Jorge X. Velasco-Hernandez

Universidad Nacional Autónoma de México | UNAM · Institute of Mathematics

Human papillomavirus (HPV) vaccines have been introduced in several countries and have shown positive results in reducing HPV infection and related diseases. Nevertheless, immunization programs remain sub-optimal and more effort is needed to design efficient vaccination deployment. We formulate a two-sex deterministic mathematical model that incorp...

Since the beginning of the COVID-19 epidemic, mitigation measures have been implemented in each country to prevent the increase in positive cases. One of the main ones has been the suspension of face-to-face classes at all levels of education. However, the reopening of schools has not been an easy decision to make, because this implies an increase...

We present a model that explicitly links the epidemiological Ross-Macdonald model with a simple immunological model through a virus inoculation term that depends on the abundance of infected mosquitoes. We explore the relationship between the reproductive numbers at the population (between-host) and individual level (within-host), in particular the...

A bstract We model the observed dynamics of COVID-19 in Mexico and Peru and explore the impact of hypothetical non-pharmaceutical interventions applied on key days of civic, religious, or political nature that increased contacts and transmission events. Using as a baseline the observed epidemic curve, we apply hypothetical reductions in the contact...

The high morbidity of acute respiratory infections constitutes a crucial global health burden. In particular, for SARS-CoV-2, non-pharmaceutical intervention geared to enforce social distancing policies, vaccination, and treatments will remain an essential part of public health policies to mitigate and control disease outbreaks. However, the implem...

We present a model that explicitly links the epidemiological Ross-Macdonald model with a simple immunological model through a virus inoculation term that depends on the abundance of infected mosquitoes. We explore the relationship between the reproductive numbers at the population (between-host) and individual level (within-host), in particular the...

The high morbidity of acute respiratory infections constitutes a crucial global health burden. In particular, for SARS-CoV-2, non-pharmaceutical intervention geared to enforce social distancing policies, vaccination, and treatments will remain an essential part of public health policies to mitigate and control disease outbreaks. However, the implem...

Health officials have stressed the importance of a more uniform distribution of SARS-CoV-2 vaccines within and among countries, yet there has been little critical assessment of the underlying reasons for this admonition. Here, we explicitly show why vaccine equity is critical to controlling the pandemic. Perhaps counter-intuitively, we find that va...

We look at some of the important topics of relevance by late 2021, for the mitigation and control of the SARS-CoV-2 pandemic. Overall, mathematical models have been a very useful tool for the efficient management of the epidemic. We review some of the main conclusions derived from their use in some of the important factors related to the evolution...

This compendium represents a set of guides to understanding the challenging scientific, epidemiological, clinical, social, and economic phenomenon that is represented by the COVID-19 pandemic. The book explains the mathematical modeling of COVID-19 infection, with emphasis on traditional epidemiological principles. It represents a rigorous, compreh...

This work presents a methodology to recreate the observed dynamics of emerging infectious diseases and to generate short-term forecasts for their evolution based on superspreading events occurring on key calendar dates. The method is illustrated by the COVID-19 pandemic dynamics in Mexico and Peru up to January 31, 2022. We also produce scenarios o...

From the beginning of the SARS-CoV-2 pandemic, mathematical models have been developed to describe, predict, and control its evolution. This chapter presents a set of useful mathematical tools to understand the epidemic dynamics. First, to obtain a rough approximation to the magnitude of the epidemic, the basic and effective reproduction numbers ar...

Significance Ecological systems can undergo abrupt and often catastrophic changes known as critical transitions. These critical transitions can be preceded by early warnings that are useful to anticipate them. But anticipating critical transitions in systems with many species is challenging because the early warnings can be absent in some species....

Since the start of the still ongoing COVID-19 pandemic, there have been many modeling efforts to assess several issues of importance to public health. In this work, we review the theory behind some important mathematical models that have been used to answer questions raised by the development of the pandemic. We start revisiting the basic propertie...

November 2020 received a string of encouraging results from leading vaccine developers raising hopes for the imminent availability of an effective and safe vaccine against the SARS-CoV-2. In the present work, we discuss the theoretical impact of introducing a vaccine across a range of scenarios. In particular, we investigate how vaccination coverag...

