RESUMEN

We construct, analyze and interpret a mathematical model for an environmental transmitted disease characterized for the existence of three disease stages: acute, severe and asymptomatic. Besides, we consider that severe and asymptomatic cases may present relapse between them. Transmission dynamics driven by the contact rates only occurs when a parameter R∗>1, as normally occur in directly-transmitted or vector-transmitted diseases, but it will not adequately correspond to a basic reproductive number as it depends on environmental parameters. In this case, the forward transcritical bifurcation that exists for R∗<1, becomes a backward bifurcation, producing multiple steady-states, a hysteresis effect and dependence on initial conditions. A threshold parameter for an epidemic outbreak, independent of R∗ is only the ratio of the external contamination inflow shedding rate to the environmental clearance rate. R∗ describes the strength of the transmission to infectious classes other than the I-(acute) type infections. The epidemic outbreak conditions and the structure of R∗ appearing in this model are both responsible for the existence of endemic states.

Asunto(s)

Enfermedades Transmisibles , Humanos , Enfermedades Transmisibles/transmisión , Enfermedades Transmisibles/epidemiología , Número Básico de Reproducción/estadística & datos numéricos , Enfermedades Endémicas/estadística & datos numéricos , Brotes de Enfermedades , Modelos Biológicos , Epidemias/estadística & datos numéricos , Conceptos Matemáticos , Modelos Teóricos

RESUMEN

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 coverage, efficacy and delivery time affect the control of the transmission dynamics in comparison to mobility restrictions. The analysis is based on a metapopulation epidemic model structured by risk. We perform a global sensitivity analysis using the Sobol method. Our analysis suggest that the reduction of mobility among patches plays a significant role in the mitigation of the disease close to the effect of immunization coverage of 30% achieved in four months. Moreover, for an immunization coverage between 20% and 50% achieved in the first half of 2021 with a vaccine efficacy between 70% and 95%, the percentage reduction in the total number of SARS-CoV-2 infections is between 30% and 50% by the end of 2021 in comparison with the no vaccination scenario.

RESUMEN

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 electrically-conducting biofluid. The Eyring-Powell fluid model is considered as the base fluid to simulate male's semen with self-propulsive sperms. An external magnetic field is applied on the flow in transverse direction. The governing partial differential system of equations is analytically solved. Creeping flow regimen is employed throughout the channel due to self-propulsion of swimmers along with long wavelength approximation. Solutions for the stream function, velocity profile, and pressure gradient (above and below the swimming sheet) are obtained and plotted with the pertinent parameters. The prominent features of pumping characteristics are also investigated. Results indicate that the propulsive velocity is reduced with an increase in the electric field which is an important feature that can be used in controlling the transport of spermatozoa inside the cervical canal. Not only is the present analysis valid for living micro-organisms, but also valid for artificially designed electro-magnetic micro-swimmers which is further utilized in electro-magnetic therapy taking place in female's lubricous cervical canal filled with mucus.

Asunto(s)

Cuello del Útero/fisiología , Imanes , Movimiento/fisiología , Espermatozoides/fisiología , Femenino , Humanos , Hidrodinámica , Masculino , Modelos Biológicos , Moco/metabolismo , Presión , Reología

RESUMEN

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 effective, and it was possible to flatten the epidemic curve and control it. In others, this objective was not or has not been achieved. In far too many cities around the world, rebounds of the epidemic are occurring or, in others, plateaulike states have appeared, where high incidence rates remain constant for relatively long periods of time. Nonetheless, faced with the challenge of urgent social need to reactivate their economies, many countries have decided to lift mitigation measures at times of high incidence. In this paper, we use a mathematical model to characterize the impact of short duration transmission events within the confinement period previous but close to the epidemic peak. The model also describes the possible consequences on the disease dynamics after mitigation measures are lifted. We use Mexico City as a case study. The results show that events of high mobility may produce either a later higher peak, a long plateau with relatively constant but high incidence or the same peak as in the original baseline epidemic curve, but with a post-peak interval of slower decay. Finally, we also show the importance of carefully timing the lifting of mitigation measures. If this occurs during a period of high incidence, then the disease transmission will rapidly increase, unless the effective contact rate keeps decreasing, which will be very difficult to achieve once the population is released.

