Portraits ◽  
Transmission Model ◽  
Reproductive Number ◽  
Discrete Version ◽  
Novel Coronavirus

Towards the end of 2019, the world witnessed the outbreak of Severe Acute Respiratory Syndrome Coronavirus-2 (COVID-19), a new strain of coronavirus that was unidentified in humans previously. In this paper, a new fractional-order Susceptible–Exposed–Infected–Hospitalized–Recovered (SEIHR) model is formulated for COVID-19, where the population is infected due to human transmission. The fractional-order discrete version of the model is obtained by the process of discretization and the basic reproductive number is calculated with the next-generation matrix approach. All equilibrium points related to the disease transmission model are then computed. Further, sufficient conditions to investigate all possible equilibria of the model are established in terms of the basic reproduction number (local stability) and are supported with time series, phase portraits and bifurcation diagrams. Finally, numerical simulations are provided to demonstrate the theoretical findings.

scholarly journals Differential effects of intervention timing on COVID-19 spread in the United States

2020 ◽  
Vol 6 (49) ◽  
pp. eabd6370 ◽  
Author(s):  
Sen Pei ◽  
Sasikiran Kandula ◽  
Jeffrey Shaman
Keyword(s):  
United States ◽  
Disease Transmission ◽  
Human Mobility ◽  
The United States ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Transmission Model ◽  
Reproductive Number ◽  
Mobility Data ◽  
Nonpharmaceutical Interventions

Assessing the effects of early nonpharmaceutical interventions on coronavirus disease 2019 (COVID-19) spread is crucial for understanding and planning future control measures to combat the pandemic. We use observations of reported infections and deaths, human mobility data, and a metapopulation transmission model to quantify changes in disease transmission rates in U.S. counties from 15 March to 3 May 2020. We find that marked, asynchronous reductions of the basic reproductive number occurred throughout the United States in association with social distancing and other control measures. Counterfactual simulations indicate that, had these same measures been implemented 1 to 2 weeks earlier, substantial cases and deaths could have been averted and that delayed responses to future increased incidence will facilitate a stronger rebound of infections and death. Our findings underscore the importance of early intervention and aggressive control in combatting the COVID-19 pandemic.

scholarly journals Stability Analysis and Clinic Phenomenon Simulation of a Fractional-Order HBV Infection Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yongmei Su ◽  
Sinuo Liu ◽  
Shurui Song ◽  
Xiaoke Li ◽  
Yongan Ye
Keyword(s):  
Fractional Order ◽  
Equilibrium Points ◽  
Mass Action ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Infection Model ◽  
Order Model ◽  
Infected Cells ◽  
Set Up ◽  
Hbv Model

In this paper, a fractional-order HBV model was set up based on standard mass action incidences and quasisteady assumption. The basic reproductive number R0 and the cytotoxic T lymphocytes’ immune-response reproductive number R1 were derived. There were three equilibrium points of the model, and stable analysis of each equilibrium point was given with corresponding hypothesis about R0 or R1. Some numerical simulations were also given based on HBeAg clinical data, and the simulation showed that there existed positive logarithmic correlation between the number of infected cells and HBeAg, which was consistent with the clinical facts. The simulation also showed that the clinical individual differences should be reflected by the fractional-order model.

Dynamics of a Food Chain Model with Two Infected Predators

2021 ◽  
Vol 31 (02) ◽  
pp. 2150019
Author(s):  
Xin-You Meng ◽  
Ni-Ni Qin ◽  
Hai-Feng Huo
Keyword(s):  
Food Chain ◽  
Disease Transmission ◽  
Sufficient Conditions ◽  
Geometric Approach ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Chain Model ◽  
Number Formula ◽  
Manifold Theory ◽  
Food Chain Model

In this paper, the dynamics of a three-species food chain model with two predators infected by an infectious disease is investigated. The positivity and boundedness of the system, the existence of the equilibria and the basic reproductive number are given. Sufficient conditions for the local stability of all equilibria are obtained by analyzing the corresponding characteristic equations. By constructing suitable Lyapunov functions and taking the geometric approach, the global stability of all equilibria is proved. According to the center manifold theory, this model undergoes the phenomenon of backward and forward bifurcations in a certain range of the basic reproductive number [Formula: see text]. By taking the disease transmission coefficient of predator as bifurcation parameter, Hopf bifurcation emerges in the neighborhood of the endemic equilibrium. Furthermore, the optimal control of the disease is discussed by the Pontryagin’s maximum principle. Various simulations are given to support the analytical results.

scholarly journals Behavior of a Discrete Fractional Order SIR Epidemic Model

2018 ◽  
Vol 7 (4.10) ◽  
pp. 675 ◽  
Author(s):  
A. George Maria Selvam ◽  
D. Abraham Vianny
Keyword(s):  
Equilibrium Point ◽  
Fractional Order ◽  
Epidemic Model ◽  
Dynamical Behavior ◽  
Basic Reproductive Number ◽  
Phase Portraits ◽  
Reproductive Number ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Parameter Values

