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  • 1.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    A Maple Module for Numerical Evaluations2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, Springer, 2011, p. 187-194Chapter in book (Refereed)
  • 2.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A new look at the critical community size for childhood infections2005In: Theoretical Population Biology, ISSN 0040-5809, E-ISSN 1096-0325, Vol. 67, no 3, p. 203-216Article in journal (Refereed)
    Abstract [en]

    Quasi-stationarity and time to extinction are studied for the classic endemic model. Attention is restricted to the transition region in parameter space where the quasi-stationary distribution is non-normal. A new approximation of the marginal distribution of infected individuals in quasi-stationarity is presented. It leads to a simple explicit expression for an approximation of the critical community size in terms of model parameters.

  • 3.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    An Alternative to Moment Closure2017In: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 79, no 9, p. 2088-2108Article in journal (Refereed)
    Abstract [en]

    Moment closure methods are widely used to analyze mathematical models. They are specifically geared toward derivation of approximations of moments of stochastic models, and of similar quantities in other models. The methods possess several weaknesses: Conditions for validity of the approximations are not known, magnitudes of approximation errors are not easily evaluated, spurious solutions can be generated that require large efforts to eliminate, and expressions for the approximations are in many cases too complex to be useful. We describe an alternative method that provides improvements in these regards. The new method leads to asymptotic approximations of the first few cumulants that are explicit in the model's parameters. We analyze the univariate stochastic logistic Verhulst model and a bivariate stochastic epidemic SIR model with the new method. Errors that were made in early applications of moment closure to the Verhulst model are explained and corrected.

  • 4.
    Nåsell, Ingemar
    KTH, Superseded Departments (pre-2005), Mathematics.
    An extension of the moment closure method2003In: Theoretical Population Biology, ISSN 0040-5809, E-ISSN 1096-0325, Vol. 64, no 2, p. 233-239Article in journal (Refereed)
    Abstract [en]

    The moment closure method was recently shown in Nasell (Theor. Popul. Biol. 63 (2) (2003a) 159) to give asymptotic approximations of the first few cumulants for the stochastic logistic model. A slight extension of the method is introduced. It is shown to be robust with regard to the specific distributional assumption that is used to achieve moment closure. The phenomenon of spurious solutions is shown to be related to the domain of attraction of the non-spurious critical point.

  • 5.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Approximation of Some Images Under Psi for the SIS Model2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, 2011, p. 119-139Chapter in book (Refereed)
  • 6.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Approximation of the Quasi-stationary Distribution q of the SIS Model2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, 2011, p. 141-147Chapter in book (Refereed)
  • 7.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Approximation of the Stationary Distribution p((0)) of the SIS Model2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, 2011, p. 115-118Chapter in book (Refereed)
  • 8.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Approximation of the Stationary Distribution p((1)) of the SIS Model2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, 2011, p. 93-99Chapter in book (Refereed)
  • 9.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Approximation of the Time to Extinction for the SIS Model2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, 2011, p. 149-154Chapter in book (Refereed)
  • 10.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Concluding Comments2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, 2011, p. 177-182Chapter in book (Refereed)
  • 11.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Extinction and Quasi-stationarity in the Stochastic Logistic SIS Model Introduction2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, Springer Berlin/Heidelberg, 2011, p. 1-7Chapter in book (Refereed)
  • 12.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Extinction and Quasi-stationarity in the Stochastic Logistic SIS Model Preface2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, 2011, p. V-+Chapter in book (Refereed)
  • 13.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Model Formulation2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, 2011, p. 9-16Chapter in book (Refereed)
  • 14.
    Nåsell, Ingemar
    KTH, Superseded Departments (pre-2005), Mathematics.
    Moment closure and the stochastic logistic model2003In: Theoretical Population Biology, ISSN 0040-5809, E-ISSN 1096-0325, Vol. 63, no 2, p. 159-168Article in journal (Refereed)
    Abstract [en]

    The quasi-stationary distribution of the stochastic logistic model is studied in the parameter region where its body is approximately normal. Improved asymptotic approximations of its first three cumulants are derived. It is shown that the same results can be derived with the aid of the moment closure method. This indicates that the moment closure method leads to expressions for the cumulants that are asymptotic approximations of the cumulants of the quasi-stationary distribution.

  • 15.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Notation2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, 2011, p. 183-186Chapter in book (Refereed)
  • 16.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Preparations for the Study of the Stationary Distribution p((0)) of the SIS Model2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, 2011, p. 101-113Chapter in book (Refereed)
  • 17.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Preparations for the Study of the Stationary Distribution p((1)) of the SIS Model2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, 2011, p. 73-91Chapter in book (Refereed)
  • 18.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Recurrence conditions for childhood infections2012In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 313, p. 212-216Article in journal (Refereed)
    Abstract [en]

    The classic endemic model is used by Kuske et al. (2007) to study recurrence of childhood infections, which is a well-known but not well understood phenomenon. The conditions for recurrence that they erive are shown to agree with conditions for persistence.

  • 19.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Some Approximations Involving the Normal Distribution2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, 2011, p. 47-72Chapter in book (Refereed)
  • 20.
    Nåsell, Ingemar
    KTH, Superseded Departments (pre-2005), Mathematics.
    Stochastic models of some endemic infections2002In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 179, no 1, p. 1-19Article in journal (Refereed)
    Abstract [en]

    Stochastic models are established and studied for several endemic infections with demography. Approximations of quasi-stationary distributions and of times to extinction are derived for stochastic versions of SI, SIS, SIR, and SIRS models. The approximations are valid for sufficiently large population sizes. Conditions for validity of the approximations are given for each of the models. These are also conditions for validity of the corresponding deterministic model. It is noted that some deterministic models are unacceptable approximations of the stochastic models for a large range of realistic parameter values.

  • 21.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Stochastic Process Background2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, 2011, p. 17-40Chapter in book (Refereed)
  • 22.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    The Influence of Immunity Loss on Persistence and Recurrence of Endemic Infections2013In: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 75, no 11, p. 2079-2092Article in journal (Refereed)
    Abstract [en]

    Conditions for persistence of endemic infections with immunity loss are derived and shown to agree with conditions for recurrence recently established by Chaffee and Kuske (Bull. Math. Biol. 73(11):2552-2574, 2011).

  • 23.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    The SIS Model: First Approximations of the Quasi-stationary Distribution2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, 2011, p. 41-46Chapter in book (Refereed)
  • 24.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Thresholds for the SIS Model2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, 2011, p. 171-175Chapter in book (Refereed)
  • 25.
    Nåsell, Ingemar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Uniform Approximations for the SIS Model2011In: EXTINCTION AND QUASI-STATIONARITY IN THE STOCHASTIC LOGISTIC SIS MODEL, 2011, p. 155-170Chapter in book (Refereed)
  • 26.
    Nåsell, Ingenar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Approximations of Cumulants of the Stochastic Power Law Logistic Model2020In: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 82, no 2, article id 19Article in journal (Refereed)
    Abstract [en]

    Asymptotic approximations of the first three cumulants of the quasi-stationary distribution of the stochastic power law logistic model are derived. The results are based on a system of ODEs for the first three cumulants. We deviate from the classical moment closure approach by determining approximations without closing the system of equations. The approximations are explicit in the model’s parameters, conditions for validity of the approximations are given, magnitudes of approximation errors are given, and spurious solutions are easily detected and eliminated. In these ways, we provide improvements on previous results for this model.

1 - 26 of 26
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