Numerical analysis of COVID-19 model with Caputo fractional order derivative
Source abstract
Abstract
This paper focuses on the numerical solutions of a six-compartment fractional model with Caputo derivative. In this model, we obtain non-negative and bounded solutions, equilibrium points, and the basic reproduction number and analyze the stability of disease free equilibrium point. The existence and uniqueness of the solution are proven by employing the Picard–Lindelof approach and fixed point theory. The product–integral trapezoidal rule is employed to simulate the system of FODEs (fractional ordinary differential equations). The numerical results are presented in the form of graphs for each compartment. Finally, the sensitivity of the most important parameter (β) and its impact on COVID-19 dynamics and the basic reproduction number are reported.
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Research context
OpenAlex topics: Fractional Differential Equations Solutions · Advanced Control Systems Design · Mathematical and Theoretical Epidemiology and Ecology Models
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Affiliations
School of Mathematics and Computer Science, Iran University of Science and Technology , Narmak, Tehran 16846-13114, Iran
References (57)
Show source-provided references
1. 2007
2. Development of a computational approach for a space–time fractional moving boundary problem arising from drug release systems10.1007/s40314-021-01474-x ↗
3. Solving fractional order differential equations by using fractional radial basis function neural network10.3390/sym15061275 ↗
4. On fractional order model of tumor growth with cancer stem cell10.3390/fractalfract7010027 ↗
5. Solution of generalized fractional Jaulent–Miodek model with uncertain initial conditions10.1063/5.0166789 ↗
6. On the asymptotic solutions of singulary perturbed differential systems of fractional order10.22436/jmcs.024.02.07 ↗
7. New group iterative schemes for solving the two-dimensional anomalous fractional sub-diffusion equation10.22436/jmcs.022.02.03 ↗
8. On approximate solutions for fractional system of differential equations with Caputo-Fabrizio fractional operator10.22436/jmcs.023.01.06 ↗
9. Optical solitons for conformable space-time fractional nonlinear model10.22436/jmcs.027.01.03 ↗
10. Solution of fractional autonomous ordinary differential equations10.22436/jmcs.027.01.05 ↗
11. A numerical study on time fractional Fisher equation using an extended cubic B-spline approximation10.22436/jmcs.022.01.08 ↗
12. Review of fractional epidemic models10.1016/j.apm.2021.03.044 ↗
13. Analysis and dynamics of a mathematical model to predict unreported cases of COVID-19 epidemic in Morocco10.1007/s40314-022-01990-4 ↗
14. Stability analysis of a fractional order model for the HIV/AIDS epidemic in a patchy environment10.1016/j.cam.2018.06.055 ↗
15. Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control10.1016/j.chaos.2020.109826 ↗
16. Regarding new positive, bounded and convergent numerical solution of nonlinear time fractional HIV/AIDS transmission model10.1016/j.chaos.2020.110096 ↗
17. Numerical and quantitative analysis of HIV/AIDS model with modified Atangana-Baleanu in Caputo sense derivative10.1016/j.aej.2022.11.034 ↗
18. Qualitative and quantitative analysis of a fractal fractional HIV/AIDS model10.1016/j.aej.2023.06.021 ↗
19. A study on the AH1N1/09 influenza transmission model with the fractional Caputo–Fabrizio derivative10.1186/s13662-020-02945-x ↗
20. Fractional transmission analysis of two strains of influenza dynamics10.1016/j.rinp.2022.105843 ↗
21. Some novel mathematical analysis on the fractal–fractional model of the AH1N1/09 virus and its generalized Caputo-type version10.1016/j.chaos.2022.112511 ↗
22. Analysis, modeling and simulation of a fractional-order influenza model10.1016/j.aej.2023.05.011 ↗
23. A numerical and analytical study of SE(Is)(Ih)AR epidemic fractional order COVID-19 model10.1186/s13662-021-03447-0 ↗
24. Sensitivity analysis of COVID-19 with quarantine and vaccination: A fractal-fractional model10.1016/j.aej.2022.02.024 ↗
25. A fractal–fractional COVID-19 model with a negative impact of quarantine on the diabetic patients10.1016/j.rico.2023.100199 ↗
