Artículos relacionados con COVID-19
Forecasting hospital demand during COVID-19 pandemic outbreaks

We present a compartmental SEIRD model aimed at forecasting hospital oc- cupancy in metropolitan areas during the current COVID-19 outbreak. The model features asymptomatic and symptomatic infections with detailed hospi- tal dynamics. We model explicitly branching probabilities and non exponential residence times in each latent and infected compartments. Using both hospi- tal admittance confirmed cases and deaths we infer the contact rate and the initial conditions of the dynamical system, considering break points to model lockdown interventions. Our Bayesian approach allows us to produce timely probabilistic forecasts of hospital demand. The model has been used by the federal government of Mexico to assist public policy, and has been applied for the analysis of more than 70 metropolitan areas and the 32 states in the coun- try.

On the dynamics of the Coronavirus epidemic and the unreported cases: the Chilean case

One of the main problems faced in the mathematical modeling of the coronavirus epi- demic has been the lack of quality data. In particular, it is estimated that a large number of cases have been unreported, especially those of asymptomatic patients. This is mostly due to the strong demand of tests required by a relatively complete report of the infected cases. Although the countries/regions that have managed to control the epidemic have been precisely those that have been able to develop a great capacity of testing, this has not been achieved in most of the situations.

Impacto de las Medidas de Control en la evolución del brote COVID-19

Presentamos un análisis basado en un modelo matemático ampliamente utilizado en el estudio de epidemias con el objetivo de comprender cuantitativamente los efectos de los medidas de mitigación adoptados en diferentes países para disminuir la tasa de contacto de COVID-19. Las medidas de control han variado tanto en la escala de severidad como en la temporalidad frente al brote epidémico en cada país. Estas variaciones en las medidas de control producen un efecto diferenciado en la evolución de la tasa de contagio que se puede medir con la metodología que desarrollamos que denominamos ''ajustes SIR dinámicos data-driven''. La metodología consiste en ajustar los parámetros del modelo SIR en intervalos variables de tiempo, donde se determinan los intervalos de ajuste directamente de los datos de infectados confirmados por la OMS en cada país. Es importante resaltar que en este trabajo analizamos diversos escenarios del binomio medidas de control impuestas y los efectos producidos en la evolución del brote epidémico de cada país lo que en conjunto nos permite concluir que la implementación oportuna o muy tardía de algunas de las medidas de control establecidas tanto por los gobiernos tienen un impacto en la evolución, la intensidad y la duración del brote epidémico. Nuestra intención es aportar algunas ideas y datos cuantitativos sobre: i) El decrecimiento de la tasa de contagio en todos los países después de un periodo de haber aplicado las medidas de control; ii) que la efectividad de estas medidas depende tanto del orden como de la severidad y temporalidad con las que fueron aplicadas en los casos analizados iii) con este análisis queremos resaltar que estas medidas son cruciales para la contención y mitigación del brote epidémico y que nos dan un atisbo de la dimensión del brote epidémico de cada país.

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Modeling the transmission dynamics and the impact of the control interventions for the COVID-19 epidemic outbreak

In this paper we develop a compartmental epidemic model to study the transmission dy- namics of the COVID-19 epidemic outbreak, with Mexico as a practical example. In particular, we evaluate the theoretical impact of plausible control interventions such as home quarantine, social dis- tancing, cautious behavior and other self-imposed measures. We also investigate the impact of environ- mental cleaning and disinfection, and government-imposed isolation of infected individuals. We use a Bayesian approach and officially published data to estimate some of the model parameters, including the basic reproduction numbers. Our findings suggest that social distancing and quarantine are the winning strategies to reduce the impact of the outbreak. Environmental cleaning can also be relevant, but its cost and effort required to bring the maximum of the outbreak under control indicate that its cost-efficacy is low.

In-host Modelling of COVID-19 Kinetics in Humans (PDF)

COVID-19 pandemic has underlined the impact of emergent pathogens as a major threat for human 2 health. The development of quantitative approaches to advance comprehension of the current outbreak 3 is urgently needed to tackle this severe disease. In this work, several mathematical models are proposed 4 to represent COVID-19 dynamics in infected patients. Considering different starting times of infection, 5 parameters sets that represent infectivity of COVID-19 are computed and compared with other viral 6 infections that can also cause pandemics.

Report on the forecast of cumulative COVID-19 cases in Mexico (PDF)

This is a technical report elaborated on behalf of the Nodo Multidisciplinario de Matem ́aticas Aplicadas del Instituto de Matem ́aticas UNAM-Juriquilla. The analysis it contains is based on the publicly available information as released by the Secretar ́ıa de Salud. Its aim is to contribute to the knowledge necessary to fight the sars-cov-2 epidemic.