Asunto(s)

Control de Enfermedades Transmisibles/legislación & jurisprudencia , Infecciones por Coronavirus/epidemiología , Infecciones por Coronavirus/transmisión , Neumonía Viral/epidemiología , Neumonía Viral/transmisión , Algoritmos , Betacoronavirus , COVID-19 , Control de Enfermedades Transmisibles/métodos , Trazado de Contacto , Conductas Relacionadas con la Salud , Humanos , México/epidemiología , Modelos Teóricos , Pandemias , Probabilidad , Política Pública , SARS-CoV-2 , Aislamiento Social

RESUMEN

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 may fit the same data reasonably well for a broad range of parameter values, and this flexibility means that predictions stemming from them will vary widely, depending on the particular values employed within the range that gives a good fit. When data are poor or incomplete, model uncertainty widens further. A way to circumvent this problem is to use Bayesian statistics to incorporate observations and use the full range of parameter estimates contained in the posterior distribution to adjust for uncertainties in model predictions. Specifically, given an epidemiological model and a probability distribution for observations, we use the posterior distribution of model parameters to generate all possible epidemic curves, whose information is encapsulated in posterior predictive distributions. From these, one can extract the worst-case scenario and study the impact of implementing contingency plans according to this assessment. We apply this approach to the evolution of COVID-19 in Mexico City and assess whether contingency plans are being successful and whether the epidemiological curve has flattened.

Asunto(s)

Betacoronavirus , Infecciones por Coronavirus/epidemiología , Epidemias , Neumonía Viral/epidemiología , Teorema de Bayes , COVID-19 , Infecciones por Coronavirus/mortalidad , Bases de Datos Factuales , Epidemias/estadística & datos numéricos , Humanos , Conceptos Matemáticos , México/epidemiología , Modelos Biológicos , Modelos Estadísticos , Pandemias , Neumonía Viral/mortalidad , Probabilidad , SARS-CoV-2 , Factores de Tiempo , Incertidumbre

RESUMEN

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 modification of the Kermack-McKendrick SEIR model we explore the effect of behavioral changes required to lower community transmission by introducing a time-varying contact rate, and the consequences of disease spread in a population subject to suspension of non-essential activities. Our study shows that there exists a trade-off between the proportion of the population under SEM and the average time an individual is committed to all the behavioral changes needed to achieve an effective social distancing. This trade-off generates an optimum value for the proportion of the population under strict mitigation measures, significantly below 1 in some cases, that minimizes maximum COVID-19 incidence. We study the population-level impact of three key factors: the implementation of behavior change control measures, the time horizon necessary to reduce the effective contact rate and the proportion of people under SEM in combating COVID-19. Our model is fitted to the available data. The initial phase of the epidemic, from February 17th to March 23rd, 2020, is used to estimate the contact rates, infectious periods and mortality rate using both confirmed cases (by date of symptoms initiation), and daily mortality. Data on deaths after March 23rd, 2020 is used to estimate the mortality rate after the mitigation measures are implemented. Our simulations indicate that the most likely dates for maximum incidence are between late May and early June, 2020 under a scenario of high SEM compliance and low SEM abandonment rate.

Asunto(s)

Control de Enfermedades Transmisibles , Infecciones por Coronavirus/prevención & control , Conductas Relacionadas con la Salud , Modelos Teóricos , Pandemias/prevención & control , Neumonía Viral/prevención & control , Conducta de Reducción del Riesgo , COVID-19 , Humanos , México , Aislamiento Social

RESUMEN

Determining the role of age on the transmission of an infection is a topic that has received significant attention. In this work, a dataset of acute respiratory infections structured by age from San Luis Potosí, 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 Potosí'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.

