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C Castillo-Chavez

Publications and source records attributed to C Castillo-Chavez.

At least 19 recordsLinked to original sources
PubMed2006

An age-structured epidemic model of rotavirus with vaccination.

The recent approval of a rotavirus vaccine in Mexico motivates this study on the potential impact of the use of such a vaccine on rotavirus prevention and control. An age-structured model that describes the rotavirus transmission dynamics of infections is introduced. Conditions that guarantee the local and global stability analysis of the disease-free steady state distribution as well as the existence of an endemic steady state distribution are established. The impact of maternal antibodies on the implementation of vaccine is evaluated. Model results are used to identify optimal age-dependent vaccination strategies. A convergent numerical scheme for the model is introduced but not implemented. This paper is dedicated to Prof. K. P. Hadeler, who continues to push the frontier of knowledge in mathematical biology.

Age Factors↗
PubMed2006

On the role of cross-immunity and vaccines on the survival of less fit flu-strains.

A pathogen's route to survival involves various mechanisms including its ability to invade (host's susceptibility) and its reproductive success within an invaded host ("infectiousness"). The immunological history of an individual often plays an important role in reducing host susceptibility or it helps the host mount a faster immunological response de facto reducing infectiousness. The cross-immunity generated by prior infections to influenza A strains from the same subtype provide a significant example. The results of this paper are based on the analytical study of a two-strain epidemic model that incorporates host isolation (during primary infection) and cross-immunity to study the role of invasion mediated cross-immunity in a population where a precursor related strain (within the same subtype, i.e. H3N2, H1N1) has already become established. An uncertainty and sensitivity analysis is carried out on the ability of the invading strain to survive for given cross-immunity levels. Our findings indicate that it is possible to support coexistence even in the case when invading strains are "unfit", that is, when the basic reproduction number of the invading strain is less than one. However, such scenarios are possible only in the presence of isolation. That is, appropriate increments in isolation rates and weak cross-immunity can facilitate the survival of less fit strains. The development of "flu" vaccines that minimally enhance herd cross-immunity levels may, by increasing genotype diversity, help facilitate the generation and survival of novel strains.

Animals↗
PubMed2006

Modelling the transmission dynamics of acute haemorrhagic conjunctivitis: application to the 2003 outbreak in Mexico.

We model an outbreak of acute haemorrhagic conjunctivitis (AHC) using a simple epidemic model that includes susceptible, infectious, reported, and recovered classes. The model's framework considers the impact of underreporting and behaviour changes on the transmission rate and is applied to a recent epidemic of AHC in Mexico, using a fit to the cumulative number of cases to estimate model parameters, which agree with those derived from clinical studies. The model predicts a 'mean time from symptomatic onset to diagnosis' of 1.43 days (95 per cent CI: 1-2.5) and that the final size of the Mexican epidemic was underreported by 39 per cent. We estimate that a primary infectious case generates approximately 3 secondary cases (R0* = 2.64, SD 0.65). We explore the impact of interventions on the final epidemic size, and estimate a 36 per cent reduction in the transmission rate due to behaviour changes. The effectiveness of the behaviour changes in slowing the epidemic is evident at 21.90 (SD 0.19) days after the first reported case. Results therefore support current public health policy including expeditious announcement of the outbreak and public health information press releases that instruct individuals on avoiding contagion and encourage them to seek diagnosis in hospital clinics.

Adenoviridae↗
PubMed2005

The role of spatial mixing in the spread of foot-and-mouth disease.

A model of epidemic dispersal (based on the assumption that susceptible cattle were homogeneously mixed over space, or non-spatial model) was compared to a partially spatially explicit and discrete model (the spatial model), which was composed of differential equations and used geo-coded data (Euclidean distances between county centroids). While the spatial model accounted for intra- and inter-county epidemic spread, the non-spatial model did not assess regional differences. A geo-coded dataset that resembled conditions favouring homogeneous mixing assumptions (based on the 2001 Uruguayan foot-and-mouth disease epidemic), was used for testing. Significant differences between models were observed in the average transmission rate between farms, both before and after a control policy (animal movement ban) was imposed. They also differed in terms of daily number of infected farms: the non-spatial model revealed a single epidemic peak (at, approximately, 25 epidemic days); while the spatial model revealed two epidemic peaks (at, approximately, 12 and 28 days, respectively). While the spatial model fitted well with the observed cumulative number of infected farms, the non-spatial model did not (P<0.01). In addition, the spatial model: (a) indicated an early intra-county reproductive number R of approximately 87 (falling to <1 within 25 days), and an inter-county R<1; (b) predicted that, if animal movement restrictions had begun 3 days before/after the estimated initiation of such policy, cases would have decreased/increased by 23 or 26%, respectively. Spatial factors (such as inter-farm distance and coverage of vaccination campaigns, absent in non-spatial models) may explain why partially explicit spatial models describe epidemic spread more accurately than non-spatial models even at early epidemic phases. Integration of geo-coded data into mathematical models is recommended.

