Related papers: Unifying incidence and prevalence under a time-var…
Throughout the course of an epidemic, the rate at which disease spreads varies with behavioral changes, the emergence of new disease variants, and the introduction of mitigation policies. Estimating such changes in transmission rates can…
To better describe the spread of a disease, we extend a discrete time stochastic SIR-type epidemic model of Tuckwell and Williams. We assume the dependence on time of the number of daily encounters and include a parameter to represent a…
Medical investigations focusing on patient survival often generate not only a failure time for each patient but also a sequence of measurements on patient health at annual or semi-annual check-ups while the patient remains alive. Such a…
This work introduces a new markovian stochastic model that can be described as a non-homogeneous Pure Birth process. We propose a functional form of birth rate that depends on the number of individuals in the population and on the elapsed…
We investigate the information-theoretical limits of inference tasks in epidemic spreading on graphs in the thermodynamic limit. The typical inference tasks consist in computing observables of the posterior distribution of the epidemic…
Mechanistic mathematical models of within-host viral dynamics are tools for understanding how a virus' biology and its interaction with the immune system shape the infectivity of a host. The biology of the process is encoded by the…
Two stochastic models are proposed to describe the evolution of the COVID-19 pandemic. In the first model the population is partitioned into four compartments: susceptible $S$, infected $I$, removed $R$ and dead people $D$. In order to have…
This study investigates the utilization of various mathematical models for comprehending and managing outbreaks of infectious diseases, with a specific focus on how different distributions of incubation times influence predictions regarding…
We determine the distributions of some random variables related to a simple model of an epidemic with contact tracing and cluster isolation. This enables us to apply general limit theorems for super-critical Crump-Mode-Jagers branching…
The COVID-19 pandemic provides new motivation for a classic problem in epidemiology: estimating the empirical rate of transmission during an outbreak (formally, the time-varying reproduction number) from case counts. While standard methods…
When dealing with time series data, causal inference methods often employ structural vector autoregressive (SVAR) processes to model time-evolving random systems. In this work, we rephrase recursive SVAR processes with possible latent…
Stem cells, through their ability to produce daughter stem cells and differentiate into specialized cells, are essential in the growth, maintenance, and repair of biological tissues. Understanding the dynamics of cell populations in the…
Infectious disease dynamics operate across multiple biological scales, with within-host viral dynamics being a key driver of between-host transmission. However, while models that explicitly link these scales exist, none have been developed…
Estimation of epidemiological and population parameters from molecular sequence data has become central to the understanding of infectious disease dynamics. Various models have been proposed to infer details of the dynamics that describe…
This study focuses on the modeling, mathematical analysis, developing theories, and numerical simulation of Influenza virus transmission. We have proved the existence, uniqueness, positivity, and boundedness of the solutions. Also,…
State-space models have been widely used to model the dynamics of communicable diseases in populations of interest by fitting to time-series data. Particle filters have enabled these models to incorporate stochasticity and so can better…
Spatio-temporal pathogen spread is often partially observed at the metapopulation scale. Available data correspond to proxies and are incomplete, censored and heterogeneous. Moreover, representing such biological systems often leads to…
In this paper we model the spreading of the SARS-CoV-2 in Mexico by introducing a new stochastic approximation constructed from first principles, structured on the basis of a Latent-Infectious- (Recovered or Deceased) (LI(RD)) compartmental…
Cancer data, particularly cancer incidence and mortality, are fundamental to understand the cancer burden, to set targets for cancer control and to evaluate the evolution of the implementation of a cancer control policy. However, the…
The SIR model is a three-compartment model of the time development of an epidemic. After normalizing the dependent variables, the model is a system of two non-linear differential equations for the susceptible proportion $S$ and the infected…