26. Optimal surveillance mitigation of COVID’19 disease outbreak: Fractional order optimal control of compartment model10.1016/j.rinp.2020.103715 ↗
27. Behavioral response of population on transmissibility and saturation incidence of deadly pandemic through fractional order dynamical system10.1016/j.rinp.2021.104438 ↗
28. Repercussions of unreported populace on disease dynamics and its optimal control through system of fractional order delay differential equations10.1016/j.chaos.2022.111997 ↗
29. A fractional-order model describing the dynamics of the novel coronavirus (COVID-19) with nonsingular kernel10.1016/j.chaos.2021.110859 ↗
30. Fractional model and numerical algorithms for predicting COVID-19 with isolation and quarantine strategies10.1007/s40819-021-01086-3 ↗
31. Mathematical modeling of COVID-19 pandemic in India using Caputo-Fabrizio fractional derivative10.1016/j.compbiomed.2022.105518 ↗
32. Fractional order epidemiological model of SARS-CoV-2 dynamism involving Alzheimer’s disease10.1016/j.health.2022.100114 ↗
33. Analysis and dynamical transmission of Covid-19 model by using Caputo-Fabrizio derivative10.1016/j.aej.2022.12.026 ↗
34. Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function10.1186/s13662-021-03546-y ↗
35. A fractional-order model for COVID-19 and tuberculosis co-infection using Atangana–Baleanu derivative10.1016/j.chaos.2021.111486 ↗
36. A fractional order control model for diabetes and COVID-19 co-dynamics with Mittag-Leffler function10.1016/j.aej.2022.01.012 ↗
37. A global report on the dynamics of COVID-19 with quarantine and hospitalization: A fractional order model with non-local kernel10.1016/j.compbiolchem.2022.107645 ↗
38. A fractional order model for dual variants of COVID-19 and HIV co-infection via Atangana-Baleanu derivative10.1016/j.aej.2022.03.013 ↗
39. A fractional order model for the co-interaction of COVID-19 and Hepatitis B virus10.1016/j.rinp.2022.105498 ↗
40. Modeling and numerical analysis of a fractional order model for dual variants of SARS-CoV-210.1016/j.aej.2022.10.025 ↗
41. Optimally analyzed fractional Coronavirus model with Atangana–Baleanu derivative10.1016/j.rinp.2023.106929 ↗
42. On fractional approaches to the dynamics of a SARS-CoV-2 infection model including singular and non-singular kernels10.1016/j.rinp.2021.104600 ↗
43. Assessing the impact of SARS-CoV-2 infection on the dynamics of dengue and HIV via fractional derivatives10.1016/j.chaos.2022.112427 ↗
44. A fractional multi-order model to predict the COVID-19 outbreak in Morocco
45. Dynamics of a fractional order mathematical model for COVID-19 epidemic10.1186/s13662-020-02873-w ↗
46. Fractional order mathematical modeling of COVID-19 transmission10.1016/j.chaos.2020.110256 ↗
47. Seir epidemic model for COVID-19 transmission by Caputo derivative of fractional order10.1186/s13662-020-02952-y ↗
48. A fractional complex network model for novel corona virus in China10.1186/s13662-020-03182-y ↗
49. Stability analysis and simulation of the novel corornavirus mathematical model via the Caputo fractional-order derivative: A case study of Algeria10.1016/j.rinp.2021.104324 ↗
50. Fractional model for the spread of COVID-19 subject to government intervention and public perception10.1016/j.apm.2021.02.006 ↗
51. A new comparative study on the general fractional model of COVID-19 with isolation and quarantine effects10.1016/j.aej.2021.10.030 ↗
52. Investigation of a time-fractional COVID-19 mathematical model with singular kernel10.1186/s13662-022-03701-z ↗
53. A Caputo fractional order epidemic model for evaluating the effectiveness of high-risk quarantine and vaccination strategies on the spread of COVID-1910.1016/j.health.2023.100179 ↗
54. Fractional model analysis of COVID-19 spread based on big data platform10.1016/j.heliyon.2022.e12670 ↗
55. A fractional-order mathematical model based on vaccinated and infected compartments of SARS-CoV-2 with a real case study during the last stages of the epidemiological event10.1016/j.cam.2022.115015 ↗
56. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission10.1016/s0025-5564(02)00108-6 ↗
57. Numerical solution of fractional differential equations: A survey and a software tutorial10.3390/math6020016 ↗