scholarly journals Mathematical model of SIR epidemic system (COVID-19) with fractional derivative: stability and numerical analysis

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rubayyi T. Alqahtani
Keyword(s):  
Steady State ◽  
Reproduction Number ◽  
Rate Function ◽  
Backward Bifurcation ◽  
Sir Epidemic ◽  
General Incidence Rate ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Steady State Solutions ◽  
Fractional Orders

AbstractIn this paper, we study and analyze the susceptible-infectious-removed (SIR) dynamics considering the effect of health system. We consider a general incidence rate function and the recovery rate as functions of the number of hospital beds. We prove the existence, uniqueness, and boundedness of the model. We investigate all possible steady-state solutions of the model and their stability. The analysis shows that the free steady state is locally stable when the basic reproduction number $R_{0}$ R 0 is less than unity and unstable when $R_{0} > 1$ R 0 > 1 . The analysis shows that the phenomenon of backward bifurcation occurs when $R_{0}<1$ R 0 < 1 . Then we investigate the model using the concept of fractional differential operator. Finally, we perform numerical simulations to illustrate the theoretical analysis and study the effect of the parameters on the model for various fractional orders.

scholarly journals Mathematical Analysis of Oxygen Uptake Rate in Continuous Process under Caputo Derivative

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 675
Author(s):  
Rubayyi T. Alqahtani ◽  
Abdullahi Yusuf ◽  
Ravi P. Agarwal
Keyword(s):  
Fractional Derivatives ◽  
Oxygen Uptake Rate ◽  
Continuous Process ◽  
Equilibrium Stability ◽  
Treatment Model ◽  
Classical Version ◽  
Fractional Differential Operator ◽  
Non Local ◽  
Fractional Differential ◽  
Steady State Solutions

In this paper, the wastewater treatment model is investigated by means of one of the most robust fractional derivatives, namely, the Caputo fractional derivative. The growth rate is assumed to obey the Contois model, which is often used to model the growth of biomass in wastewaters. The characteristics of the model under consideration are derived and evaluated, such as equilibrium, stability analysis, and steady-state solutions. Further, important characteristics of the fractional wastewater model allow us to understand the dynamics of the model in detail. To this end, we discuss several important analyses of the fractional variant of the model under consideration. To observe the efficiency of the non-local fractional differential operator of Caputo over its counter-classical version, we perform numerical simulations.

Analysis of the COVID-19 Pandemic Spreading in India by an Epidemiological Model and Fractional Differential Operator

2020 ◽  
Author(s):  
Amjad S. Shaikh ◽  
Vikas S. Jadhav ◽  
Munir G. Timol ◽  
Kottakkaran S. Nisar ◽  
I. Khan
Keyword(s):  
Differential Operator ◽  
Reproduction Number ◽  
Control Strategies ◽  
Approximate Solutions ◽  
Transform Method ◽  
Potential Control ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Sensitive Parameters ◽  
Future Outbreak

Fractional differential mathematical model unfolding the dynamics of the COVID-19 pandemic in India is presented and explored in this paper. The purpose of this study is to estimate the future outbreak of disease and potential control strategies using mathematical models in India as a whole country as well as in some of the states of the country. This model is calibrated based on reported cases of infections over the month of April 2020 in India. We have used iterative fractional complex transform method to find approximate solutions of the model having modified Riemann Liouville fractional differential operator. We have also carried out a comparative analysis between actual and estimated cumulative cases graphically, moreover, most sensitive parameters for basic reproduction number$(R_0)$ are computed and their effect on transmission dynamics of COVID-19 pandemic is investigated in detail.

Effect of pollution on dynamics of SIR model with treatment

2015 ◽  
Vol 08 (06) ◽  
pp. 1550083 ◽  
Author(s):  
Sudipa Chauhan ◽  
Sumit Kaur Bhatia ◽  
Surbhi Gupta
Keyword(s):  
Reproduction Number ◽  
Sir Model ◽  
Backward Bifurcation ◽  
Global Dynamics ◽  
Sir Epidemic Model ◽  
Disease Eradication ◽  
Sir Epidemic ◽  
Local And Global Dynamics ◽  
High Level ◽  
Very High

