Research

Search-and-capture models with sequential consumption

  • We have developed a search-and-capture model, in which a source cell randomly searches for a target cell and delivers a burst of a given resource. First-passage times theory can be used to compute the Mean first-passage times (MFPTs) for the searching cell to find a given target cell.
  • To track the accumulation of resources within the target after several deliveries from the search-and-capture process, we resort to classical queueing theory. Assuming sequential consumption implies that the G/M/c queue the appropriate system for studying the accumulation of resources in the target.
  • We studied the existence and behaviour of steady-state statistics in function of the search process configurations.
  • Current projects include the following: (a) Modelling the accumulation of target cell resources as a G/M/c queue in high-dimension domains. (b) Study the idle periods under heavy traffic approximations, linked with the configuration of the search process.
Accumulation and sequential consumption of resources in a single target with sequential consumption after several rounds of search-and-capture processes.


Mathematical epidemiology

  • We have developed a stochastic model based on the idea that transitions between epidemiological stages are alike sampling processes that may involve more than one subset of the population or may be mostly dependent on time intervals defined by pathological or clinical criteria.
  • We applied the model to simulate epidemics, analyse the final distribution of the case fatality ratio, and define a basic reproductive number to determine the existence of a probabilistic phase transition for the dynamics.
  • We introduced an extension of the stochastic epidemiological model to consider heterogeneous populations. The central assumption is that individuals with similar profiles will have similar trajectories relative to infection.
  • The model allows estimation of realistic Case Fatality Ratios (CFRs) and extends the basic reproductive number.
Schemes of different dynamical scenarios considered by the model.