PubMed Health⌕ Search

Biomedical subjects

I Nåsell

Publications and source records attributed to I Nåsell.

9 recordsLinked to original sources
PubMed2001

Extinction and quasi-stationarity in the Verhulst logistic model.

We formulate and analyse a stochastic version of the Verhulst deterministic model for density-dependent growth of a single population. Three parameter regions with qualitatively different behaviours are identified. Explicit approximations of the quasi-stationary distribution and of the expected time to extinction are presented in each of these regions. The quasi-stationary distribution is approximately normal, and the time to extinction is long, in one of these regions. Another region has a short time to extinction and a quasi-stationary distribution that is approximately truncated geometric. A third region is a transition region between these two. Here the time to extinction is moderately long and the quasi-stationary distribution has a more complicated behaviour. Numerical illustrations are given.

Animals↗
PubMed1999

On the quasi-stationary distribution of the stochastic logistic epidemic.

An approximation is derived for the quasi-stationary distribution of the stochastic logistic epidemic in the intricate case where the transmission factor R0 lies in the transition region near the deterministic threshold value 1. An approximation for the expected time to extinction from quasi-stationarity in the same parameter region is also given.

Endemic Diseases↗
PubMed1994

The shape of the size distribution of an epidemic in a finite population.

Qualitative changes in the shape of the distribution of the final size of the susceptible-->infected-->removed (S-I-R) epidemic are used by Nåsell to define a threshold concept for the stochastic S-I-R epidemic. Numerical evaluations indicate that this threshold depends on the population size N according to the formula R0 approximately 1 + p/N1/3 for large N, where R0 is the basic reproduction ratio for the model. We derive an approximation of the final size distribution that supports this numerical result.

Disease Outbreaks↗
PubMed1991

On the quasi-stationary distribution of the Ross malaria model.

Approximations are derived for the quasi-stationary distribution of the fully stochastic version of the classical Ross malaria model. The approximations are developed in two stages. In the first stage, the Ross process is approximated with a bivariate Markov chain without an absorbing state. The second stage of the approximation uses ideas from perturbation theory to derive explicit expressions that serve as approximations of the joint stationary distribution of the approximating process. Numerical comparisons are made between the approximations and the quasi-stationary distribution.

Humans↗
PubMed1986

On superinfection in malaria.

The task of proving or disproving that there is superinfection of human beings in malaria has been unresolved since the concept of superinfection was introduced by Macdonald (1950). We present a method of analysis the results of which indicate that there is superinfection in children up to the age of about five years, but not in older human hosts. We use maximum-likelihood estimation in an extension of ideas introduced by Bekessy, Molineaux, & Storey (1976). The estimation is based on a model for the infection of human hosts with variable degree of superinfection. This model contains a parameter S that equals the maximum number of infections in the host. In the absence of superinfection, S = 1, while S = infinity in the unlimited superinfection assumed by Macdonald. The estimation of S in a number of age bands allows us to identify the age bands where superinfection occurs.

Adult↗
PubMed1978

Mating for schistosomes.

A mathematical model for schistosomiasis is developed under the hypothesis of promiscuous mating between mature schistosomes. The model is used to study epidemiology, control, and eradication of schistosome infections. Comparisons are made with previously published models that deal with monogamous mating and with parthenogenesis. We find that the two modes of mating give results that are essentially similar. On the other hand, essential differences exist between either mode of mating and the parthenogenetic case. Thus, we conclude that it is not of essential importance to find out if mature schistosomes are monogamous or promiscuous. A second conclusion is that the simplifying assumption of parthenogenetic egg-laying of schistosomes is not acceptable.

Animals↗