In this paper, an SIR epidemic model with treatment affected by pollution is proposed. The existence, local and global dynamics of the model are studied. It is shown that backward bifurcation occurs at R0 < 1 and p0 < 1 because of insufficient capacity of treatment. It is also found that due to pollution the number of infective has gone to a very high level. As a result, backward bifurcation occurs for R0 < 1, even when p0 > 1. Further, there exist bistable endemic equilibria for a very low capacity for R0 > 1. Thus, we found that disease can be eradicated for R0 < 1 only by increasing the capacity to a sufficiently high level. Persistence of endemicity of the system is obtained and the mathematical results suggest that the basic reproduction number is insufficient for disease eradication. Numerical simulations are presented to illustrate the results obtained.

scholarly journals Impact of fractional order over time response for DC-DC converters with fractional capacitors

2020 ◽  
Vol 25 (2) ◽  
pp. 234-239
Author(s):  
Jesús María López Lezama ◽  
David Esteban Betancur Herrera ◽  
Juan Bernardo Cano ◽  
Nicolás Muñoz Galeano
Keyword(s):  
Steady State ◽  
Fractional Order ◽  
Output Voltage ◽  
Fractional Model ◽  
Switching Model ◽  
Capacitor Voltage ◽  
Fractional Differential ◽  
The Impact ◽  
Fractional Orders ◽  
3D Representations

This paper analyses the impact of fractional orders of derivatives over the response of DC-DC converters which includes fractional capacitors and their parasitic losses for a more realistic approximation of the converter. A fractional model is proposed and is applied for a Boost DC-DC with a fractional capacitor in its DC bus. The fractional model is obtained using Kirchhoff laws and applying the conventional switching model. Then, the resulting set of fractional differential equations is in the Caputo’s sense and was solved using Wavelets method. Solutions were appropriately shown using 3D representations, varying the duty cycle and the fractional order to determine the behaviour of the fractional capacitor voltage, inductor current and output voltage. Ripples and steady state values were determined. Results show high dependence of the fractional order in the variables related to the voltage in the fractional capacitor. With respect to the current, results show that the fractional order does not significantly affect its steady state and ripple.

On the kinetics of Hadamard-type fractional differential systems

2020 ◽  
Vol 23 (2) ◽  
pp. 553-570 ◽  
Author(s):  
Li Ma
Keyword(s):  
Differential Operator ◽  
Numerical Simulations ◽  
Type Inequality ◽  
The Other ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Kinetics Of ◽  
Theoretical Results

AbstractThis paper is devoted to the investigation of the kinetics of Hadamard-type fractional differential systems (HTFDSs) in two aspects. On one hand, the nonexistence of non-trivial periodic solutions for general HTFDSs, which are considered in some functional spaces, is proved and the corresponding eigenfunction of Hadamard-type fractional differential operator is also discussed. On the other hand, by the generalized Gronwall-type inequality, we estimate the bound of the Lyapunov exponents for HTFDSs. In addition, numerical simulations are addressed to verify the obtained theoretical results.

scholarly journals Global dynamics of a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaodong Wang ◽  
Chunxia Wang ◽  
Kai Wang
Keyword(s):  
Vertical Transmission ◽  
Epidemic Model ◽  
Media Coverage ◽  
Existence And Uniqueness ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Global Dynamics ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Stochastic Sir

AbstractIn this paper, we study a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage. For the deterministic model, we give the basic reproduction number $R_{0}$ R 0 which determines the extinction or prevalence of the disease. In addition, for the stochastic model, we prove existence and uniqueness of the positive solution, and extinction and persistence in mean. Furthermore, we give numerical simulations to verify our results.

scholarly journals On a fractional-order p-Laplacian boundary value problem at resonance on the half-line with two dimensional kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. F. Imaga ◽  
S. A. Iyase
Keyword(s):  
Differential Operator ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Half Line ◽  
At Resonance ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Problem At Resonance

AbstractIn this work, we consider the solvability of a fractional-order p-Laplacian boundary value problem on the half-line where the fractional differential operator is nonlinear and has a kernel dimension equal to two. Due to the nonlinearity of the fractional differential operator, the Ge and Ren extension of Mawhin’s coincidence degree theory is applied to obtain existence results for the boundary value problem at resonance. Two examples are used to validate the established results.

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