PubMed Health⌕ Search

Biomedical subjects

C Castillo-Chavez

Publications and source records attributed to C Castillo-Chavez.

12 recordsLinked to original sources
PubMed1996

Effects of treatment and prevalence-dependent recruitment on the dynamics of a fatal disease.

This paper studies models for the sexual transmission of HIV/AIDS that incorporate changes in behaviour and the effects associated with HIV treatment. The recruitment rate into the core is assumed to be a function of the prevalence of the disease within the core, and it may trigger the existence of periodic solutions through Hopf bifurcations, provided that there is at least a weak demographic interaction with the noncore. The recruitment function is set up for two cases: dependence on the total proportion of infectious individuals and dependence on the proportion of treated infectious individuals only. In the general model, numerical evidence suggests that both cases may produce periodic solutions when the perception of the risk of joining the core group is sufficiently high. Two limiting cases are also studied: when the growth rate of the core and noncore groups are essentially the same, and when treatment has no effect on the transmission rate of infected individuals.

Acquired Immunodeficiency Syndrome↗
PubMed1992

Using mark-recapture methodology to estimate the size of a population at risk for sexually transmitted diseases.

To study the spread of sexually transmitted diseases (STDs) using social/sexual mixing models, one must have quantitative information about sexual mixing. An unavoidable complication in gathering such information by survey is that members of the surveyed population will almost certainly have sexual contacts outside that population. The number of these outsiders may be substantial and, hence, important for the modelling process. In this paper, we develop a mark-recapture model for estimating the size of the population at risk for contracting a STD due to direct sexual contact with a specified population targeted by a survey. This mark-recapture methodology provides a reliable method of estimating the number of outsiders. Because not everyone in the targeted population may be sexually active, the size of the sexually active subset, used as the number marked in our tag-recapture formulation, must be estimated, which introduces extra variability. We derive an estimator of the variance of the estimated total number at risk that accounts for this extra variability and an expression for the bias of that estimator. We extend the methodology to stratified surveys and illustrate its use with data collected from a population of university undergraduates to estimate sexual mixing parameters of a deterministic model of the spread of STDs.

Analysis of Variance↗
PubMed1991

Toward a unified theory of sexual mixing and pair formation.

Sexually transmitted diseases such as gonorrhea, syphilis, herpes, and AIDS are driven and maintained in populations by epidemiological and sociological factors that are not completely understood. One such factor is the way in which people mix sexually. In this paper, we outline a unified approach to modeling sexual mixing structures, where such structures are defined in terms of a set of axioms for a finite number of distinct groups of people. Theorems for homosexual, heterosexual, and arbitrary group mixing are presented, leading to a representation of all mixing structures defined by the axioms. The representation and its parameters are interpreted in terms of intergroup affinities for sexual mixing. The use of the approach in sexually transmitted disease modeling is discussed.

Female↗
PubMed1991

A general solution of the problem of mixing of subpopulations and its application to risk- and age-structured epidemic models for the spread of AIDS.

A central aspect in the study of the dynamics of sexually transmitted diseases is that of mixing. The study of the effects of social structure in disease dynamics has received considerable attention over the last few years as a result of the AIDS epidemic. In this paper, we formulate a generalization of the Blythe and Castillo-Chavez social/sexual framework for human interactions through the incorporation of age structure, and derive an explicit expression in terms of a preference function for the general solution to this formulation. We emphasize the role played by proportionate mixing, the only separable solution to this mixing framework, through the discussion of several specific cases, and we formulate an age-structured epidemic model for a single sexually active homosexual population, stratified by risk and age, with arbitrary risk- and age-dependent mixing as well as variable infectivity. In the special case of proportionate mixing in age and risk, an explicit expression for the basic reproductive number is computed.

Acquired Immunodeficiency Syndrome↗
PubMed1989

Epidemiological models with age structure, proportionate mixing, and cross-immunity.

Infection by one strain of influenza type A provides some protection (cross-immunity) against infection by a related strain. It is important to determine how this influences the observed co-circulation of comparatively minor variants of the H1N1 and H3N2 subtypes. To this end, we formulate discrete and continuous time models with two viral strains, cross-immunity, age structure, and infectious disease dynamics. Simulation and analysis of models with cross-immunity indicate that sustained oscillations cannot be maintained by age-specific infection activity level rates when the mortality rate is constant; but are possible if mortalities are age-specific, even if activity levels are independent of age. Sustained oscillations do not seem possible for a single-strain model, even in the presence of age-specific mortalities; and thus it is suggested that the interplay between cross-immunity and age-specific mortalities may underlie observed oscillations.

