Artalejo, Jesús R. and Economou, A. and LópezHerrero, M.J. (2010) The maximum number of infected individuals in SIS epidemic models: Computational techniques and quasistationary distributions. Journal of Computational and Applied Mathematics, 233 (10). pp. 25632574. ISSN 03770427
This is the latest version of this item.
PDF
Restricted to Repository staff only until 31 December 2020. 876kB 
Official URL: http://www.sciencedirect.com/science/article/pii/S0377042709007341
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 quasistationary distributions of a related process are also discussed.
Item Type:  Article 

Uncontrolled Keywords:  Stochastic SIS epidemic model; Maximum number of infected individuals; Extinction time; Transient distribution; Quasistationary distribution; Absorption probabilities 
Subjects:  Medical sciences > Biology > Ecology 
ID Code:  15803 
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. PrenticeHall, New Jersey (2003) S.M. Moghadas, A.B. Gumel. A mathematical study of a model for childhood diseases with nonpermanent 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. CoolenSchrijner, E.A. van Doorn Quasistationarydistributions for a class of discretetime 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 twotype version of Bartlett’s epidemic model. Mathematical Biosciences, 212 (2008), pp. 99–108 P. Stone, H. WilkinsonHerbots, V. Isham. A stochastic model for head lice infections. Journal of Mathematical Biology, 56 (2008), pp. 743–763 I. Nasell. Extinction and quasistationarity in the Verhulst logistic model. Journal of Theoretical Biology, 211 (2001), pp. 11–27 E.A. van Doorn, P.K. Pollett Survival in a quasideath 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. GomezCorral 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 generalblock twodimensional 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. Nonnegative 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 
Deposited On:  02 Jul 2012 11:19 
Last Modified:  06 Feb 2014 10:31 
Available Versions of this Item

The maximum number of infected individuals in SIS epidemic models: Computational techniques and quasistationary distributions. (deposited 09 May 2012 09:20)
 The maximum number of infected individuals in SIS epidemic models: Computational techniques and quasistationary distributions. (deposited 02 Jul 2012 11:19) [Currently Displayed]
Repository Staff Only: item control page