arXiv subjects

Ingemar Nåsell

Publications and source records attributed to Ingemar Nåsell.

3 recordsLinked to original sources

arXiv2022

Approximations of the Quasi-Stationary Distribution of a Logistic SIS Model for Endemic Infections

Errors of approximations of the quasi-stationary distribution (the QSD) of the logistic SIS model are evaluated numerically. The results are used to derive asymptotic approximations of the approximation errors for large populations. We show in particular that there are two approximations above threshold for which the approximation errors are exponentially small. One of these approximations has been known for some time, while the other one is new. The result that the older one of these two approximations has an exponentially small approximation error is new.

math.PR↗

arXiv2019

Approximations of Cumulants of the Stochastic Power Law Logistic Model

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 known, and spurious solutions are easily detected and eliminated. In these ways, we provide improvements on previous results for this model.

math.PR↗

arXiv2017

An Alternative to Moment Closure

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 are generated that require large efforts to eliminate, 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.

math.PR↗