Consequences of delays and imperfect implementation of isolation in epidemic control

For centuries isolation has been the main control strategy of unforeseen epidemic outbreaks. When implemented in full and without delay, isolation is very effective. However, flawless implementation is seldom feasible in practice. We present an epidemic model called SIQ with an isolation protocol, focusing on the consequences of delays and incomplete identification of infected hosts. The continuum limit of this model is a system of Delay Differential Equations, the analysis of which reveals clearly the dependence of epidemic evolution on model parameters including disease reproductive number, isolation probability, speed of identification of infected hosts and recovery rates. Our model offers estimates on minimum response capabilities needed to curb outbreaks, and predictions of endemic states when containment fails. Critical response capability is expressed explicitly in terms of parameters that are easy to obtain, to assist in the evaluation of funding priorities involving preparedness and epidemics management.

In-host Modelling of COVID-19 Kinetics in Humans

COVID-19 pandemic has underlined the impact of emergent pathogens as a major threat for human health. The development of quantitative approaches to advance comprehension of the current outbreak is urgently needed to tackle this severe disease. In this work, several mathematical models are proposed to represent COVID-19 dynamics in infected patients. Considering different starting times of infection, parameters sets that represent infectivity of COVID-19 are computed and compared with other viral infections that can also cause pandemics. Based on the target cell model, COVID-19 infecting time between susceptible cells (mean of 30 days approximately) is much slower than those reported for Ebola (about 3 times slower) and influenza (60 times slower). The within-host reproductive number for COVID-19 is consistent to the values of influenza infection (1.7-5.35). The best model to fit the data was including immune responses, which suggest a slow cell response peaking between 5 to 10 days post onset of symptoms. The model with eclipse phase, time in a latent phase before becoming productively infected cells, was not supported. Interestingly, both, the target cell model and the model with immune responses, predict that virus may replicate very slowly in the first days after infection, and it could be below detection levels during the first 4 days post infection. A quantitative comprehension of COVID-19 dynamics and the estimation of standard parameters of viral infections is the key contribution of this pioneering work.

Dispersion of a new coronavirus SARS-CoV-2 by airlines in 2020: Temporal estimates of the outbreak in Mexico

On January 23, 2020, China imposed a quarantine on the city of Wuhan to contain the SARS-CoV-2 outbreak. Regardless of this measure the new infection has spread to several countries around the world. Here, we developed a method to study the dissemination of this infection by the airline routes and we give estimations of the time of arrival of the outbreaks to the different cities. In this work we show an analysis of the dispersion of this infection to other cities by airlines based on the classic model the Kermack and McKendrick complemented with diffusion on a graph composed of nodes which represent the cities and edges which represent the airline routes. We do several numerical simulations to estimate the date of arrival to different cities starting the infection at Wuhan, China and to show the robustness of the estimation respect to changes in the epidemiological parameters and to changes on the graph. We use Mexico City as an example. In this case, our estimate of the arrival time is between March 20 and March 30, 2020. This analysis is limited to the analysis of dispersion by airlines, so this estimate should be taken as an overestimate since the infection can arrive by other means. This model estimates the arrival of the infectious outbreak to Mexico between March 20 and March 30. This estimation gives a time period to implement and strengthen preventive measures aimed at the general population, as well as to strengthen hospital infrastructure and training of human resources in health.

The SARS-CoV-2 epidemic outbreak: a review of plausible scenarios of containment and mitigation for Mexico

We present here several variants of a mathematical model to explore three main issues related to SARS-CoV-2 spread in scenarios similar to those present in Mexico and elsewhere in Latin America. We explore the consequences for travel inside a given region, in this case Mexico, particularly focusing on airplane transportation but attempting to give a gross approximation to terrestrial movement since this is the main form of population movement across geographical areas in the country; then we proceed to study the effect of behavioral changes required to lower transmission by lowering the contact rate and infection probability and lastly, we explore the consequences of disease spread in a population subject to social isolation.These models are not suitable for predictive purposes although some rough predictions can be extracted from them. They are presented as a tool that can serve to explore plausible scenarios of spread and impact, effectiveness and consequences of contention and mitigation policies. Given the early stage at which the epidemic is at the date of writing in Mexico, we hope these ideas can be helpful for the understanding of the importance of isolation, social distancing and screening of the general population.