The purpose of this study is to theoretically investigate the electro-magneto-biomechanics of the swimming of sperms through cervical canal in the female reproductive system. During sexual intercourse, millions of sperms migrate into the cervix in large groups, hence we can approximately model their movement activity by a swimming sheet through the...

As a zoonotic disease, leptospirosis has now been identified as one of the emerging infectious diseases. In this paper, we analyze the propagation of leptospirosis and find a schedule for control programs to eradicate the disease in a cattle ranch. A mathematical model has been built with ordinary differential equations (ODEs) to understand the epi...

For mitigating the COVID-19 pandemic, much emphasis is made on implementing non-pharmaceutical interventions to keep the reproduction number below one. However, using that objective ignores that some of these interventions, like bans of public events or lockdowns, must be transitory and as short as possible because of their significant economic and...

Key high transmission dates for the year 2020 are used to create scenarios to model the evolution of the COVID-19 pandemic in several states of Mexico for 2021. These scenarios are obtained through the estimation of a time-dependent contact rate, where the main assumption is that the dynamic of the disease is heavily determined by the mobility and...

Since the start of the still ongoing COVID-19 pandemic, there have been many modeling efforts to assess several issues of importance to public health. In this work, we review the theory behind some important mathematical models that have been used to answer questions raised by the development of the pandemic. We start revisiting the basic propertie...

In this work we look at several mathematical models that have been constructed during the present pandemic to address different issues of importance to public health policies about epidemic scenarios and thier causes. We start by briefly reviewing the most basic properties of the classic Kermack-McKendrick models and then proceed to look at some ge...

Health officials warn that SARS-CoV-2 vaccines must be uniformly distributed within and among countries if we are to quell the ongoing pandemic. Yet there has been little critical assessment of the underlying reasons for this warning. Here, we explicitly show why vaccine equity is necessary. Perhaps counter-intuitively, we find that vaccine escape...

Health officials warn that SARS-CoV-2 vaccines must be uniformly distributed within and among countries if we are to quell the ongoing pandemic. Yet there has been little critical assessment of the underlying reasons for this warning. Here, we explicitly show why vaccine equity is necessary. Perhaps counter-intuitively, we find that vaccine escape...

In this document we present the parametrization of COVIDESTIM (see references in the document) a model developed by the Yale School of Public Health, to estimate the instantaneous reproductive number and total incidence for the epidemic in Mexico and each of the States of the Mexican Republic. The model has been reparametrized with probability dist...

The characterization of dengue serotypes to account for phenomena observed in its population dynamics, has been largely done in terms of cross-reactivity that includes cross-protection and cross-enhancement. The four dengue serotypes (DENV1-DENV4) are generally classified by their genetic and antigenic properties. Studies report that DENV2 and DENV...

Este es un artículo de divulgación donde presento una discusión general de los fundamentos, estructura, resultados básicos de modelos matemáticos en epidemiología, demografía basados en ecuaciones diferenciales. Comento sobre el número reproductivo básico sus fundamentos poniendo especial énfasis en su aplicación. En general comento, desde mi punto...

The interaction and possibly interference between viruses infecting a common host population is the problem addressed in this work. We model two viral diseases both of the SIRS type that have similar mechanism of transmission and for which a vaccine exists. The vaccine is characterized by its coverage, induced temporal immunity and efficacy. The po...

Highlights: • We address the migration of the human population and its effect on pathogen reinfection. • We use a Markov-chain SIS metapopulation model over a network. • The contact rate is based on the infected hosts and the incidence of their neighboring locations. • We estimate from Dengue data in Mexico the dynamics of migration incorporating...

We present several mathematical models to analyze the SARS-CoV-2 pandemic that is currently impacting the world population. The chapter starts by introducing epidemiological measurements and models useful to characterize the beginning of the epidemic and to obtain a rough understanding of its magnitude. Specially, we discuss the use and estimation...

November 2020 received a string of encouraging results from leading vaccine developers raising hopes for the imminent availability of an effective and safe vaccine against the SARS-CoV-2. In the present work, we discuss the theoretical impact of introducing a vaccine across a range of scenarios. In particular, we investigate how vaccination coverag...