Animals↗
PubMed2005

Effects of behavioral changes in a smallpox attack model.

The impact of individual and community behavioral changes in response to an outbreak of a disease with high mortality is often not appreciated. Response strategies to a smallpox bioterrorist attack have focused on interventions such as isolation of infectives, contact tracing, quarantine of contacts, ring vaccination, and mass vaccination. We formulate and analyze a mathematical model in which some individuals lower their daily contact activity rates once an epidemic has been identified in a community. Transmission parameters are estimated from data and an expression is derived for the effective reproduction number. We use computer simulations to analyze the effects of behavior change alone and in combination with other control measures. We demonstrate that the spread of the disease is highly sensitive to how rapidly people reduce their contact activity rates and to the precautions that the population takes to reduce the transmission of the disease. Even gradual and mild behavioral changes can have a dramatic impact in slowing an epidemic. When behavioral changes are combined with other interventions, the epidemic is shortened and the number of smallpox cases is reduced. We conclude that for simulations of a smallpox outbreak to be useful, they must consider the impact of behavioral changes. This is especially true if the model predictions are being used to guide public health policy.

Behavior↗
PubMed2005

Pediatric electrocardiograph abnormalities following Centruroides limpidus tecomanus scorpion envenomation.

Scorpionism is an endemic public health problem in Mexico [Hoffmann, C.C., 1936. La distribucion geografica de los alacranes peligrosos en la Republica Mexicana. Bol. Inst. Hygiene Mex. 2, 321; Hoffmann, C.C., Nieto, D.R., 1939. Segunda contribucion al conocimiento de los alacranes mexicanos. Anal. Inst. Biol. 10, 83-92; Mazzoti, L., Bravo-Becherelle, M.A., 1963. Scorpionism in the Mexican Republic. In: Keegan, H.L., McFarlane, W.V. (Eds.), Venomous and Poissonous Animals and Noxious Plants of the Pacific Area. Pergamon Press, London, pp. 119-131; Monroy-Velasco, J., 1961. Alacranes venenosos de Mexico. Rev. Mex. Cien. Med. Biol., Mex. 1, 1-23; Diaz-Najera, A., 1975. Listas y datos de distribucion geografica de los alacranes de Mexico. Rev. Inv. Salud. Publica. (Mex.) 35, 1; Velasco-Castrejon, O., Lara-Aguilera, R., Alatorre, H., 1976. Aspectos epidemiologicos y clinicos de la picadura de alacran en una area hiperendemica. Rev. Inv. Salud Publica. (Mex.) 36, 93-103; Dehesa-Davila, M., Possani, L.D., 1994. Scorpionism and serotherapy in Mexico. Toxicon 32 (9), 1015-1018]. In this prospective study, we assess cardiovascular disorders in children via electrocardiographic (ECG) recordings following envenomation by scorpion species Centruroides limpidus tecomanus found in the state of Colima, Mexico. We analyzed 113 cases between the ages of 5 and 14 years. Among the most frequent symptoms presented included local pain (99.1%) and paresthesia (75.2%), pruritus (36.3%), sialorrhoea (35.4%), and nystagmus (24.8%). Cardiovascular disorders were observed in 39.8% of cases, 71% of which were rhythm abnormalities. We find a significant association between the frequency of ECG alterations and age, whereby 8-9-year-old children are more likely to experience ECG alterations when compared with other tested age groups.

Adolescent↗
PubMed2004

The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda.

Despite improved control measures, Ebola remains a serious public health risk in African regions where recurrent outbreaks have been observed since the initial epidemic in 1976. Using epidemic modeling and data from two well-documented Ebola outbreaks (Congo 1995 and Uganda 2000), we estimate the number of secondary cases generated by an index case in the absence of control interventions R0. Our estimate of R0 is 1.83 (SD 0.06) for Congo (1995) and 1.34 (SD 0.03) for Uganda (2000). We model the course of the outbreaks via an SEIR (susceptible-exposed-infectious-removed) epidemic model that includes a smooth transition in the transmission rate after control interventions are put in place. We perform an uncertainty analysis of the basic reproductive number R0 to quantify its sensitivity to other disease-related parameters. We also analyse the sensitivity of the final epidemic size to the time interventions begin and provide a distribution for the final epidemic size. The control measures implemented during these two outbreaks (including education and contact tracing followed by quarantine) reduce the final epidemic size by a factor of 2 relative the final size with a 2-week delay in their implementation.