In this paper we investigate the dynamical behavior of a SIR epidemic model of fractional order. Disease Free Equilibrium point, Endemic Equilibrium point and basic reproductive number are obtained. Time series plots, phase portraits and bifurcation diagrams are presented for suitable parameter values. Also some numerical examples are provided to illustrate the dynamics of the system.  

scholarly journals Stability analysis of fractional order SEIR model for malaria disease in Khyber Pakhtunkhwa

2021 ◽  
Vol 54 (1) ◽  
pp. 326-334
Author(s):  
Noor Badshah ◽  
Haji Akbar
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Next Generation ◽  
Seir Model ◽  
Khyber Pakhtunkhwa

Abstract We discussed stability analysis of susceptible-exposed-infectious-removed (SEIR) model for malaria disease through fractional order and check that malaria is epidemic or endemic in Khyber Pakhtunkhwa (Pakistan). We show that the model has two types of equilibrium points and check their stability through Routh-Hurwitz criterion. We find basic reproductive number using next-generation method. Finally, numerical simulations are also presented.

scholarly journals Novel coronavirus 2019-nCoV: early estimation of epidemiological parameters and epidemic predictions

2020 ◽  
Author(s):  
Jonathan M. Read ◽  
Jessica R.E. Bridgen ◽  
Derek A.T. Cummings ◽  
Antonia Ho ◽  
Chris P. Jewell
Keyword(s):  
Large Scale ◽  
Likelihood Function ◽  
Restriction Analysis ◽  
Basic Reproductive Number ◽  
Transmission Model ◽  
Reproductive Number ◽  
List Type ◽  
Novel Coronavirus ◽  
Scale Control

AbstractSince first identified, the epidemic scale of the recently emerged novel coronavirus (2019-nCoV) in Wuhan, China, has increased rapidly, with cases arising across China and other countries and regions. using a transmission model, we estimate a basic reproductive number of 3.11 (95%CI, 2.39–4.13); 58–76% of transmissions must be prevented to stop increasing; Wuhan case ascertainment of 5.0% (3.6–7.4); 21022 (11090–33490) total infections in Wuhan 1 to 22 January.Changes to previous versioncase data updated to include 22 Jan 2020; we did not use cases reported after this period as cases were reported at the province level hereafter, and large-scale control interventions were initiated on 23 Jan 2020;improved likelihood function, better accounting for first 41 confirmed cases, and now using all infections (rather than just cases detected) in Wuhan for prediction of infection in international travellers;improved characterization of uncertainty in parameters, and calculation of epidemic trajectory confidence intervals using a more statistically rigorous method;extended range of latent period in sensitivity analysis to reflect reports of up to 6 day incubation period in household clusters;removed travel restriction analysis, as different modelling approaches (e.g. stochastic transmission, rather than deterministic transmission) are more appropriate to such analyses.

scholarly journals Novel coronavirus 2019-nCoV (COVID-19): early estimation of epidemiological parameters and epidemic size estimates

2021 ◽  
Vol 376 (1829) ◽  
pp. 20200265
Author(s):  
Jonathan M. Read ◽  
Jessica R. E. Bridgen ◽  
Derek A. T. Cummings ◽  
Antonia Ho ◽  
Chris P. Jewell
Keyword(s):  
Prediction Interval ◽  
Basic Reproductive Number ◽  
Transmission Model ◽  
Reproductive Number ◽  
Theme Issue ◽  
Epidemic Size ◽  
Pandemic Response ◽  
Novel Coronavirus ◽  
The Uk ◽  
Size Estimates

Since it was first identified, the epidemic scale of the recently emerged novel coronavirus (2019-nCoV) in Wuhan, China, has increased rapidly, with cases arising across China and other countries and regions. Using a transmission model, we estimate a basic reproductive number of 3.11 (95% CI, 2.39–4.13), indicating that 58–76% of transmissions must be prevented to stop increasing. We also estimate a case ascertainment rate in Wuhan of 5.0% (95% CI, 3.6–7.4). The true size of the epidemic may be significantly greater than the published case counts suggest, with our model estimating 21 022 (prediction interval, 11 090–33 490) total infections in Wuhan between 1 and 22 January. We discuss our findings in the light of more recent information. This article is part of the theme issue ‘Modelling that shaped the early COVID-19 pandemic response in the UK’.

scholarly journals Mask-Ematics: Modeling the Effects of Masks in COVID-19 Transmission in High-Risk Environments