Aging↗
PubMed1989

On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS). Part 1: Single population models.

In this study, we investigate systematically the role played by the reproductive number (the number of secondary infections generated by an infectious individual in a population of susceptibles) on single group populations models of the spread of HIV/AIDS. Our results for a single group model show that if R less than or equal to 1, the disease will die out, and strongly suggest that if R greater than 1 the disease will persist regardless of initial conditions. Our extensive (but incomplete) mathematical analysis and the numerical simulations of various research groups support the conclusion that the reproductive number R is a global bifurcation parameter. The bifurcation that takes place as R is varied is a transcritical bifurcation; in other words, when R crosses 1 there is a global transfer of stability from the infection-free state to the endemic equilibrium, and vice versa. These results do not depend on the distribution of times spent in the infectious categories (the survivorship functions). Furthermore, by keeping all the key statistics fixed, we can compare two extremes: exponential survivorship versus piecewise constant survivorship (individuals remain infectious for a fixed length of time). By choosing some realistic parameters we can see (at least in these cases) that the reproductive numbers corresponding to these two extreme cases do not differ significantly whenever the two distributions have the same mean. At any rate a formula is provided that allows us to estimate the role played by the survivorship function (and hence the incubation period) in the global dynamics of HIV. These results support the conclusion that single population models of this type are robust and hence are good building blocks for the construction of multiple group models. Our understanding of the dynamics of HIV in the context of mathematical models for multiple groups is critical to our understanding of the dynamics of HIV in a highly heterogeneous population.

Acquired Immunodeficiency Syndrome↗
PubMed1989

Like-with-like preference and sexual mixing models.

Two new general methods for incorporating like-with-like preference into one-sex mixing models in epidemiology are presented. The first is a generalization of the preferred mixing equation, while the second comprises a transformation of a general preference function for partners of similar sexual activity levels. Both methods satisfy the constraints implicit in a mixing model. The behavior of the transformation preference method is illustrated, and it is compared with the standard proportionate mixing model.

Female↗
PubMedDate not supplied

A core group model for disease transmission.

Models for sexually transmitted diseases generally assume that the size of the core group is fixed. Publicly available information on disease prevalence may influence the recruitment of new susceptibles into highly sexually active populations. It is assumed that the recruitment rate into the core population is low while disease prevalence is high, core group members mix only with each other, disease levels outside the core are negligible, and some core group members reduce their risk through the use of a partially effective vaccine or prophylactics. A demographic-epidemic model is formulated in which the combined size of the core and non-core population is constant. A simpler version models the epidemic in an isolated core population of constant size under the influence of educational programs and measures that reduce susceptibility. The threshold condition for an endemic infection is determined. Backward bifurcations, multiple infective stationary states, and hysteresis phenomena can be observed even in the simplified version. Abrupt changes in disease prevalence levels may result from small changes in the disease management parameters and do not occur in the absence of such a program. The general conclusion is that partially effective vaccination or education programs may increase the total number of cases while decreasing the relative frequency of cases in the core group. The study throws some new light on the role of the reproduction number in connection with elimination attempts. It shows that although the reproduction number defines the threshold for the spread of the disease in a susceptible population, it is of limited value when elimination of an existing epidemic is planned.

Demography↗
PubMedDate not supplied

Affinity in paired event probability.

It is shown that a general parametric functional generates the conditional and joint probabilities of event pairs when the order within paired events is irrelevant. The parameters represent affinities or associations between single events. If the marginal probabilities of the single events are known, then these parameters specify a hypersurface on which all the joint probabilities of event pairs must lie. Examples are presented, and applications in probability, ecology, epidemiology, genetics, and distribution theory are offered.

Ecology↗
PubMedDate not supplied

The logistic equation revisited: the two-sex case.

The goal of this article is to formulate and analyze the simplest logistic pair-formation model and to contrast its dynamics to that of the corresponding Malthusian pair-formation model, that is, a generalization of the Kendall-Keyfitz model. The Malthusian pair-formation model supports a unique nontrivial stable exponential solution, and it is shown that the logistic pair-formation model supports a unique stable nontrivial bounded solution.

Animals↗