American Institute of Mathematical Sciences

Advanced
2006, 3(3): 527-544. doi: 10.3934/mbe.2006.3.527

Sensitivity and uncertainty analyses for a SARS model with time-varying inputs and outputs

Robert G. McLeod 1, , John F. Brewster 2, , Abba B. Gumel 3, and  Dean A. Slonowsky 4,

1. 

Department of Mathematics and Statistics, University of Winnipeg, Winnipeg, MB, Canada R3B 2E9, Canada
2. 

Department of Statistics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2, Canada
3. 

Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada
4. 

Department of Mathematics, Malaspina University-College, Nanaimo, BC, Canada V9R 5S5, Canada

Received  April 2005 Revised  February 2006 Published  May 2006

This paper presents a statistical study of a deterministic model for the transmission dynamics and control of severe acute respiratory syndrome (SARS). The effect of the model parameters on the dynamics of the disease is analyzed using sensitivity and uncertainty analyses. The response (or output) of interest is the control reproduction number, which is an epidemiological threshold governing the persistence or elimination of SARS in a given population. The compartmental model includes parameters associated with control measures such as quarantine and isolation of asymptomatic and symptomatic individuals. One feature of our analysis is the incorporation of time-dependent functions into the model to reflect the progressive refinement of these SARS control measures over time. Consequently, the model contains continuous time-varying inputs and outputs. In this setting, sensitivity and uncertainty analytical techniques are used in order to analyze the impact of the uncertainty in the parameter estimates on the results obtained and to determine which parameters have the largest impact on driving the disease dynamics.
Keywords: epidemiological model, functional out-put, control reproduction number, Latin hypercube sampling, partial rank correlation coefficients..
Mathematics Subject Classification: 92D3.
Citation: Robert G. McLeod, John F. Brewster, Abba B. Gumel, Dean A. Slonowsky. Sensitivity and uncertainty analyses for a SARS model with time-varying inputs and outputs. Mathematical Biosciences & Engineering, 2006, 3 (3) : 527-544. doi: 10.3934/mbe.2006.3.527
[1]

Mariantonia Cotronei, Tomas Sauer. Full rank filters and polynomial reproduction. Communications on Pure and Applied Analysis, 2007, 6 (3) : 667-687. doi: 10.3934/cpaa.2007.6.667
[2]

Qiumei Zhang, Daqing Jiang, Li Zu. The stability of a perturbed eco-epidemiological model with Holling type II functional response by white noise. Discrete and Continuous Dynamical Systems - B, 2015, 20 (1) : 295-321. doi: 10.3934/dcdsb.2015.20.295
[3]

Jérôme Coville. Nonlocal refuge model with a partial control. Discrete and Continuous Dynamical Systems, 2015, 35 (4) : 1421-1446. doi: 10.3934/dcds.2015.35.1421
[4]

Tom Burr, Gerardo Chowell. The reproduction number $R_t$ in structured and nonstructured populations. Mathematical Biosciences & Engineering, 2009, 6 (2) : 239-259. doi: 10.3934/mbe.2009.6.239
[5]

Hui Cao, Yicang Zhou. The basic reproduction number of discrete SIR and SEIS models with periodic parameters. Discrete and Continuous Dynamical Systems - B, 2013, 18 (1) : 37-56. doi: 10.3934/dcdsb.2013.18.37
[6]

Tianhui Yang, Lei Zhang. Remarks on basic reproduction ratios for periodic abstract functional differential equations. Discrete and Continuous Dynamical Systems - B, 2019, 24 (12) : 6771-6782. doi: 10.3934/dcdsb.2019166
[7]

E. González-Olivares, B. González-Yañez, Eduardo Sáez, I. Szántó. On the number of limit cycles in a predator prey model with non-monotonic functional response. Discrete and Continuous Dynamical Systems - B, 2006, 6 (3) : 525-534. doi: 10.3934/dcdsb.2006.6.525
[8]

Sebastian Aniţa, Bedreddine Ainseba. Internal eradicability for an epidemiological model with diffusion. Mathematical Biosciences & Engineering, 2005, 2 (3) : 437-443. doi: 10.3934/mbe.2005.2.437
[9]

Haiying Jing, Zhaoyu Yang. The impact of state feedback control on a predator-prey model with functional response. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 607-614. doi: 10.3934/dcdsb.2004.4.607
[10]

Pei Zhang, Siyan Liu, Dan Lu, Ramanan Sankaran, Guannan Zhang. An out-of-distribution-aware autoencoder model for reduced chemical kinetics. Discrete and Continuous Dynamical Systems - S, 2022, 15 (4) : 913-930. doi: 10.3934/dcdss.2021138
[11]

Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595-607. doi: 10.3934/mbe.2007.4.595
[12]

Gerardo Chowell, Catherine E. Ammon, Nicolas W. Hengartner, James M. Hyman. Estimating the reproduction number from the initial phase of the Spanish flu pandemic waves in Geneva, Switzerland. Mathematical Biosciences & Engineering, 2007, 4 (3) : 457-470. doi: 10.3934/mbe.2007.4.457
[13]

Ling Xue, Caterina Scoglio. Network-level reproduction number and extinction threshold for vector-borne diseases. Mathematical Biosciences & Engineering, 2015, 12 (3) : 565-584. doi: 10.3934/mbe.2015.12.565
[14]

Nitu Kumari, Sumit Kumar, Sandeep Sharma, Fateh Singh, Rana Parshad. Basic reproduction number estimation and forecasting of COVID-19: A case study of India, Brazil and Peru. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2021170
[15]

Gergely Röst, Jianhong Wu. SEIR epidemiological model with varying infectivity and infinite delay. Mathematical Biosciences & Engineering, 2008, 5 (2) : 389-402. doi: 10.3934/mbe.2008.5.389
[16]

Jinliang Wang, Gang Huang, Yasuhiro Takeuchi, Shengqiang Liu. Sveir epidemiological model with varying infectivity and distributed delays. Mathematical Biosciences & Engineering, 2011, 8 (3) : 875-888. doi: 10.3934/mbe.2011.8.875
[17]

Wisdom S. Avusuglo, Kenzu Abdella, Wenying Feng. Stability analysis on an economic epidemiological model with vaccination. Mathematical Biosciences & Engineering, 2017, 14 (4) : 975-999. doi: 10.3934/mbe.2017051
[18]

Lopo F. de Jesus, César M. Silva, Helder Vilarinho. Random perturbations of an eco-epidemiological model. Discrete and Continuous Dynamical Systems - B, 2022, 27 (1) : 257-275. doi: 10.3934/dcdsb.2021040
[19]

Wei Wang, Linyi Qian, Xiaonan Su. Pricing and hedging catastrophe equity put options under a Markov-modulated jump diffusion model. Journal of Industrial and Management Optimization, 2015, 11 (2) : 493-514. doi: 10.3934/jimo.2015.11.493
[20]

Vitalii G. Kurbatov, Valentina I. Kuznetsova. On stability of functional differential equations with rapidly oscillating coefficients. Communications on Pure and Applied Analysis, 2018, 17 (1) : 267-283. doi: 10.3934/cpaa.2018016

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (143)
  • HTML views (0)
  • Cited by (40)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy