Dynamics of a Model of Coronavirus Disease with Fear Effect, Treatment Function, and Variable Recovery Rate
In this work, we developed, validated, and analysed the behaviour of a compartmental model of COVID-19 transmission in Saudi Arabia. The population was structured into four classes: susceptible (S), exposed (E), infectious (I), and removed (R) individuals. This SEIR model assumes a bilinear incidenc...
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| Published in | Mathematics (Basel) Vol. 12; no. 11; p. 1678 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Basel
MDPI AG
01.06.2024
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| ISSN | 2227-7390 2227-7390 |
| DOI | 10.3390/math12111678 |
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| Abstract | In this work, we developed, validated, and analysed the behaviour of a compartmental model of COVID-19 transmission in Saudi Arabia. The population was structured into four classes: susceptible (S), exposed (E), infectious (I), and removed (R) individuals. This SEIR model assumes a bilinear incidence rate and a nonlinear recovery rate that depends on the quality of health services. The model also considers a treatment function and incorporates the effect of fear due to the disease. We derived the expression of the basic reproduction number and the equilibrium points of the model and demonstrated that when the reproduction number is less than one, the disease-free equilibrium is stable, and the model predicts a backward bifurcation. We further found that when the reproduction number is larger than one, the model predicts stable periodic behaviour. Finally, we used numerical simulations with parameter values fitted to Saudi Arabia to analyse the effects of the model parameters on the model-predicted dynamic behaviours. |
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| AbstractList | In this work, we developed, validated, and analysed the behaviour of a compartmental model of COVID-19 transmission in Saudi Arabia. The population was structured into four classes: susceptible (S), exposed (E), infectious (I), and removed (R) individuals. This SEIR model assumes a bilinear incidence rate and a nonlinear recovery rate that depends on the quality of health services. The model also considers a treatment function and incorporates the effect of fear due to the disease. We derived the expression of the basic reproduction number and the equilibrium points of the model and demonstrated that when the reproduction number is less than one, the disease-free equilibrium is stable, and the model predicts a backward bifurcation. We further found that when the reproduction number is larger than one, the model predicts stable periodic behaviour. Finally, we used numerical simulations with parameter values fitted to Saudi Arabia to analyse the effects of the model parameters on the model-predicted dynamic behaviours. |
| Audience | Academic |
| Author | Alharthi, Nadiyah Hussain Alqahtani, Rubayyi T. Ajbar, Abdelhamid |
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| References | Thirthar (ref_28) 2023; 8 Das (ref_13) 2020; 2020 Aletreby (ref_37) 2020; 4 Namasudra (ref_16) 2023; 55 ref_36 ref_35 ref_34 ref_11 Mpeshe (ref_26) 2021; 2021 Bozkurt (ref_23) 2021; 152 Sapkota (ref_39) 2021; 9 Feng (ref_6) 2020; 17 Buonomo (ref_41) 2023; 174 Wang (ref_30) 2006; 201 Gnanvi (ref_10) 2021; 6 Dokuyucu (ref_15) 2021; 20 Song (ref_33) 2004; 1 Brugnago (ref_40) 2023; 33 Chan (ref_19) 2014; 257 Li (ref_42) 2017; 14 Alshammari (ref_38) 2020; 2020 Rahimi (ref_9) 2023; 35 ref_24 ref_22 ref_21 Watmough (ref_32) 2002; 180 Khalilpourazari (ref_4) 2023; 61 Ajbar (ref_12) 2020; 2020 ref_20 Wang (ref_29) 2004; 291 ref_1 ref_3 Hu (ref_18) 2012; 238 Sher (ref_14) 2020; 59 ref_27 Zhang (ref_31) 2008; 348 Xiang (ref_17) 2021; 6 Francesco (ref_8) 2021; 18 ref_5 Maji (ref_25) 2021; 2021 Kiselev (ref_2) 2023; 13 Sardar (ref_7) 2020; 139 |
