Contributions to Stochastic Models in Epidemics

Supported by: Ministry of Science and Innovation, Government of Spain

Reference number: PGC2018-097704-B-I00

Description: The main objective of CMEEpi (Spanish acronym of Contributions to Stochastic Models in Epidemics) is to develop four long-term research lines in Mathematical Epidemiology and Immunology. According to the statistical, probabilistic and physical specialization of the research team at Universidad Complutense de Madrid (UCM) and our partners at Universidad Pontificia Comillas (UComillas), University of Leeds (ULeeds), Universidade Nova de Lisboa (UNLisboa), Universitá degli Studi di Salerno (USalerno) and University of Tsukuba (UTsukuba), and the experimental specialization of the researchers at the Centro de Edafología y Biología Aplicada del Segura (CEBAS-CSIC) and Peter MacCallum Cancer Center (Melbourne), the general scientific objectives of CMEEpi are as follows:

  • Line 1: To develop stochastic models in epidemics that incorporate imperfect vaccination and non-permanent immunity of vaccinated individuals, as well as pre- and post-exposure vaccination strategies, showing their relevance in the case of tuberculosis infections.
  • Line 2: To develop stochastic models in epidemics with vertical and horizontal transmission of the disease, and co-infection in the case of multiple types of infection, as well as the mutation between strains which are sensible and resistant to antibiotics.
  • Line 3: To develop suitable stochastic models in epidemics making use of queueing models, relax the classical exponential assumption by using time-dependent infectious and/or recovery patterns and non-Markovian stochastic processes at occurrence epochs, and apply anticipative Stochastic Calculus in solving problems in optimal control of epidemics with privileged information.
  • Line 4: To develop advanced bayesian statistical tools to parametrize stochastic epidemic models validated with experimental data, in particular, in reference to the process of maduration of T cells in the thymus, and improvement programs through genetic selection.

The CMEEpi proposal will generate new collaborations between the UCM research team and its partners in UComillas, UNLisboa, USalerno and UTsukuba, and will reinforce the existing ones between the UCM research team and their partners in ULeeds, especially in the setting of Mathematical Epidemiology and Immunology. These collaborations aim to facilitate research, innovation and training between partners, and to set up specific actions to allow the transfer of knowledge with experimentalists at CEBAS-CSIC and Melbourne.

Keywords: Epidemics; Immunology; Stochastic Processes; Stochastic Calculus; Bayesian Inference

Scheduling dates: 01/01/2019-31/12/2021

Members of the UCM research team:

Collaborators and students at the UCM:

  • María Gamboa Pérez, PhD student
  • Jorge Lemos Peralta, graduate student
  • Diana Taipe Hidalgo, PhD student

Collaborators outside the UCM:

Scientific papers:

Communications in scientific conferences:

