The maximum number of infected individuals in SIS epidemic models: Computational techniques and quasi-stationary distributions
| dc.contributor.author | Artalejo Rodríguez, Jesús Manuel | |
| dc.contributor.author | Economou, A. | |
| dc.contributor.author | López Herrero, María Jesús | |
| dc.date.accessioned | 2023-06-15T07:49:03Z | |
| dc.date.available | 2023-06-15T07:49:03Z | |
| dc.date.issued | 2010-03-15 | |
| dc.description.abstract | We study the maximumn umber of infected individuals observed during an epidemic for a Susceptible–Infected–Susceptible (SIS) model which corresponds to a birth–death process with an absorbing state. We develop computational schemes for the corresponding distributions in a transient regime and till absorption. Moreover, we study the distribution of the current number of infectedindividuals given that the maximum number during the epidemic has not exceeded a given threshold. In this sense, some quasi-stationary distributions of a related process are also discussed. | |
| dc.description.department | Depto. de Estadística e Investigación Operativa | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Government of Spain (Department of Science and Innovation) | |
| dc.description.sponsorship | European Commission | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15803 | |
| dc.identifier.doi | 10.1016/j.cam.2009.11.003 | |
| dc.identifier.issn | 0377-0427 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0377042709007341 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/149.1 | |
| dc.issue.number | 10 | |
| dc.journal.title | Journal of Computational and Applied Mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 2574 | |
| dc.page.initial | 2563 | |
| dc.publisher | Elsevier Science Bv | |
| dc.relation.projectID | MTM 2008-01121 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 574 | |
| dc.subject.keyword | Stochastic SIS epidemic model | |
| dc.subject.keyword | Maximum number of infected individuals | |
| dc.subject.keyword | Extinction time | |
| dc.subject.keyword | Transient distribution | |
| dc.subject.keyword | Quasi-stationary distribution | |
| dc.subject.keyword | Absorption probabilities | |
| dc.subject.ucm | Ecología (Biología) | |
| dc.subject.unesco | 2401.06 Ecología animal | |
| dc.title | The maximum number of infected individuals in SIS epidemic models: Computational techniques and quasi-stationary distributions | |
| dc.type | journal article | |
| dc.volume.number | 233 | |
| dcterms.references | N.T.J. Bailey. The Elements of Stochastic Processes with Applications to the Natural Sciences. John Wiley & Sons, New York (1990) D.J. Daley, J. Gani. Epidemic Modelling: An Introduction. Cambridge Studies in Mathematical Biology, 15Cambridge University Press, Cambridge (1999) O. Diekmann, J.A.P. Heesterbeek. Mathematical Epidemiology of Infectious Diseases: Model Building. Analysis and Interpretation, John Wiley & Sons, Chichester (2000) L.J.S. Allen. An Introduction to Stochastic Processes with Applications to Biology. Prentice-Hall, New Jersey (2003) S.M. Moghadas, A.B. Gumel. A mathematical study of a model for childhood diseases with non-permanent immunity. Journal of Computational and Applied Mathematics, 157 (2003), pp. 347–363 J. Wei, X. Zou. Bifurcation analysis of a population model and the resulting SISepidemic model with delay. Journal of Computational and Applied Mathematics, 197 (2006), pp. 169–187 M. Song, W. Ma, Y. Takeuchi. Permanence of a delayed SIR epidemic model with density dependent birth rate. Journal of Computational and Applied Mathematics, 201 (2007), pp. 389–394 N. Yoshida, T. Hara. Global stability of a delayed SIR epidemic model with density dependent birth and death rates. Journal of Computational and Applied Mathematics, 201 (2007), pp. 339–347 D. Clancy. A stochastic SIS infection model incorporating indirect transmission. Journal of Applied Probability, 42 (2005), pp. 726–737 P. Coolen-Schrijner, E.A. van Doorn Quasi-stationarydistributions for a class of discrete-time Markov chains. Methodology and Computing in Applied Probability, 8 (2006), pp. 449–465 Y. Xu, L.J.S. Allen, A.S. Perelson. Stochastic model of an influenza epidemic with drug resistance. Journal of Theoretical Biology, 248 (2007), pp. 179–193 F. Ball, P. Neal. Network epidemic models with two leels of mixing. Mathematical Biosciences, 212 (2008), pp. 69–87 M. Lindholm. On the time to extinction for a two-type version of Bartlett’s epidemic model. Mathematical Biosciences, 212 (2008), pp. 99–108 P. Stone, H. Wilkinson-Herbots, V. Isham. A stochastic model for head lice infections. Journal of Mathematical Biology, 56 (2008), pp. 743–763 I. Nasell. Extinction and quasi-stationarity in the Verhulst logistic model. Journal of Theoretical Biology, 211 (2001), pp. 11–27 E.A. van Doorn, P.K. Pollett Survival in a quasi-death process. Linear Algebra and Its Applications, 429 (2008), pp. 776–791 M.F. Neuts. The distribution of the maximum length of a Poisson queue during a busy period. Operations Research, 12 (1964), pp. 281–285 R.F. Serfozo. Extreme values of birth and death processes and queues. Stochastic Processes and Their Applications, 27 (1988), pp. 291–306 J.R. Artalejo, A. Economou, A. Gomez-Corral Applications of maximum queue lengths to call center management. Computers and Operations Research, 34 (2007), pp. 983–996 J.R. Artalejo, S.R. Chakravarthy. Algorithmic analysis of the maximal level length in general-block two-dimensional Markov processes. Mathematical Problems in Engineering (2006), pp. 1–15 Article ID 53570 J.R. Artalejo. On the transient behavior of the maximum level length in structured Markov chains, 2009 (submitted for publication) A.M. Cohen. Numerical Methods for Laplace Transform Inversion. Springer, New York (2007) E. Seneta. Non-negative Matrices and Markov Chains. Springer, New York (1981) P.G. Ciarlet. Introduction to Numerical Linear Algebra and Optimization. Cambridge University Press, Cambridge (1989) J.V. Ross, T. Taimre, P.K. Pollett. On parameter estimation in population models. Theoretical Population Biology, 70 (2006), pp. 498–510 M.J. Keeling, P. Rohani. Modeling Infectious Diseases in Humans and Animals. Princeton University Press, Princeton (2008) L. Han, S. Han, Q. Deng, J. Yu, Y. He Source tracing and pursuing of network virus. IEEE 8th International Conference on Computer and Information Technology Workshops (2008), pp. 230–235 | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | db4b8a04-44b0-48e9-8b2c-c80ffae94799 | |
| relation.isAuthorOfPublication | 64a702cc-f8f5-468f-baeb-e37e92492a68 | |
| relation.isAuthorOfPublication.latestForDiscovery | 64a702cc-f8f5-468f-baeb-e37e92492a68 |
Download
Original bundle
1 - 1 of 1