Bayesian inference of a non-local proliferation model.

From a systems biology perspective, the majority of cancer models, although interesting and providing a qualitative explanation of some problems, have a major disadvantage in that they usually miss a genuine connection with experimental data. Having this in mind, in this paper, we aim at contributing to the improvement of many cancer models which contain a proliferation term. To this end, we propose a new non-local model of cell proliferation.

Onsager's conjecture in bounded domains for the conservation of entropy and other companion laws.

We show that weak solutions of general conservation laws in bounded domains conserve their generalized entropy, and other respective companion laws, if they possess a certain fractional differentiability of order one-third in the interior of the domain, and if the normal component of the corresponding fluxes tend to zero as one approaches the boundary. This extends various recent results of the authors.

Bayesian inference for age-structured population model of infectious disease with application to varicella in Poland.

The dynamics of the infectious disease transmission are often best understood by taking into account the structure of population with respect to specific features, for example age or immunity level. The practical utility of such models depends on the appropriate calibration with the observed data. Here, we discuss the Bayesian approach to data assimilation in the case of a two-state age-structured model.

Mass concentration in a nonlocal model of clonal selection.

Self-renewal is a constitutive property of stem cells. Testing the cancer stem cell hypothesis requires investigation of the impact of self-renewal on cancer expansion. To better understand this impact, we propose a mathematical model describing the dynamics of a continuum of cell clones structured by the self-renewal potential.

Bayesian evidence synthesis to estimate HIV prevalence in men who have sex with men in Poland at the end of 2009.

HIV spread in men who have sex with men (MSM) is an increasing problem in Poland. Despite the existence of a surveillance system, there is no direct evidence to allow estimation of HIV prevalence and the proportion undiagnosed in MSM. We extracted data on HIV and the MSM population in Poland, including case-based surveillance data, diagnostic testing prevalence data and behavioural data relating to self-reported prior diagnosis, stratified by age (⩽35, >35 years) and region (Mazowieckie including the capital city of Warsaw; other regions).