Artículos relacionados con otro tipo de epidemias
Modeling Public Health Campaigns for Sexually Transmitted Infections via Optimal and Feedback Control (PDF)

Control of sexually transmitted infections (STIs) poses important challenges to public health authorities. Obstacles for STIs control include low priority in public health programs and disease transmission mechanisms. This work uses a compartmental pair model to explore different public health strategies on the evolution of STIs. Optimal and feedback control are used to model realistic strategies for reducing the prevalence of these infections. Feedback control is proposed to model the reaction of public health authorities relative to an alert level. Optimal control is used to model optimization of available resources for implementing strategies. Numerical simulations are performed using trichomoniasis, gonorrhea, chlamydia and human papillomavirus (HPV) as study cases. HPV is non-curable and it is analyzed only under transmission control such as condom promotion campaigns. Trichomoniasis, gonorrhea, and chlamydia are curable STIs that are modeled here additionally under treatment control. Increased cost-effectiveness ratio (ICER) is employed as a criterion to measure control strategies performance. The features and drawbacks of control strategies under the pair formation process are discussed.

Transmission dynamics of acute respiratory diseases in a population structured by age (PDF)

Determiningtheroleofageonthetransmissionofaninfectionisatopicthathasreceived significant attention. In this work, a dataset of acute respiratory infections structured by age from San Luis Potos ́ı, Mexico, is analyzed to understand the age impact on this class of diseases. To do that, a compartmental SEIRS multigroup model is proposed to describe the infection dynamics among age groups. Then, a Bayesian inference approach is used to estimate relevant parameters in the model such as the probability of infection, the average time that one individual remains infectious, the average time that one individual remains immune, and the force of infection, among others. Based on those estimates, our analysis leads us to conclude that children less than 5 years old are the primary spreaders of respiratory infections in San Luis Potos ́ı’s population from 2000 to 2008 since they are more prone to get sick, remain infectious for longer periods and they are reinfected more rapidly. On the other hand, the group of young adults (20–59) is the one that differs the most from the little children’s group because it does not get sick often, it remains infectious only a few days and it stays healthy for longer periods. These observations allow us to infer that the group of young adults is the one that, on average, less contributed to the spread of this class of infections during the years represented in our database.

A Bayesian Outbreak Detection Method for Influenza-Like Illness (PDF)

Epidemic outbreak detection is an important problem in public health and the development of reliable methods for outbreak detection remains an active research area. In this paper we introduce a Bayesian method to detect outbreaks of influenza-like illness from surveillance data. The rationale is that, during the early phase of the outbreak, surveillance data changes from autoregressive dynamics to a regime of exponential growth. Our method uses Bayesian model selection and Bayesian regression to identify the breakpoint. No free parameters need to be tuned. However, historical information regarding influenza-like illnesses needs to be incorporated into the model. In order to show and discuss the performance of our method we analyze synthetic, seasonal, and pandemic outbreak data.

A new surveillance and spatio-temporal visualization tool SIMID: SIMulation of Infectious Diseases using random networks and GIS (PDF)

In this paper we discuss the SIMID tool for simulation of the spread of infectious disease, enabling spatio-temporal visualization of the dynamics of influenza outbreaks. SIMID is based on modern random network methodology and implemented within the R and GIS frameworks. The key advantage of SIMID is that it allows not only for the construction of a possible scenario for the spread of an infectious disease but also for the assessment of mitigation strategies, variation and uncertainty in disease parameters and randomness in the progression of an outbreak. We illustrate SIMID by application to an influenza epidemic simulation in a population constructed to resemble the Region of Peel, Ontario, Canada.

Applications of the Variance of Final Outbreak Size for Disease Spreading in Networks (PDF)

Theassumptionthatallsusceptibleindividualsareequallylikelytoacquire the disease during an outbreak (by direct contact with an infective individual) can be relaxed by bringing into the disease spread model a contact structure between individuals in the population. The structure is a random network or random graph that describes the kind of contacts that can result in transmission. In this paper we use an approach similar to the approaches of Andersson (Ann Appl Probab 8(4):1331–1349, 1998) and Newman (Phys Rev E 66:16128, 2002) to study not only the expected values of final sizes of small outbreaks, but also their variability. Using these first two moments, a probability interval for the outbreak size is suggested based on Chebyshev’s inequality. We examine its utility in results from simulated small outbreaks evolving in simulated random networks. We also revisit and modify two related results from Newman (Phys Rev E 66:16128, 2002) to take into account the important fact that the infectious period of an infected individual is the same from the perspective of all the individual’s contacts. The theory developed in this area can be extended to describe other “infectious” processes such as the spread of rumors, ideas, information, and habits.