  • The deterministic SIS epidemic model in a Markovian environment, by MJ Lopez-Herrero. 10th Conference on Dynamical Systems Applied to Biology and Natrural Sciences (DSABNS 2019). Naples, Italy.
  • Extreme values in SIR epidemic models with two strains and full cross-immunity, by A Gómez-Corral. Meeting of the British Society for Immunology. Microsoft Research Cambridge, Cambridge, UK.
  • A comparative analysis between two time-discretized versions of the SIS epidemic model, by A Gómez-Corral. Mathematical and Statistical Explorations in Disease Modelling and Public Health (DMPH 2019). ICTS, Tata Institute of Fundamental Research, Bangalore, India.
  • Cuantificación de la infección en un modelo de epidemias con cambios aleatorios en el entorno, by MJ Lopez-Herrero. XXXVIII Congreso Nacional de Estadística e Investigación Operativa (SEIO 2019). Universitat Politècnica de València, Alcoi, Spain.
  • Procesos LD-QBD aplicados a la propagación de epidemias, by A Gómez-Corral. XXXVIII Congreso Nacional de Estadística e Investigación Operativa (SEIO 2019). Universitat Politècnica de València, Alcoi, Spain.
  • Markov chains and the imaginary Itô interpretation, by C Escudero. Conference of the Southern Africa Mathematical Sciences Association (SAMSA 2019). Blantyre, Malawi.
  • Exact approaches for the analysis of stochastic epidemic processes on networks, by M López-García. 1st International Workshop on Stochastic Processes and their Applications. A virtual workshop (IWSPA 2020). Madrid, Spain.
  • Quantifying infection transmission in a stochastic SIV model with imperfect vaccine, by MJ Lopez-Herrero. 1st International Workshop on Stochastic Processes and their Applications. A virtual workshop (IWSPA 2020). Madrid, Spain.
  • Markovian discrete-time study of the distribution of the number of infected during the active phase of a non-immunizing communicable disease, by D Taipe. 1st International Workshop on Stochastic Processes and their Applications. A virtual workshop (IWSPA 2020). Madrid, Spain
  • On the number of inspections of the population that find an active process: A first approach to estimate the contact rate of a disease, by M Gamboa. 1st International Workshop on Stochastic Processes and their Applications. A virtual workshop (IWSPA 2020). Madrid, Spain.
  • Itö vs Stratonovich in the Langevin model of brownian motion, by C Escudero. 1st International Workshop on Stochastic Processes and their Applications. A virtual workshop (IWSPA 2020). Madrid, Spain.
  • On the stochastic methodology for different applications, by C Escudero. Conference of the Southern Africa Mathematical Sciences Association, a virtual conference (SAMSA 2020). Auburn University.
  • Rethinking Itô vs Stratonovich, by C Escudero. Conference on Complex Systems, a virtual conference (CCS 2020). Aristotle University of Thessaloniki.
  • Anticipating stochastic calculus. Optimal investment strategies under insider trading, by S. Ranilla-Cortina and C Escudero. Conference on Complex Systems, a virtual conference (CCS 2020). Aristotle University of Thessaloniki.
  • Portfolio optimization in anticipating settings, by C Escudero. 2021 Annual Conference of Southern Africa Mathematical Sciences Association, a virtual event (SAMSA 2021).
  • Stochastic measures for vaccine-preventable disease transmission when vaccine is partially effective, by MJ Lopez-Herrero. Mathematical Population Dynamics, Ecology and Evolution, a virtual conference (MPDEE21). Marseille, France.
  • Quantifying the spread of an epidemic process on a discrete-time stochastic SIS model, by M Gamboa. Mathematical Population Dynamics, Ecology and Evolution (MPDEE21). Marseille, France.
  • Study of the exact reproduction number for SIS models with vertical and horizontal transmissions, by F Palacios-Rodríguez. 2nd International Workshop on Stochastic Processes and their Applications. A virtual workshop (IWSPA 2021). Madrid, Spain.
  • A stochastic SVIR model with imperfect vaccine and external source of infection, by M Gamboa. 2nd International Workshop on Stochastic Processes and their Applications. A virtual workshop (IWSPA 2021). Madrid, Spain.
  • Portfolio optimization for different anticipating integrals, by C Escudero. 2nd International Workshop on Stochastic Processes and their Applications. A virtual workshop (IWSPA 2021). Madrid, Spain.
  • On first-passage times and sojourn times in a finite QBD processes: an application to varicella-zoster infections, by D Taipe. 2nd International Workshop on Stochastic Processes and their Applications. A virtual workshop (IWSPA 2021). Madrid, Spain.
  • Extinction thresholds in discrete-time stochastic SIS epidemic models and some applications, by M Gamboa. V Jornadas Científicas de Estudiantes de la Sociedad Española de Bioestadística, a virtual conference  (V JSEB 2021). Madrid, Spain.
  • On the distribution of the number of infectives during an active epidemic of discrete-time SIS stochastic model, by D Taipe. V Jornadas Científicas de Estudiantes de la Sociedad Española de Bioestadística, a virtual conference (V JSEB 2021). Madrid, Spain.
  • A stochastic SVIR model with imperfect vaccine and external source of infection, by M Gamboa. 26th International Conference on Analytical & Stochastic Modelling Techniques & Applications, a virtual event (ASMTA 2021). University of Tsukuba, Japan.
  • Tiempos de primer paso en las versiones uniformizadas y los esqueletos discretos de una cadena de Markov en tiempo continuo y sus aplicaciones al modelo SIS de epidemias, by A Gómez-Corral. V Encuentro de la SMM y la RSME, 2021. Guanajuato, México.
  • Measures to assess an optimal vaccination coverage in a stochastic SIV model with imperfect vaccine, by M Gamboa. Virtual Society of Mathematics Biology Annual Meeting, 2021. University of California, Riverside, EE.UU.
  • Setting a waning vaccination level on a stochastic model with infection reintroduction when vaccine is partially effective, by MJ Lopez-Herrero. 13th Conference on Dynamical Systems Applied o Biology and Natural Sciences, a virtual event (DSABNS 2022).
  • Sobre la formalización matemática de la inversión financiera en presencia de información privilegiada, by C Escudero. Incertidumbre en Modelos Financieros, UNED, Spain.
  • Análisis del tiempo hasta alcanzar un umbral sobre el número de individuos vacunados de una población finita protegida preventivamente por una vacuna imperfecta, by MJ Lopez-Herrero. XXXIX Congreso Nacional de Estadística e Investigación Operativa, SEIO 2022. Universidad de Granada, Spain.
  • Evaluating an immediate re-vaccination program, by M Gamboa. XXXIX Congreso Nacional de Estadística e Investigación Operativa, SEIO 2022. Universidad de Granada, Spain.
  • Normal and anomalous diffusion in evolving domains: a brief overview of some recent results, by F Le Vot, E Abad, C Escudero and SB Yuste. XXXVIII Reunión Bienal de la Real Sociedad Española de Física, 2022. Murcia, Spain.
  • On the use of time-discretized models as approximations to continuous-time epidemic models, by MT Rodríguez-Bernal. 12th European Conference of Mathematical and Theoretical Biology, ECMTB 2022. Heidelberg, Germany.
  • Some measures to establish a threshold on the number of vaccinated individuals in a stochastic SVIS model with imperfect vaccine, by M Gamboa. International Conference on Models in Population Dynamics, Ecology and Evolution, MPDEE’22. Torino, Italy.

Other contributions:

  • Anticipating Stochastic Integration, S Ranilla Cortina. Master thesis, Universidad Nacional de Educación a Distancia, 2019. Supervisor: C Escudero.
  • Estudio Markoviano en Tiempo Discreto de la Distribución del Número de Infectados Durante la Fase Activa de una Enfermedad Contagiosa sin Inmunidad, D Taipe Hidalgo. Master thesis, Universidad Complutense de Madrid, 2019. Supervisor: MJ López-Herrero.
  • A New Pre-exposure Tuberculosis Vaccine Stochastic Model, R Fernández Peralta. Master thesis, Universidad Complutense de Madrid, 2019. Supervisor: A Gómez-Corral.
  • Reaction-Diffusion Processes and their Interdisciplinary Applications, A Correales Fernández. Doctoral thesis, Universidad Autónoma de Madrid, 2019. Supervisor: C Escudero.
  • Studying the effect of vaccination in epidemic models with stochastic transmission, M Gamboa. Doctoral thesis. Universidad Complutense de Madrid, 2022. Supervisor: MJ Lopez-Herrero.

Popularization and dissemination of mathematics in epidemics:

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