Congo↗
PubMed2003

Scaling laws for the movement of people between locations in a large city.

Large scale simulations of the movements of people in a "virtual" city and their analyses are used to generate insights into understanding the dynamic processes that depend on the interactions between people. Models, based on these interactions, can be used in optimizing traffic flow, slowing the spread of infectious diseases, or predicting the change in cell phone usage in a disaster. We analyzed cumulative and aggregated data generated from the simulated movements of 1.6 x 10(6) individuals in a computer (pseudo-agent-based) model during a typical day in Portland, Oregon. This city is mapped into a graph with 181,206 nodes representing physical locations such as buildings. Connecting edges model individual's flow between nodes. Edge weights are constructed from the daily traffic of individuals moving between locations. The number of edges leaving a node (out-degree), the edge weights (out-traffic), and the edge weights per location (total out-traffic) are fitted well by power-law distributions. The power-law distributions also fit subgraphs based on work, school, and social/recreational activities. The resulting weighted graph is a "small world" and has scaling laws consistent with an underlying hierarchical structure. We also explore the time evolution of the largest connected component and the distribution of the component sizes. We observe a strong linear correlation between the out-degree and total out-traffic distributions and significant levels of clustering. We discuss how these network features can be used to characterize social networks and their relationship to dynamic processes.

Community Networks↗
PubMed2003

SARS outbreaks in Ontario, Hong Kong and Singapore: the role of diagnosis and isolation as a control mechanism.

In this article we use global and regional data from the SARS epidemic in conjunction with a model of susceptible, exposed, infective, diagnosed, and recovered classes of people ("SEIJR") to extract average properties and rate constants for those populations. The model is fitted to data from the Ontario (Toronto) in Canada, Hong Kong in China and Singapore outbreaks and predictions are made based on various assumptions and observations, including the current effect of isolating individuals diagnosed with SARS. The epidemic dynamics for Hong Kong and Singapore appear to be different from the dynamics in Toronto, Ontario. Toronto shows a very rapid increase in the number of cases between March 31st and April 6th, followed by a significant slowing in the number of new cases. We explain this as the result of an increase in the diagnostic rate and in the effectiveness of patient isolation after March 26th. Our best estimates are consistent with SARS eventually being contained in Toronto, although the time of containment is sensitive to the parameters in our model. It is shown that despite the empirically modeled heterogeneity in transmission, SARS' average reproductive number is 1.2, a value quite similar to that computed for some strains of influenza (J. Math. Biol. 27 (1989) 233). Although it would not be surprising to see levels of SARS infection higher than 10% in some regions of the world (if unchecked), lack of data and the observed heterogeneity and sensitivity of parameters prevent us from predicting the long-term impact of SARS. The possibility that 10 or more percent of the world population at risk could eventually be infected with the virus in conjunction with a mortality rate of 3-7% or more, and indications of significant improvement in Toronto support the stringent measures that have been taken to isolate diagnosed cases.

Disease Outbreaks↗
PubMed2001

Dispersal, disease and life-history evolution.

Discrete-time susceptible-infective-susceptible (S-I-S) disease transmission models can exhibit bistability (alternative stable equilibria) over a wide range of parameter values. We illustrate the richness generated by such 'simple' non-linear systems in the study of two patch epidemic models with disease-enhanced or disease-suppressed dispersal. Dispersal between patches can have a profound impact on local patch disease dynamics. In fact, dispersal between patches may give rise to bistability in parameter regimes without bistability in single patch models.

Animals↗
PubMed2000

Transmission and dynamics of tuberculosis on generalized households.

Tuberculosis (TB) transmission is enhanced by systematic exposure to an infectious individual. This enhancement usually takes place at either the home, workplace, and/or school (generalized household). Typical epidemiological models do not incorporate the impact of generalized households on the study of disease dynamics. Models that incorporate cluster (generalized household) effects and focus on their impact on TB's transmission dynamics are developed. Detailed models that consider the effect of casual infections, that is, those generated outside a cluster, are also presented. We find expressions for the Basic Reproductive Number as a function of cluster size. The formula for R0 separates the contributions of cluster and casual infections in the generation of secondary TB infections. Relationships between cluster and classical epidemic models are discussed as well as the concept of critical cluster size.