Forecasting influenza in Hong Kong with Google search queries and statistical model fusion (PDF)

The objective of this study is to investigate predictive utility of online social media and web search queries, particularly, Google search data, to forecast new cases of influenza-like-ill- ness (ILI) in general outpatient clinics (GOPC) in Hong Kong. To mitigate the impact of sen- sitivity to self-excitement (i.e., fickle media interest) and other artifacts of online social media data, in our approach we fuse multiple offline and online data sources.

Competencia y Superinfección en Plagas y Enfermedades (PDF)

Una de las observaciones m ́as famosas de Darwin es la que se refiere al argumento de Thomas Malthus respecto del crecimiento geometrico de las poblaciones y el crecimiento lineal de los recursos que las proveen de alimento, vestido, casa y otras necesidades basicas. Transpuesta esta observación al contexto de los sistemas naturales da como resultado la lucha por la vida y el concepto de seleccion natural que, en el contexto de las comunidades ecológicas, se expresa particularmente en la competencia por recursos que es determinante en la conformación de la estructura de las comunidades biológicas y ha sido objeto de muy amplios estudios (de particular interes para el modelo aquí presentado ver Nowak&May (1994) y Tilman (1994)). En este artículo revisaremos esta idea, la competencia por recursos, en el contexto de las enfermedades infecciosas. La epidemiologıa es, hoy por hoy, una de las ́areas de aplicación de las matematicas con más impacto en la sociedad, particularmente debido a la potencia que sus métodos proporcionan a la definición de políticas de control y prevención de brotes epidémicos.

Transmission dynamics of two dengue serotypes with vaccination scenarios (PDF)

In this work we present a mathematical model that incorporates two Dengue serotypes. The model has been constructed to study both the epidemiological trends of the disease and conditions that allow co- existence in competing strains under vaccination. We consider two viral strains and temporary cross- immunity with one vector mosquito population. Results suggest that vaccination scenarios will not only reduce disease incidence but will also modify the transmission dynamics. Indeed, vaccination and cross immunity period are seen to decrease the frequency and magnitude of outbreaks but in a differentiated manner with specific effects depending upon the interaction vaccine and strain type.

Extracellular dynamics of early HIV infection (PDF)

In this paper, we explore the interplay of virus contact rate, virus production rates, and initial viral load during early HIV infection. First, we consider an early HIV infection model formulated as a bivariate branching process and provide conditions for its criticality R0 > 1.

Superinfection between Influenza and RSV Alternating Patterns in San Luis Potosí State, México (PDF)

The objective of this paper is to explain through the ecological hypothesis superinfection and competitive interaction between two viral populations and niche (host) availability, the alternating patterns of Respiratory Syncytial Virus (RSV) and influenza observed in a re- gional hospital in San Luis Potosí State, México using a mathematical model as a methodo- logical tool. The data analyzed consists of community-based and hospital-based Acute Respiratory Infections (ARI) consultations provided by health-care institutions reported to the State Health Service Epidemiology Department from 2003 through 2009.

Regional reinfection by Dengue: a network approach using data from Mexico (PDF)

Most of the recent epidemic outbreaks in the world have a strong immigration component as a trigger rather than the dynamics implied by the basic reproduction number. In this work we present and discuss an approach to the problem of pathogen reinfections in a given area that associates people mobility and transmission of dengue, using a Markov-chain Susceptible-Infected-Susceptible (SIS) metapopulation model over a network. Our model postulates a parameter that we have named the effective inoculum size which represents a local measure of the population size of infected hosts that arrive at a given location as a function of population size, current incidence at neighboring locations and the connectivity of the patches. This parameter can be interpreted as an indicator of outbreak risk of any location. Our model also incorporates climate variability represented by an index based upon precipitation data. We replicate observed patterns of incidence at a regional scale using data from epidemics in Mexico.

Equivalence of the Erlang-Distributed SEIR Epidemic Model and the Renewal Equation

Artículo técnico para modelar correctamente el tiempo de residencia de las clases latente e infecciosa. La mayoría de los modelos epidemiológicos se pueden representar usando una ecuación de renovación (Euler 1767). El artículo deriva expresiones analíticas para establecer la equivalencia entre la ecuación de renovación y un modelo SEIR donde el tiempo de residencia sigue una distribución Erlang.

Artículos relacionados con logística
¿Por qué el semáforo está en rojo?

La respuesta rápida es porque la epidemia, en la mayoría de los lugares del país, no ha llegado ni a la mitad. Un semáforo rojo es esencialmente lo mismo que la jornada de su sana distancia. De relajar ahora las medidas, todo el esfuerzo que hemos hecho hasta ahora, servirá de muy poco.
Hacer un pronóstico preciso del futuro es muy difícil. De hecho, es ya difícil entender lo que vemos, entender lo que ha pasado, lo que está pasando. Empecemos por ahí.