Asunto(s)

Susceptibilidad a Enfermedades , Infecciones por Virus Sincitial Respiratorio/transmisión , Infecciones del Sistema Respiratorio/transmisión , Adolescente , Adulto , Factores de Edad , Anciano , Teorema de Bayes , Niño , Preescolar , Control de Enfermedades Transmisibles , Brotes de Enfermedades , Femenino , Humanos , Lactante , Recién Nacido , Masculino , México/epidemiología , Persona de Mediana Edad , Modelos Estadísticos , Dinámica Poblacional , Probabilidad , Adulto Joven

RESUMEN

We will inevitably face new epidemics where the lack of long time-series data and the uncertainty about the outbreak dynamics make difficult to obtain quantitative predictions. Here we present an algorithm to qualitatively infer time-varying contact rates from short time-series data, letting us predict the start, relative magnitude and decline of epidemic outbreaks. Using real time-series data of measles, dengue, and the current zika outbreak, we demonstrate our algorithm can outperform existing algorithms based on estimating reproductive numbers.

Asunto(s)

Dengue/epidemiología , Epidemias/estadística & datos numéricos , Sarampión/epidemiología , Incertidumbre , Infección por el Virus Zika/epidemiología , Algoritmos , Brasil/epidemiología , Colombia/epidemiología , Estudios de Evaluación como Asunto , Humanos , New York/epidemiología

RESUMEN

Since the first major outbreak reported on the island Yap in 2007, the Zika virus spread has alerted the scientific community worldwide. Zika is an arbovirus transmitted by Aedes mosquitoes; particularly in Central and South America, the main vector is the same mosquito that transmits dengue and chikungunya, Aedes aegypti. Seeking to understand the dynamics of spread of the Zika, in this paper, three mathematical models are presented, in which vector transmission of the virus, sexual contact transmission and migration are considered. Numerical analysis of these models allows us to have a clear view of the effects of sexual transmission and migration in the spread of the virus, showing that sexual transmission influences the magnitude of the outbreaks and migration generates outbreaks over time, each of lower intensity than the previous.

Asunto(s)

Infección por el Virus Zika/epidemiología , Infección por el Virus Zika/transmisión , Aedes/virología , Animales , Epidemias/estadística & datos numéricos , Femenino , Migración Humana , Humanos , Masculino , Conceptos Matemáticos , Modelos Biológicos , Mosquitos Vectores/virología , Conducta Sexual , Virus Zika

RESUMEN

In this paper we address the problem of estimating the parameters of Markov jump processes modeling epidemics and introduce a novel method to conduct inference when data consists on partial observations in one of the state variables. We take the classical stochastic SIR model as a case study. Using the inverse-size expansion of van Kampen we obtain approximations for the first and second moments of the state variables. These approximate moments are in turn matched to the moments of an inputed Generic Discrete distribution aimed at generating an approximate likelihood that is valid both for low count or high count data. We conduct a full Bayesian inference using informative priors. Estimations and predictions are obtained both in a synthetic data scenario and in two Dengue fever case studies.

Asunto(s)

Epidemias , Modelos Biológicos , Número Básico de Reproducción , Teorema de Bayes , Simulación por Computador , Dengue/epidemiología , Virus del Dengue/crecimiento & desarrollo , Métodos Epidemiológicos , Humanos , Modelos Estadísticos

RESUMEN

BACKGROUND: In the aftermath of the global spread of 2009 influenza A (pH1N1) virus, still very little is known of the early stages of the outbreak in Mexico during the early months of the year, before the virus was identified. METHODOLOGY/MAIN FINDINGS: We fit a simple mathematical model, the Richards model, to the number of excess laboratory-confirmed influenza cases in Mexico and Mexico City during the first 15 weeks in 2009 over the average influenza case number of the previous five baseline years of 2004-2008 during the same period to ascertain the turning point (or the peak incidence) of a wave of early influenza infections, and to estimate the transmissibility of the virus during these early months in terms of its basic reproduction number. The results indicate that there may have been an early epidemic in Mexico City as well as in all of Mexico during February/March. Based on excess influenza cases, the estimated basic reproduction number R0 for the early outbreak was 1.59 (0.55 to 2.62) for Mexico City during weeks 5-9, and 1.25 (0.76, 1.74) for all of Mexico during weeks 5-14. CONCLUSIONS: We established the existence of an early epidemic in Mexico City and in all of Mexico during February/March utilizing the routine influenza surveillance data, although the location of seeding is unknown. Moreover, estimates of R0 as well as the time of peak incidence (the turning point) for Mexico City and all of Mexico indicate that the early epidemic in Mexico City in February/March had been more transmissible (larger R0) and peaked earlier than the rest of the country. Our conclusion lends support to the possibility that the virus could have already spread to other continents prior to the identification of the virus and the reporting of lab-confirmed pH1N1 cases in North America in April.

