Publications

2026

1. arXiv

   Universality in the target arrival statistics of non-conservative search processes

   José Giral-Barajas, Samantha Linn, and Paul C. Bressloff

   Jun 2026

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   Stochastic search processes in which searchers are continuously introduced to and removed from a target search domain are fundamental to a wide class of physical and artificial systems. The theory of such non-conservative search processes is, however, much less developed than for search processes with a fixed number of particles. Here we exploit a natural mapping between non-conservative stochastic search and queueing theory to derive the full time-dependent distribution of target arrivals under minimal assumptions on the underlying search process. Remarkably, we find that the steady-state inter-arrival time distribution is exactly exponential, regardless of the details of the search process, showing a robust universality that emerges directly from the queueing framework. Thus, counterintuitively, the arrival statistics of a non-conservative search process are much simpler than sequential search-and-capture processes involving a fixed number of searchers. This has major implications for target resource accumulation, where the delivery of resources is counter-balanced by their downstream consumption.

2. Phys. Rev. E

   Resetting-induced instability in queues fed by a search process in an interval

   José Giral-Barajas, and Paul C. Bressloff

   Physical Review E, Jun 2026

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   Proper management of resources whose arrival and consumption are subject to environmental randomness is an intrinsic process in both natural and artificial systems. This phenomenon can be modeled as a queuing process whose arrival distribution is determined by a search process with stochastic resetting. When the queuing system has a limited number of servers and the search process occurs within a bounded domain, the dynamics of expediting or delaying the search through stochastic resetting interact with the long-term dynamics of the number of resources in the queue. We combine results from queuing theory with those from search processes with stochastic resetting in a bounded domain to obtain regions of the parameter space of the search process that ensure convergence of the number of resources in the queue to a steady state. Furthermore, we find a threshold resetting rate at which the effects of stochastic resetting shift from reducing convergence regions to expanding them. Finally, we demonstrate that this threshold value grows exponentially with the number of servers, making it harder for stochastic resetting to improve the convergence of the queueing system.

2025

1. J. Phys. A.

   Stochastic 1D search-and-capture as a G/M/c queueing model

   José Giral-Barajas, and Paul C Bressloff

   Journal of Physics A: Mathematical and Theoretical, Aug 2025

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   We study the accumulation of resources within a target due to the interplay between continual delivery, driven by 1D stochastic search processes, and sequential consumption. The assumption of sequential consumption is key because it changes the commonly used G/M/∞queue to a G/M/c queue. Combining the theory of G/M/c queues with the theory of first-passage times, we derive general conditions for the search process to ensure that the number of resources within the queue converges to a steady state and compute explicit expressions for the mean and variance of the number of resources within the queue at steady state. We then compare the performance of the G/M/c queue with that of the G/M/∞queue for an increasing number of servers. We extend the model to consider two competing targets and show that, under specific scenarios, an additional target is beneficial to the original target. Finally, we study the effects of multiple searchers. Using renewal theory, we numerically compute the inter-arrival time density for M searchers in the Laplace space, which allows us to exploit the explicit expressions for the steady-state statistics of the number of resources within G/M/1 and G/M/∞queues, and compare their behaviour with different numbers of searchers. Overall, the G/M/c queue shows a tighter dependence on the configuration of the search process than the G/M/∞queue does.

2023

1. J. Theor. Biol.

   A probabilistic approach for the study of epidemiological dynamics of infectious diseases: Basic model and properties

   José Giral-Barajas, Carlos Ignacio Herrera-Nolasco, Marco Arieli Herrera-Valdez, and Sergio I. López

   Journal of Theoretical Biology, Sep 2023

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   The dynamics of epidemiological phenomena associated to infectious diseases have long been modelled taking different approaches. However, recent pandemic events exposed many areas of opportunity to improve the existing models. We develop 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 apply 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. The resulting modelling scheme is robust, easy to implement, and can readily lend itself for extensions aimed at answering questions that emerge from close examination of data trends, such as those emerging from the COVID-19 pandemic, and other infectious diseases.