ADVERTENCIA: • Este documento resume resultados técnicos preliminares para efectos de informaciónúnicamente. • Estos resultados no han sido certificados por la revisión de pares y, por ello, en seguimiento de los estándares académicos internacionales, no pueden usarse para guiar decisiones clínicas ni de salud. • Estos resultados no deben ser repor...

9 de noviembre de 2020 ADVERTENCIA: • Este documento resume resultados técnicos preliminares para efectos de informaciónúnicamente. • Estos resultados no han sido certificados por la revisión de pares y, por ello, en seguimiento de los estándares académicos internacionales, no pueden usarse para guiar decisiones clínicas ni de salud. • Estos result...

ADVERTENCIA: • Este documento resume resultados técnicos preliminares para efectos de informaciónúnicamente. • Estos resultados no han sido certificados por la revisión de pares y, por ello, en seguimiento de los estándares académicos internacionales, no pueden usarse para guiar decisiones clínicas ni de salud. • Estos resultados no deben ser repor...

26 de octubre de 2020 ADVERTENCIA: • Este documento resume resultados técnicos preliminares para efectos de informaciónúnicamente. • Estos resultados no han sido certificados por la revisión de pares y, por ello, en seguimiento de los estándares académicos internacionales, no pueden usarse para guiar decisiones clínicas ni de salud. • Estos resulta...

Charla plenaria en el Congreso Virtual de la Sociedad Matematica Mexicana. Video disponoble en https://www.youtube.com/watch?v=G5PvbL5UFU8

----(Paper available until Feb 4, 2021 at https://authors.elsevier.com/c/1cFPX4syv1oKzU.)---- COVID-19 pandemic has underlined the impact of emergent pathogens as a major threat to human health. The development of quantitative approaches to advance comprehension of the current outbreak is urgently needed to tackle this severe disease. Considering...

El presente reporte incluye la comparación de estimaciones de números reproductivos instántaneos de COVID-19 para la Ciudad de México, sus alcaldías y también para los estados y sus capitales, además de algunas ciudades importantes del país con datos actualizados el 20 de Septiembre y recortados hasta el 06 de Septiembre para no sesgar la estimació...

ADVERTENCIA: • Este documento resume resultados de investigación preliminares para efectos de información unicamente. • Estos resultados no han sido certificados por la revisión de pares y, por ello, en seguimiento de los estándares académicos internacionales, no pueden usarse para guiar decisiones clínicas ni de salud. • Estos resultados no deben...

En este reporte se intenta reproducir el calculo del semaforo epidemiologico de�nido por la Secretaria de Salud. Es importante enfatizar que estos calculos estan basados en datos y una aproximacion a la metodologia usada por la DGE. Se usan los 10 indicadores establecidos por la Subsecretaria de Prevencion y Promocion de la Salud, en el documento "...

El presente reporte incluye la comparación de estimaciones de números reproductivos instántaneos de COVID-19 para la Ciudad de México, sus alcaldías y también para los estados y sus capitales, además de algunas ciudades importantes del país con datos actualizados el 12 de Septiembre y recortados hasta el 29 de Agosto para no sesgar la estimaci\'on...

En este reporte se intenta reproducir el calculo del semaforo epidemiologico definido por la Secretaria de Salud. Es importante enfatizar que estos calculos son solo una aproximacion basada en datos y una aproximacion a la metodologia usada por la DGE. Se usan los 10 indicadores establecidos por la Subsecretaria de Prevencion y Promocion de la Salu...

SARS-CoV-2 has now infected 15 million people and produced more than six hundred thousand deaths around the world. Due to high transmission levels, many governments implemented social-distancing and confinement measures with different levels of required compliance to mitigate the COVID-19 epidemic. In several countries, these measures were effectiv...

El presente reporte incluye la comparación de Rts calculados hasta el 08 de agosto, usando datos actualizados el 22 de agosto, con respecto al nowcasting de la serie de tiempo de Rts con información hasta el 25 de Julio y 01 de Agosto. Los métodos usados fueron extraídos o basados en las referencias al final del documento. Este documento va acompañ...