| References_xml | – volume: 291 start-page: 775 year: 2004 ident: ref_29 article-title: Bifurcations in an epidemic model with constant removal rate of incentives publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2003.11.043 – volume: 2020 start-page: 541 year: 2020 ident: ref_12 article-title: Bifurcation analysis of a SEIR epidemic system with governmental action and individual reaction publication-title: Adv. Differ. Equ. doi: 10.1186/s13662-020-02997-z – ident: ref_3 doi: 10.3390/math12010055 – volume: 59 start-page: 3133 year: 2020 ident: ref_14 article-title: Computational and theoretical modeling of the transmission dynamics of novel COVID-19 under Mittag–Leffler Power law publication-title: Alex. Eng. J. doi: 10.1016/j.aej.2020.07.014 – volume: 2020 start-page: 140 year: 2020 ident: ref_13 article-title: Forecasting incidences of COVID-19 using Box-Jenkins method for the period 12 July –11 September 2020: A study on highly affected countries publication-title: Chaos Solit. Fractals – ident: ref_5 doi: 10.3390/sym12091404 – volume: 2021 start-page: 2129490 year: 2021 ident: ref_25 article-title: Impact of media-induced fear on the control of COVID-19 outbreak: A mathematical study publication-title: Int. J. Differ. Equ. – volume: 14 start-page: 1279 year: 2017 ident: ref_42 article-title: A mathematical model for the seasonal transmission of schistosomiasis in the lake and marshland regions of China publication-title: Math. Biosci. Eng. doi: 10.3934/mbe.2017066 – volume: 8 start-page: 6447 year: 2023 ident: ref_28 article-title: Mathematical modeling of the COVID-19 epidemic with fear impact publication-title: J. AIMS Math. doi: 10.3934/math.2023326 – ident: ref_34 – volume: 17 start-page: 3618 year: 2020 ident: ref_6 article-title: Modelling the effects of media coverage and quarantine on the COVID-19 infections in the UK publication-title: Math. Biosci. Eng. doi: 10.3934/mbe.2020204 – volume: 20 start-page: 49 year: 2021 ident: ref_15 article-title: Analyzing a novel coronavirus model (COVID-19) in the sense of Caputo-Fabrizio fractional operator publication-title: Appl. Comput. Math. Ean. Int. J. – volume: 2021 start-page: 6647425 year: 2021 ident: ref_26 article-title: Modeling the dynamics of coronavirus disease pandemic coupled with fear epidemics publication-title: Comput. Math. Methods Med. doi: 10.1155/2021/6647425 – volume: 139 start-page: 110078 year: 2020 ident: ref_7 article-title: Assessment of lockdown effect in some states and overall India: A predictive mathematical study on COVID-19 outbreak publication-title: Chaos Solit. Fractals doi: 10.1016/j.chaos.2020.110078 – volume: 9 start-page: 0692 year: 2021 ident: ref_39 article-title: The chaotic behavior of the spread of infection during the COVID-19 pandemic in the United States and globally publication-title: IEEE Access doi: 10.1109/ACCESS.2021.3085240 – volume: 152 start-page: 111403 year: 2021 ident: ref_23 article-title: A fractional-order model of COVID-19 considering the fear effect of the media and social networks on the community publication-title: Chaos Solit. Fractals doi: 10.1016/j.chaos.2021.111403 – volume: 257 start-page: 1662 year: 2014 ident: ref_19 article-title: Bifurcations and complex dynamics of an SIR model with the impact of the number of hospital beds publication-title: J. Diff. Equ. doi: 10.1016/j.jde.2014.05.030 – ident: ref_35 – ident: ref_24 doi: 10.3390/app11125367 – ident: ref_1 doi: 10.1016/j.bspc.2022.104416 – volume: 180 start-page: 29 year: 2002 ident: ref_32 article-title: Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission publication-title: Math. Biosci. doi: 10.1016/S0025-5564(02)00108-6 – volume: 238 start-page: 12 year: 2012 ident: ref_18 article-title: Analysis of SIR epidemic models with nonlinear incidence rate and treatment publication-title: