Stochastic Processes in Epidemiology

Mode, Charles J.; Sleeman, Candace K

doi:10.1142/4243

Cited by 76 publications

(52 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, we apply Bellman-Harris branching processes 59 the obtained results in an epidemiological context. Actually, the problem of how to model the evolution of an infectious disease is very important and widely considered in the recent literature (see, for example, [8], [11], [15], [21], and [23]). However, in only a few papers (see, for example, [2], [7], [10], and [22]) has the waiting time to the extinction of the disease been used as a main tool to determine a vaccination policy.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Monotonicity and Continuity Properties of the Extinction Time of Bellman-Harris Branching Processes: An Application to Epidemic Modelling

2010

View full text Add to dashboard Cite

The aim of this paper is to study the stochastic monotonicity and continuity properties of the extinction time of Bellman-Harris branching processes depending on their reproduction laws. Moreover, we show their applications in an epidemiological context, obtaining an optimal criterion to establish the proportion of susceptible individuals in a given population that must be vaccinated in order to eliminate an infectious disease. First the spread of infection is modelled by a Bellman-Harris branching process. Finally, we provide a simulation-based method to determine the optimal vaccination policies.

show abstract

Section: Introductionmentioning

confidence: 99%

Stochastic Monotonicity and Continuity Properties of the Extinction Time of Bellman-Harris Branching Processes: An Application to Epidemic Modelling

2010

View full text Add to dashboard Cite

show abstract

“…Branching models have been applied to many biological problems in such fields as epidemiology, genetics, and cell dynamics. Examples include the evolution of infectious diseases (e.g., Mode and Sleemam (2000), Ball et al (2004), or Garske and Rhodes (2008)), population genetics (e.g., Campbell (2003) or Iwasa et al (2005)), and stem cells (e.g., Yakovlev and Yanev (2006)). Further examples are reviewed in the recent monographs of Kimmel and Axelrod (2002) and Pakes (2003), and in the communication of Caron-Lormier et al (2006).…”

Section: Introductionmentioning

confidence: 99%

Bisexual branching processes to model extinction conditions for Y-linked genes

González

Martínez

Mota

2009

Journal of Theoretical Biology

View full text Add to dashboard Cite

In a two-sex monogamic population, the evolution of the number of carriers of the two alleles of a Y-linked gene is considered. To this end, a multitype bisexual branching model is presented in which it is assumed that the gene has no influence on the mating process. It is deduced from this model that the average numbers of female and male descendants per mating unit constitute the key to determining the extinction or survival of each allele. Moreover, the destiny of each allele in the population is found not to depend on the behaviour of the other.

show abstract

“…The age-dependent AST is a generalization of the Bellman-Harris [10] and Crum-Mode-Jagers [4,5] age-dependent branching processes. The key new elements are the degree correlations and the truncation at a maximum generation, allowing us to consider the topological properties of real networks.…”

Section: Sir Model Of Disease Spreadingmentioning

confidence: 99%

“…In this work I extend the theory of age-dependent branching processes [4,5,10] to consider the topological properties of real networks. First, I generalize my previous study [8,9] to include degree correlations.…”

Section: Introductionmentioning

confidence: 99%

Spreading dynamics on small-world networks with connectivity fluctuations and correlations

Vázquez

2006

Phys. Rev. E

View full text Add to dashboard Cite

Infectious diseases and computer malwares spread among humans and computers through the network of contacts among them. These networks are characterized by wide connectivity fluctuations, connectivity correlations and the small-world property. In a previous work [A. Vazquez, Phys. Rev. Lett. 96, 038702 (2006)] I have shown that the connectivity fluctuations together with the smallworld property lead to a novel spreading law, characterized by an initial power law growth with an exponent determined by the average node distance on the network. Here I extend these results to consider the influence of connectivity correlations which are generally observed in real networks. I show that assortative and disassortative connectivity correlations enhance and diminish, respectively, the range of validity of this spreading law. As a corollary I obtain the region of connectivity fluctuations and degree correlations characterized by the absence of an epidemic threshold. These results are relevant for the spreading of infectious diseases, rumors, and information among humans and the spreading of computer viruses, email worms and hoaxes among computer users.

show abstract

Stochastic Processes in Epidemiology

Cited by 76 publications

References 0 publications

Stochastic Monotonicity and Continuity Properties of the Extinction Time of Bellman-Harris Branching Processes: An Application to Epidemic Modelling

Stochastic Monotonicity and Continuity Properties of the Extinction Time of Bellman-Harris Branching Processes: An Application to Epidemic Modelling

Bisexual branching processes to model extinction conditions for Y-linked genes

Spreading dynamics on small-world networks with connectivity fluctuations and correlations

Contact Info

Product

Resources

About