A probabilistic approach for the study of epidemiological dynamics of infectious diseases: Basic model and properties
Por:
Giral-Barajas, Jose, Herrera-Nolasco, Carlos Ignacio, Herrera-Valdez, Marco Arieli, Lopez, Sergio I.
Publicada:
7 sep 2023
Resumen:
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.
Filiaciones:
Giral-Barajas, Jose:
Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico
Univ Nacl Autonoma Mexico, Fac Ciencias, Dept Matemat, Mexico City, DF, Mexico
Herrera-Nolasco, Carlos Ignacio:
Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico
Laboratorio de Dinámica, Biofísica, y Fisiología de Sistemas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico
Univ Nacl Autonoma Mexico, Fac Ciencias, Dept Matemat, Mexico City, DF, Mexico
Univ Nacl Autonoma Mexico, Fac Ciencias, Lab Dinam Biofis & Fisiol Sistemas, Mexico City, DF, Mexico
Herrera-Valdez, Marco Arieli:
Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico
Laboratorio de Dinámica, Biofísica, y Fisiología de Sistemas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico
Univ Nacl Autonoma Mexico, Fac Ciencias, Dept Matemat, Mexico City, DF, Mexico
Univ Nacl Autonoma Mexico, Fac Ciencias, Lab Dinam Biofis & Fisiol Sistemas, Mexico City, DF, Mexico
Lopez, Sergio I.:
Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico
Univ Nacl Autonoma Mexico, Fac Ciencias, Dept Matemat, Mexico City, DF, Mexico
Green Submitted
|