Ponencias presentadas en el Foro 2020: lecciones de la pandemia, organizado por la UNAM. https://www.facebook.com/watch/?v=315536649683276&extid=qFLEY6ySWdFxNDjI

Epidemiological models usually contain a set of parameters that must be adjusted based on available observations. Once a model has been calibrated, it can be used as a forecasting tool to make predictions and to evaluate contingency plans. It is customary to employ only point estimators of model parameters for such predictions. However, some models...

El presente reporte es un resumen sintético que unicamente incluye las gráficas comparativas de proyecciones de $R_t$s calculados hasta el 01 de Agosto, usando datos actualizados hasta el 15 de Agosto para evitar sesgos debidos a retrasos en reportaje y período de incubación del virus, con las respectivas proyecciones de $R_t$s con datos hasta el 1...

Models developed for the COVID-19 in Mexico: transparency, free exchange of ideas, interchange of knowledge, open results.

SARS-CoV-2 has now infected 15 million people and produced more than six hundred thousand deaths around the world. Due to high transmission levels, many governments implemented social-distancing measures and confinement with different levels of required compliance to mitigate the COVID-19 epidemic. In several countries, these measures were effectiv...

C\'alculo de Rt hasta el 21 de junio para la incidencia estatal de casos.

Análisis del incremento inusual de casos probables de influenza en México durante 2020 y su posible relación con la epidemia causada por el virus SARS-CoV-2.

Reporte de evolución de la epidemia (aparición de mesetas, eventos de movilidad atípicos previos al máximo de incidencia).

Most of the recent epidemic outbreaks in the world have as a trigger, a strong migratory component as has been evident in the recent Covid-19 pandemic. In this work we address the problem of migration of human populations and its effect on pathogen reinfections in the case of Dengue, using a Markov-chain susceptible-infected-susceptible (SIS) metap...

Proyecciones de la epidemia para Querétaro (realizadas para el municipio y el estado) el 7 de junio del 2020.

La presentación pretende explicar y aclarar las funciones, características, limitaciones de un modelo matemático epidemiológico, particularmente aquellos hechos y usados para la epidemia de COVID-19. Se enfatiza que el resultado de un modelo no es la verdad, un resultado de un modelo no se debe "creer". Los resultados de un modelo deben ser vistos...

On 23 and 30 March 2020 the Mexican Federal government implemented social distancing measures to mitigate the COVID-19 epidemic. We use a mathematical model to explore atypical transmission events within the confinement period, triggered by the timing and strength of short time perturbations of social distancing. We show that social distancing meas...

To mitigate the COVID-19 pandemic, much emphasis exists on implementing non-pharmaceutical interventions to keep the reproduction number below one. But using that objective ignores that some of these interventions, like bans of public events or lockdowns, must be transitory and as short as possible because of their significative economic and societ...

Resumen de trabajos de modelado matemático para las proyecciones de COVID-19 en la CDMX y evaluación de medidas de mitigación. Con datos al 4 de mayo del 2020. Trabajo colectivo de investigadores de la UNAM y colaboradores de otras instituciones.

To mitigate the COVID-19 pandemic, much emphasis exists on implementing non-pharmaceutical interventions to keep the reproduction number below one. But using that objective ignores that some of these interventions, like bans of public events or lockdowns, must be transitory and as short as possible because of their significative economic and societ...

La presentación pretende explicar y aclarar las funciones, características, limitaciones de un modelo matemático epidemiológico, particularmente aquellos hechos y usados para la epidemia de COVID-19. Se enfatiza que el resultado de un modelo no es la verdad, un resultado de un modelo no se debe "creer". Los resultados de un modelo deben ser vistos...

COVID-19: Número reproductivo instantáneo en algunas ciudades de la República y una nota sobre la estimación de incidencia

Epidemiological models contain a set of parameters that must be adjusted based on available observations. Once a model has been calibrated, it can be used as a forecasting tool to make predictions and to evaluate contingency plans. It is customary to employ only point estimators for such predictions. However, some models may fit the same data reaso...

Sanitary Emergency Measures (SEM) were implemented in Mexico on March 30th, 2020 requiring the suspension of non-essential activities. This action followed a Healthy Distance Sanitary action on March 23rd, 2020. The aim of both measures was to reduce community transmission of COVID-19 in Mexico by lowering the effective contact rate. Using a modif...