Math. Biosci. doi: 10.1016/j.mbs.2012.03.010 – ident: ref_11 doi: 10.3390/jcm9020596 – ident: ref_27 doi: 10.1371/journal.pone.0263610 – volume: 33 start-page: 123123 year: 2023 ident: ref_40 article-title: Multistability and chaos in SEIRS epidemic model with a periodic time-dependent transmission rate publication-title: Chaos doi: 10.1063/5.0156452 – volume: 2020 start-page: 9136157 year: 2020 ident: ref_38 article-title: A Mathematical model to investigate the transmission of COVID-19 in the kingdom of Saudi Arabia publication-title: Comput. Math. Method Med. doi: 10.1155/2020/9136157 – volume: 6 start-page: 258 year: 2021 ident: ref_10 article-title: On the reliability of predictions on COVID-19 dynamics: A systematic and critical review of modelling techniques publication-title: Infect. Dis. Model. – ident: ref_20 doi: 10.3390/e19070305 – volume: 13 start-page: 13439 year: 2023 ident: ref_2 article-title: Delay-differential SEIR modeling for improved modelling of infection dynamics publication-title: Sci. Rep. doi: 10.1038/s41598-023-40008-9 – ident: ref_21 doi: 10.1371/journal.pone.0003955 – ident: ref_22 doi: 10.1007/978-1-4614-5474-8 – volume: 61 start-page: 8367 year: 2023 ident: ref_4 article-title: Robust modelling and prediction of the COVID-19 pandemic in Canada publication-title: Int. J. Prod. Res. doi: 10.1080/00207543.2021.1936261 – volume: 18 start-page: 182020087520200875 year: 2021 ident: ref_8 article-title: Modelling and predicting the effect of social distancing and travel restrictions on COVID-19 spreading publication-title: J. R. Soc. Interface – volume: 4 start-page: 79 year: 2020 ident: ref_37 article-title: Dynamics of SARS-CoV-2 outbreak in the Kingdom of Saudi Arabia: A predictive model publication-title: Saudi Crit. Care. J. doi: 10.4103/sccj.sccj_19_20 – volume: 348 start-page: 433 year: 2008 ident: ref_31 article-title: Backward bifurcation of an epidemic model with saturated treatment publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2008.07.042 – volume: 35 start-page: 23671 year: 2023 ident: ref_9 article-title: A review on COVID-19 forecasting models publication-title: Neural Comput. Appl. doi: 10.1007/s00521-020-05626-8 – volume: 55 start-page: 171 year: 2023 ident: ref_16 article-title: Nonlinear neural network based forecasting model for predicting COVID-19 Cases publication-title: Neural Process Lett. doi: 10.1007/s11063-021-10495-w – volume: 201 start-page: 58 year: 2006 ident: ref_30 article-title: Backward Bifurcation of an Epidemic Model with Treatment publication-title: Math. Biosci. doi: 10.1016/j.mbs.2005.12.022 – ident: ref_36 – volume: 174 start-page: 113782 year: 2023 ident: ref_41 article-title: Oscillations in SIR behavioural epidemic models: The interplay between behaviour and overexposure to infection publication-title: Chaos Solit. Fractals doi: 10.1016/j.chaos.2023.113782 – volume: 6 start-page: 324 year: 2021 ident: ref_17 article-title: COVID-19 epidemic prediction and the impact of public health interventions: A review of COVID-19 epidemic models publication-title: Infect. Dis. Model. – volume: 1 start-page: 361 year: 2004 ident: ref_33 article-title: Dynamical models of tuberculosis and their applications publication-title: Math. Biosci. Eng. doi: 10.3934/mbe.2004.1.361 |
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| SubjectTerms | backward bifurcation Bifurcations Coronaviruses COVID-19 Disease transmission Fear fear effect Health services Hopf bifurcation Hospitals Infectious diseases Mathematical models Medical personnel Pandemics Parameters Per capita Recovery Recruitment SEIR model variable recovery rate Viral diseases |
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| Title | Dynamics of a Model of Coronavirus Disease with Fear Effect, Treatment Function, and Variable Recovery Rate |
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