Feedback linearization-based vaccination control strategies for true-mass action type SEIR epidemic models

This paper presents a feedback linearization-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes more difficult contacts among susceptible and infected. The control objective is novel in the sense that the asymptotically tracking of the removed-by-immunity population to the total population while achieving simultaneously the remaining population (i.e. susceptible plus infected plus infectious) to asymptotically converge to zero. The vaccination policy is firstly designed on the above proposed tracking objective. Then, it is proven that identical vaccination rules might be found based on a general feedback linearization technique. Such a formal technique is very useful in control theory which provides a general method to generate families of vaccination policies with sound technical background which include those proposed in the former sections of the paper. The output zero dynamics of the normal canonical form in the theoretical feedback linearization analysis is identified with that of the removed-by-immunity population. The various proposed vaccination feedback rules involved one of more of the partial populations and there is a certain flexibility in their designs since some control parameters being multiplicative coefficients of the various populations may be zeroed. The basic properties of stability and positivity of the solutions are investigated in a joint way. The equilibrium points and their stability properties as well as the positivity of the solutions are also investigated

An observer-based vaccination control law for an Seir epidemic model based on feedback linearization techniques for nonlinear systems

This paper presents a vaccination strategy for fighting against the propagation of epidemic diseases. The disease propagation is described by an SEIR (susceptible plus infected plus infectious plus removed populations) epidemic model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes the contacts among susceptible and infected more difficult. The vaccination strategy is based on a continuous-time nonlinear control law synthesised via an exact feedback input-output linearization approach. An observer is incorporated into the control scheme to provide online estimates for the susceptible and infected populations in the case when their values are not available from online measurement but they are necessary to implement the control law. The vaccination control is generated based on the information provided by the observer. The control objective is to asymptotically eradicate the infection from the population so that the removed-by-immunity population asymptotically tracks the whole one without precise knowledge of the partial populations. The model positivity, the eradication of the infection under feedback vaccination laws and the stability properties as well as the asymptotic convergence of the estimation errors to zero as time tends to infinity are investigated

Activity‑driven network modeling and control of the spread of two concurrent epidemic strains

The emergency generated by the current COVID-19 pandemic has claimed millions of lives worldwide. There have been multiple waves across the globe that emerged as a result of new variants, due to arising from unavoidable mutations. The existing network toolbox to study epidemic spreading cannot be readily adapted to the study of multiple, coexisting strains. In this context, particularly lacking are models that could elucidate re-infection with the same strain or a different strain—phenomena that we are seeing experiencing more and more with COVID-19. Here, we establish a novel mathematical model to study the simultaneous spreading of two strains over a class of temporal networks. We build on the classical susceptible–exposed–infectious–removed model, by incorporating additional states that account for infections and re-infections with multiple strains. The temporal network is based on the activity-driven network paradigm, which has emerged as a model of choice to study dynamic processes that unfold at a time scale comparable to the network evolution. We draw analytical insight from the dynamics of the stochastic network systems through a mean-field approach, which allows for characterizing the onset of different behavioral phenotypes (non-epidemic, epidemic, and endemic). To demonstrate the practical use of the model, we examine an intermittent stay-at-home containment strategy, in which a fraction of the population is randomly required to isolate for a fixed period of time

Statistical physics of vaccination

Historically, infectious diseases caused considerable damage to human societies, and they continue to do so today. To help reduce their impact, mathematical models of disease transmission have been studied to help understand disease dynamics and inform prevention strategies. Vaccination–one of the most important preventive measures of modern times–is of great interest both theoretically and empirically. And in contrast to traditional approaches, recent research increasingly explores the pivotal implications of individual behavior and heterogeneous contact patterns in populations. Our report reviews the developmental arc of theoretical epidemiology with emphasis on vaccination, as it led from classical models assuming homogeneously mixing (mean-field) populations and ignoring human behavior, to recent models that account for behavioral feedback and/or population spatial/social structure. Many of the methods used originated in statistical physics, such as lattice and network models, and their associated analytical frameworks. Similarly, the feedback loop between vaccinating behavior and disease propagation forms a coupled nonlinear system with analogs in physics. We also review the new paradigm of digital epidemiology, wherein sources of digital data such as online social media are mined for high-resolution information on epidemiologically relevant individual behavior. Armed with the tools and concepts of statistical physics, and further assisted by new sources of digital data, models that capture nonlinear interactions between behavior and disease dynamics offer a novel way of modeling real-world phenomena, and can help improve health outcomes. We conclude the review by discussing open problems in the field and promising directions for future research

Tackling complexity in biological systems: Multi-scale approaches to tuberculosis infection