Asunto(s)

Brotes de Enfermedades/estadística & datos numéricos , Subtipo H1N1 del Virus de la Influenza A/fisiología , Gripe Humana/epidemiología , Gripe Humana/virología , Humanos , México/epidemiología , Modelos Biológicos , Estaciones del Año , Factores de Tiempo

RESUMEN

OBJECTIVE: We present a model for the 2009 influenza epidemic in Mexico to describe the observed pattern of the epidemic from March through the end of August (before the onset of the expected winter epidemic) in terms of the reproduction number and social isolation measures. MATERIAL AND METHODS: The model uses a system of ordinary differential equations. Computer simulations are performed to optimize trajectories as a function of parameters. RESULTS: We report on the theoretical consequences of social isolation using published estimates of the basic reproduction number. The comparison with actual data provides a reasonable good fit. CONCLUSIONS: The pattern of the epidemic outbreak in Mexico is characterized by two peaks resulting from the application of very drastic social isolation measures and other prophylactic measures that lasted for about two weeks. Our model is capable of reproducing the observed pattern.

Asunto(s)

Simulación por Computador , Subtipo H1N1 del Virus de la Influenza A , Gripe Humana/epidemiología , Modelos Teóricos , Aislamiento de Pacientes , Cuarentena , Brotes de Enfermedades/prevención & control , Brotes de Enfermedades/estadística & datos numéricos , Susceptibilidad a Enfermedades , Humanos , Inmunidad Innata , Gripe Humana/prevención & control , Gripe Humana/virología , México/epidemiología , Aislamiento de Pacientes/legislación & jurisprudencia , Cuarentena/legislación & jurisprudencia , Estaciones del Año , Factores de Tiempo , Viaje

RESUMEN

OBJECTIVE: We present a model for the 2009 influenza epidemic in Mexico to describe the observed pattern of the epidemic from March through the end of August (before the onset of the expected winter epidemic) in terms of the reproduction number and social isolation measures. MATERIAL AND METHODS: The model uses a system of ordinary differential equations. Computer simulations are performed to optimize trajectories as a function of parameters. RESULTS: We report on the theoretical consequences of social isolation using published estimates of the basic reproduction number. The comparison with actual data provides a reasonable good fit. CONCLUSIONS: The pattern of the epidemic outbreak in Mexico is characterized by two peaks resulting from the application of very drastic social isolation measures and other prophylactic measures that lasted for about two weeks. Our model is capable of reproducing the observed pattern.

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OBJETIVO: Se presenta un modelo de la epidemia de influenza en México en 2009 para describir el patrón observado desde marzo hasta finales de agosto (antes del inicio de la epidemia invernal), en términos del número reproductivo y las medidas de aislamiento social. MATERIAL Y MÉTODOS: El modelo es un sistema de ecuaciones diferenciales ordinarias. Se realizaron simulaciones computacionales para la optimización de trayectorias como función de los parámetros. RESULTADOS: Se exploran las consecuencias de esta última medida combinada con los valores estimados en la literatura médica del número reproductivo básico. CONCLUSIONES: El patrón de la epidemia mexicana de influenza es bimodal debido a la aplicación del aislamiento social y otras medidas profilácticas que duró aproximadamente dos semanas. Este modelo es capaz de reproducir el patrón observado.