Causality↗
PubMed2000

Urn models and vaccine efficacy estimation.

We derive the distribution of the number of infections among unvaccinated and vaccinated individuals for model 1 (leaky) and model 2 (all/nothing) vaccines, assuming random mixing of a homogeneous population. For all/nothing vaccines, we show that the distribution of the number of infected vaccinated individuals conditioning on n observed infections follows a hypergeometric distribution, and the vaccine efficacy estimate (VE) can be derived from the usual estimate of the total population size in a capture-recapture sampling program. For leaky vaccines, we show that the number of vaccinated infected follows a distribution that was first derived by Wallenius. We found that the current point estimates of VE for each model perform very well, but the urn model construction presented here provides a strong framework for estimation and hypothesis testing on the parameters, and can be applied when the available data are a sample of the population. Since the method does not require an underlying transmission model, it can be applied to estimate the VE for non-contagious diseases.

Adolescent↗
PubMed2000

A model for tuberculosis with exogenous reinfection.

Following primary tuberculosis (TB) infection, only approximately 10% of individuals develop active T.B. Most people are assumed to mount an effective immune response to the initial infection that limits proliferation of the bacilli and leads to long-lasting partial immunity both to further infection and to reactivation of latent bacilli remaining from the original infection. Infected individuals may develop active TB as a consequence of exogenous reinfection, i.e., acquiring a new infection from another infectious individual. Our results in this paper suggest that exogenous reinfection has a drastic effect on the qualitative dynamics of TB. The incorporation of exogenous reinfection into our TB model allows the possibility of a subcritical bifurcation at the critical value of the basic reproductive number R(0)=1, and hence the existence of multiple endemic equilibria for R(0)<1 and the exogenous reinfection rate larger than a threshold. Our results suggest that reducing R(0) to be smaller than one may not be sufficient to eradicate the disease. An additional reduction in reinfection rate may be required. These results may also partially explain the recently observed resurgence of TB.

Disease Susceptibility↗
PubMed1999

A basic result on the integral for birth-death Markov processes.

In this paper a regenerative argument is used to derive an expression for the expectation of the integral under the stochastic path of a birth-death Markov process up to extinction time as well as for the expected time to extinction. Some applications to classical-birth-death processes are given.

Birth Rate↗
PubMed1999

Density-dependent dynamics and superinfection in an epidemic model.

A mathematical model of the interaction between two pathogen strains and a single host population is studied. Variable population size, density-dependent mortality, disease-related deaths (virulence), and superinfection are incorporated into the model. Results indicate that coexistence of the two strains is possible depending on the magnitude of superinfection. Global asymptotic stability of the steady-state that gives coexistence for both strains under suitable and biologically feasible constraints is proved.

Communicable Diseases↗
PubMed1998

Global stability of an age-structure model for TB and its applications to optimal vaccination strategies.

This article focuses on the study of an age-structure model for the disease transmission dynamics of tuberculosis in populations that are subjected to a vaccination program. We first show that the infection-free steady state is globally stable if the basic reproductive number R0 is below one, and that an endemic steady state exists when the reproductive number in the presence of vaccine is above one. We then apply the theoretical results to vaccination policies to determine the optimal age or ages at which an individual should be vaccinated. It is shown that the optimal strategies can be either one- or two-age strategies.

Age Distribution↗
PubMed1998

On the Relationship Between Evolution of Virulence and Host Demography.

The effects of density-dependence on the evolution of virulence in super-infection models is the theme of this paper. The qualitative dynamics of three host-pathogen systems are studied numerically in a virulence-superinfection parameter landscape. It is shown numerically that pathogen's competitive exclusion coexistence and host population extinction depend heavily of the population dynamics of the host population. Reported patterns of diversity found using models without demography, are insufficient to account for the coevolutionary dynamics under defined selective pressures. Specifically, virulence and superinfection in the presence of a variable host population give rise to threshold values that divide (as switches) the regions of coexistence and competitive exclusion. Tight coevolution on a variable host population may occur within regions of parameter space that are not connected. We present our numerical results using a simple host-disease system where a homogeneous host population is invaded by two competing pathogen strains (partial analytical results will be published elsewhere).Copyright 1998 Academic Press Limited

Journal Article↗