Tuberculosis is an ancient disease responsible for more than a million deaths per year worldwide, whose complex infection cycle involves dynamical processes that take place at different spatial and temporal scales, from single pathogenic cells to entire hosts' populations. In this thesis we study TB disease at different levels of description from the perspective of complex systems sciences. On the one hand, we use complex networks theory for the analysis of cell interactomes of the causative agent of the disease: the bacillus Mycobacterium tuberculosis. Here, we analyze the gene regulatory network of the bacterium, as well as its network of protein interactions and the way in which it is transformed as a consequence of gene expression adaptation to disparate environments. On the other hand, at the level of human societies, we develop new models for the description of TB spreading on complex populations. First, we develop mathematical models aimed at addressing, from a conceptual perspective, the interplay between complexity of hosts' populations and certain dynamical traits characteristic of TB spreading, like long latency periods and syndemic associations with other diseases. On the other hand, we develop a novel data-driven model for TB spreading with the objective of providing faithful impact evaluations for novel TB vaccines of different types

Updating the Lambda modes of a nuclear power reactor

[EN] Starting from a steady state configuration of a nuclear power reactor some situations arise in which the reactor configuration is perturbed. The Lambda modes are eigenfunctions associated with a given configuration of the reactor, which have successfully been used to describe unstable events in BWRs. To compute several eigenvalues and its corresponding eigenfunctions for a nuclear reactor is quite expensive from the computational point of view. Krylov subspace methods are efficient methods to compute the dominant Lambda modes associated with a given configuration of the reactor, but if the Lambda modes have to be computed for different perturbed configurations of the reactor more efficient methods can be used. In this paper, different methods for the updating Lambda modes problem will be proposed and compared by computing the dominant Lambda modes of different configurations associated with a Boron injection transient in a typical BWR reactor. (C) 2010 Elsevier Ltd. All rights reserved.This work has been partially supported by the Spanish Ministerio de Educacion y Ciencia under projects ENE2008-02669 and MTM2007-64477-AR07, the Generalitat Valenciana under project ACOMP/2009/058, and the Universidad Politecnica de Valencia under project PAID-05-09-4285.González Pintor, S.; Ginestar Peiro, D.; Verdú Martín, GJ. (2011). Updating the Lambda modes of a nuclear power reactor. Mathematical and Computer Modelling. 54(7):1796-1801. https://doi.org/10.1016/j.mcm.2010.12.013S1796180154

Physics of interdependent dynamical processes.

La emergencia de fenómenos colectivos a escalas macroscópicas no observados en escalas microscópicas cuestiona la validez de las teorías reduccionistas. Para explicar estos fenómenos se necesitan enfoques sistémicos que den cuenta de los patrones de interacción no triviales existentes entre los constituyentes de los sistemas sociales, biológicos o económicos, lo que ha dado lugar al nacimiento de la disciplina conocida como ciencia de los sistemas complejos. Una vía habitual para caracterizar los sistemas complejos ha sido la búsqueda de la conexión entre la estructura de interacciones y el comportamiento colectivo observado en sistemas reales mediante el estudio individual de dinámicas aisladas. No obstante, los sistemas complejos no son inmutables y se encuentran constantemente intercambiando información mediante estímulos internos y externos. Esta tesis se centra en la adaptación de modelos sobre diferentes dinámicas en el campo de los sistemas complejos para caracterizar el impacto de este flujo de información, ya sea entre escalas microscópicas y macroscópicas de un mismo sistema o mediante la existencia de interdependencias entre procesos dinámicos que se propagan de forma simultánea.La primera parte de la tesis aborda el estudio dinámicas acopladas en redes de contacto estáticas. Adaptando los modelos compartimentales introducidos en el siglo XX a la naturaleza de cada dinámica, caracterizamos cuatro problemas diferentes: la propagación de patógenos que interactúan, cuya coexistencia puede ser beneficiosa o perjudicial para su evolución, el control de brotes epidémicos con el uso del rastreo de contactos digital, la aparición de movimientos sociales desencadenados por pequeñas minorías sociales bien coordinadas y la competencia entre honestidad y la corrupción en las sociedades modernas. En todas estas dinámicas, encontramos que el flujo de información cambia las propiedades críticas del sistema así como algunas de las conclusiones extraídas sobre el papel de la estructura de contactos al estudiar cada dinámica de forma individual.La segunda parte de la tesis se centra en el impacto de la movilidad recurrente en la propagación de epidemias en entornos urbanos. Derivamos un modelo sencillo que permite incorporar fácilmente la distribución de la población en las ciudades reales y sus patrones habituales de desplazamiento sin ninguna pérdida de información. Demostramos que los efectos de las políticas de contención basadas en la reducción de la movilidad no son universales y dependen en gran medida de las características estructurales de las ciudades y los parámetros epidemiológicos del virus circulante en la población. En particular, descubrimos y caracterizamos un nuevo fenómeno, el detrimento epidémico, que refleja el efecto beneficioso de la movilidad en algunos escenarios para contener un brote epidémico. Por último, exploramos tres casos de estudio reales, mostrando que nuestro modelo permite capturar algunos de los mecanismos que han convertido a los núcleos urbanos en importantes focos de contagio en recientes epidemias y que el modelo desarrollado puede servir como base para desarrollar marcos teóricos más realistas que reproducen la evolución de distintas enfermedades como la COVID-19 o el dengue.<br /