Asunto(s)

Humanos , Simulación por Computador , Subtipo H1N1 del Virus de la Influenza A , Gripe Humana/epidemiología , Modelos Teóricos , Aislamiento de Pacientes , Cuarentena , Brotes de Enfermedades/prevención & control , Brotes de Enfermedades/estadística & datos numéricos , Susceptibilidad a Enfermedades , Inmunidad Innata , Gripe Humana/prevención & control , Gripe Humana/virología , México/epidemiología , Aislamiento de Pacientes/legislación & jurisprudencia , Cuarentena/legislación & jurisprudencia , Estaciones del Año , Factores de Tiempo , Viaje

RESUMEN

Both dengue fever and its more serious clinical manifestation, dengue hemorrhagic fever, represent major public health concerns in the Americas. To understand the patterns and dynamics of virus transmission in Mexico, a country characterized by a marked increase in dengue incidence in recent years, we undertook a molecular evolutionary analysis of the largest sample of Mexican strains of dengue virus compiled to date. Our E gene data set comprises sequences sampled over a period of 27 years and representing all of the Mexican states that are endemic for dengue. Our phylogenetic analysis reveals that, for each of the four dengue viruses (DENV-1 to DENV-4), there have been multiple introductions of viral lineages in Mexico, with viruses similar to those observed throughout the Americas, but there has been strikingly little co-circulation. Rather, dengue virus evolution in Mexico is typified by frequent lineage replacement, such that only a single viral lineage dominates in a specific serotype at a specific time point. Most lineage replacement events involve members of the same viral genotype, although a replacement event involving different genotypes was observed with DENV-2, and viral lineages that are new to Mexico are described for DENV-1, DENV-3 and DENV-4.

Asunto(s)

Virus del Dengue/genética , Dengue/virología , Evolución Molecular , Filogenia , Dengue/epidemiología , Virus del Dengue/clasificación , Virus del Dengue/aislamiento & purificación , Genotipo , México/epidemiología , Datos de Secuencia Molecular

RESUMEN

Simple patch-occupancy models of competitive metacommunities have shown that coexistence is possible as long as there is a competition-colonization tradeoff such as that of superior competitors and dispersers. In this paper, we present a model of competition between three species in a dynamic landscape, where patches are being created and destroyed at a different rate. In our model, species interact according to a linear non-transitive hierarchy, such that species Y(3) outcompetes and can invade patches occupied by species Y(2) and this species in turn can outcompete and invade patches occupied by the inferior competitor Y(1). In this hierarchy, inferior competitors cannot invade patches of species with higher competitive ability. Analytical results show that there are regions in the parameter space where coexistence can occur, as well as regions where each of the species exists in isolation depending on species' life-history traits associated with their colonization abilities and extinction proneness as well as with the dynamics of habitat patches. In our model, the condition for coexistence depends explicitly on patch dynamics, which in turn modulate the limiting similarity for species coexistence. Coexistence in metacommunities inhabiting dynamic landscapes although possible is harder to attain than in static ones.

Asunto(s)

Ecosistema , Modelos Biológicos , Matemática , Árboles

RESUMEN

The main objective of this work is to determine the conditions for coexistence and competitive exclusion in a discrete model for a community of three species: a stage-structured host and two competing parasitoids sharing the same host developmental stage. Coexistence of the community of the species is found to depend on the host life history parameters in the first place, and on competitive ability and parasitoid efficiency in the second place. In particular, parasitoids equilibrium densities are defined by the size of the refuge. Extinction is expected with low growth rate and with low adult survival. Host life histories are also associated with oscillations in population density, and depending on the combination of host adult survival from one generation to the next and host growth rate, the minimum of fluctuations approaches zero, implying a higher potential risk of extinction because of stochastic factors. Our results suggest that equally reduced survival of parasitoids in hosts parasitized by both species determines extinction of the parasitoid with lower population density, in contrast to the case when both parasitoids benefit with 50% of all doubly parasitized hosts, leading to the hypothesis that a community where competitors in multiparasitized hosts die, easily becomes extinct. Competitive exclusion is expected for highly asymmetric competitive interactions, independent of population densities, allowing us to hypothesize that coexistence of competitors in systems with limited resources and refuges is associated with a clearly defined competitive hierarchy.

Asunto(s)

Conducta Competitiva , Interacciones Huésped-Parásitos , Modelos Biológicos , Animales , Estadios del Ciclo de Vida , Densidad de Población , Dinámica Poblacional