Epidemiologia ◽  
2021 ◽  
Vol 2 (2) ◽  
pp. 207-226
Author(s):  
Anthony Morciglio ◽  
Bin Zhang ◽  
Gerardo Chowell ◽  
James M. Hyman ◽  
Yi Jiang
Keyword(s):  
Public Health ◽  
High Risk ◽  
Disease Transmission ◽  
Large Fraction ◽  
Critical Mass ◽  
Transmission Model ◽  
Reproductive Number ◽  
High Quality ◽  
Moderate Quality ◽  
Epidemic Size

The COVID-19 pandemic has placed an unprecedented burden on public health and strained the worldwide economy. The rapid spread of COVID-19 has been predominantly driven by aerosol transmission, and scientific research supports the use of face masks to reduce transmission. However, a systematic and quantitative understanding of how face masks reduce disease transmission is still lacking. We used epidemic data from the Diamond Princess cruise ship to calibrate a transmission model in a high-risk setting and derive the reproductive number for the model. We explain how the terms in the reproductive number reflect the contributions of the different infectious states to the spread of the infection. We used that model to compare the infection spread within a homogeneously mixed population for different types of masks, the timing of mask policy, and compliance of wearing masks. Our results suggest substantial reductions in epidemic size and mortality rate provided by at least 75% of people wearing masks (robust for different mask types). We also evaluated the timing of the mask implementation. We illustrate how ample compliance with moderate-quality masks at the start of an epidemic attained similar mortality reductions to less compliance and the use of high-quality masks after the epidemic took off. We observed that a critical mass of 84% of the population wearing masks can completely stop the spread of the disease. These results highlight the significance of a large fraction of the population needing to wear face masks to effectively reduce the spread of the epidemic. The simulations show that early implementation of mask policy using moderate-quality masks is more effective than a later implementation with high-quality masks. These findings may inform public health mask-use policies for an infectious respiratory disease outbreak (such as one of COVID-19) in high-risk settings.

Dynamical Analysis and Circuit Simulation of a New Fractional-Order Hyperchaotic System and Its Discretization

2016 ◽  
Vol 26 (13) ◽  
pp. 1650222 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
A. Elsonbaty ◽  
A. A. Elsadany ◽  
A. E. Matouk
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Control Technique ◽  
Order System ◽  
Qualitative Behavior ◽  
Hyperchaotic System

This paper presents an analytical framework to investigate the dynamical behavior of a new fractional-order hyperchaotic circuit system. A sufficient condition for existence, uniqueness and continuous dependence on initial conditions of the solution of the proposed system is derived. The local stability of all the system’s equilibrium points are discussed using fractional Routh–Hurwitz test. Then the analytical conditions for the existence of a pitchfork bifurcation in this system with fractional-order parameter less than 1/3 are provided. Conditions for the existence of Hopf bifurcation in this system are also investigated. The dynamics of discretized form of our fractional-order hyperchaotic system are explored. Chaos control is also achieved in discretized system using delay feedback control technique. The numerical simulation are presented to confirm our theoretical analysis via phase portraits, bifurcation diagrams and Lyapunov exponents. A text encryption algorithm is presented based on the proposed fractional-order system. The results show that the new system exhibits a rich variety of dynamical behaviors such as limit cycles, chaos and transient phenomena where fractional-order derivative represents a key parameter in determining system qualitative behavior.

scholarly journals A Simulation on Potential Secondary Spread of Novel Coronavirus in an Exported Country Using a Stochastic Epidemic SEIR Model

2020 ◽  
Vol 9 (4) ◽  
pp. 944 ◽  
Author(s):  
Kentaro Iwata ◽  
Chisato Miyakoshi
Keyword(s):  
Healthcare Professionals ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Asian Countries ◽  
Hospital Visit ◽  
Seir Model ◽  
Stochastic Epidemic ◽  
Novel Coronavirus ◽  
The Impact ◽  
Multiple Scenarios

Ongoing outbreak of pneumonia caused by novel coronavirus (2019-nCoV) began in December 2019 in Wuhan, China, and the number of new patients continues to increase. Even though it began to spread to many other parts of the world, such as other Asian countries, the Americas, Europe, and the Middle East, the impact of secondary outbreaks caused by exported cases outside China remains unclear. We conducted simulations to estimate the impact of potential secondary outbreaks in a community outside China. Simulations using stochastic SEIR model were conducted, assuming one patient was imported to a community. Among 45 possible scenarios we prepared, the worst scenario resulted in the total number of persons recovered or removed to be 997 (95% CrI 990–1000) at day 100 and a maximum number of symptomatic infectious patients per day of 335 (95% CrI 232–478). Calculated mean basic reproductive number (R0) was 6.5 (Interquartile range, IQR 5.6–7.2). However, better case scenarios with different parameters led to no secondary cases. Altering parameters, especially time to hospital visit. could change the impact of a secondary outbreak. With these multiple scenarios with different parameters, healthcare professionals might be able to better prepare for this viral infection.

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