Científicos Mexicanos en el Extranjero

Conforman un grupo de jóvenes Científicos Mexicanos en el Extranjero que colaboran con diversas instituciones de investigación en México. Están comprometidos con la sociedad y su motivación es estrechar la brecha que existe entre el conocimiento científico especializado y el saber popular.
Ven con preocupación cómo las redes sociales han sido una vía para la propagación de noticias falsas y rumores que solo infunden incertidumbre y confusión. Desean revertir este fenómeno y convertir estos medios en el canal para acercarse a la sociedad y crear una alternativa confiable para informar a la población. También quieren poner al alcance del público su trabajo científico y vincularse con la comunidad de trabajadores de la ciencia en el país para el desarrollo de proyectos que ayuden a resolver los problemas que aquejan a la sociedad.

COVID19 | ConCiencia Social

Es un grupo compuesto por investigadores de ciencias exactas y humanistas. Su misión es realizar proyectos que tengan un impacto en la sociedad desde un enfoque multidisciplinario.

¿Qué pasará ahora?

Los futuros de la COVID-19 explicados con simulaciones

Lo que podemos esperar

En unas pocas semanas el coronavirus ha irrumpido abruptamente en nuestras vidas y muy pronto tendremos que tomar como sociedad muchas decisiones. ¿Qué podemos esperar?

COVID-19: What We Know and What’s Next, with Arnold J. Levine

Arnold J. Levine is Professor Emeritus at the Institute for Advanced Study and leads the Institute’s Simons Center for Systems Biology in the School of Natural Sciences. An acclaimed leader in cancer research, he is also an expert on influenza and has advised the Canadian government and private industry on response to COVID-19. He spoke with Joanne Lipman, the Institute’s Peretsman Scully Distinguished Journalism Fellow, about the novel coronavirus outbreak, how it compares to previous pandemics, and potential therapies in the works that may help stop the spread. This interview was conducted on March 27, 2020. It has been edited for length and clarity.

MODELAMIENTO DE UNA EPIDEMIA, SEGUNDA PARTE: Otros modelos y resolución numérica

La crisis sanitaria del Coronavirus Covid-19 ha demostrado el papel del modelamiento matemático en la toma de decisiones políticas y de salud. En el artículo precedente, discutimos el modelo SIR y discutimos el efecto de las medidas sanitarias, ilustrando el impacto sobre la evolución de la epidemia. Introduciremos ahora el modelo SEIR y lo extenderemos a modelos con estructura de edad. Además, una pequeña parte (difícil, pero no esencial, de modo que puede ser evitada en una primera lectura) tiene por objetivo discutir los métodos de resolución numérica utilizados. Al final del artículo está disponible una simulación interactiva variando parámetros.


La AMS pone a disposición estos libros gratis durante la pandemia

Modelling in Healthcare

The Complex Systems Modelling Group (CSMG), The IRMACS Center, Simon Fraser University, Burnaby, BC, Canada

This volume is both a broad overview of how modelling works and a practical and usable introduction to the styles of modelling most applicable to healthcare.

Mathematical Methods in Immunology

By Jerome K. Percus, Courant Institute of Mathematical Sciences, New York, NY and Department of Physics, New York University, New York, NY

This book aims to describe the adaptive immune system via mathematical models, introducing tools that should be in the armory of any current or aspiring applied mathematician interested in immunology.

Modeling Paradigms and Analysis of Disease Transmission Models

Edited by Abba B. Gumel, University of Manitoba, Winnipeg, MB, Canada, and Suzanne Lenhart, University of Tennessee, Knoxville, TN

Based on two DIMACS activities on Mathematical Modeling of Infectious Diseases in Africa, this volume introduces basic principles of disease modeling and stability in tutorial papers where continuous and discrete time models, optimal control, and stochastic features are introduced.

Selected Materials from Differential Equations: Techniques, Theory, and Applications

By Barbara D. MacCluer, Paul S. Bourdon, Thomas L. Kriete, University of Virginia, Charlottesville, VA

Chapter 10, covering Nonlinear Systems, with a section on modeling the spread of disease, is freely downloadable.

CONACYT frente a COVID-19

Ecosistema Nacional Informático COVID-19 (ENI/COVID-19)

Repositorio CONACYT COVID-19

International Mathematical Union: COVID-19 Resource Website

Springer Nature

New England Journal of Medicine