Carlos Castillo-Chavez
Joaquin Bustoz Jr. Professor of Mathematical Biology 

Los Alamos National Laboratories
Center for Nonlinear Studies at Los Alamos
Department of Mathematics and Statistics
Mathematical and Theoretical Biology Institute

Department of Mathematics & Statistics
Arizona State University Tempe, AZ - 85287 - 1804

Selected Publications

1991

Castillo-Chavez, C. and H. Thieme, Asymptotically Autonomous Epidemic Models, In, Mathematical Populations Dynamics: Analysis of Heterogeneity, Volume 1, Theory of Epidemics, O. Arino, D. Axelrod, M. Kimmel and M. Langlais(eds.), pp. 33-50. [PDF]
 

1992

Castillo-Chavez, C., J.X. Velasco-Hernández and S. Fridman, Modeling Contact Structures in Biology. (1994), In, Frontiers of Theoretical Biology, Lecture Notes in Biomathematics 100, S.A. Levin (ed.), pp. 454-91. Springer-Veralg,Berlin-Heidelberg-New York. [PDF]
 

1993

Thieme, H. and C. Castillo-Chavez, How May Infection-Age-Dependent Infectivity Affect the Dynamics of HIV/AIDS? SIAM J. Applied Math. 53, (5), 1447-79. [PDF]
 

1994

 
Castillo-Chavez, C., W. Huang and J. Li, Dynamics of Multiple Pathogen Strains in Heterosexual Epidemiological Models, In: Differential equations and applications to biology and to industry: Proceedings of the June 1-4, 1994, Claremont international conference dedicated to the memory of Stavros Busenberg (1941-1993): 129-298. [PDF]
 

1995

Lubkin, S., S-F, Hsu Schmitz and C. Castillo-Chavez, A Framework for Modeling Inheritance of Social Traits, In, Mathematical Population Dynamics: Analysis of Heterogeneity, O. Arino, D.E. Axelrod, and M. Kimmel (eds.), pp. 131-46, 1995. [PDF]
Castillo-Chavez, C. and W. Huang, The Logistic Equation Revisited: The Two-Sex Case, Math. Biosci. 128: 299-316. [PDF]
 

1996

Castillo-Chavez, C., W. Huang and J. Li, Competitive Exclusion in Gonorrhea Models and Other Sexually-Transmitted Diseases, SIAM Journal of Applied. Mathematics. 56(2):494-508. [PDF]
Brauer, F, C. Castillo-Chavez and J. X. Velasco-Hernandez, Recruitment Effects in Heterosexually Transmitted Disease Models, In: Advances in Mathematical Modeling of Biological Processes, Denise Kirschner (editor), International Journal of Applied Science and Computation, 3:1, 78-90. [PDF]
Castillo-Chavez, C., W. Huang and J. Li, On the Existence of Stable Pair Distributions, Journal of Mathematical Biology, 34: 413-441. [PDF]
Velasco-Hernández, J.X., F. Brauer and C. Castillo-Chavez, Effects of Treatment and Prevalence-dependent Recruitment on the Dynamics of a fatal disease, IMA Journal of Math. Medicinal Biology, 13: (3) 175-192. [PDF]

1998

Castillo-Chavez, C. and Z. Feng, Mathematical Models for the Disease Dynamics of Tuberculosis, Advances In Mathematical Population Dynamics - Molecules, Cells, and Man (O. , D. Axelrod, M. Kimmel, (eds), World Scientific Press (1998), 629-656. [PDF]
 

1999

Castillo-Chavez, C., W. Huang and J. Li, Competitive Exclusion in Gonorrhea Models and Other Sexually-Transmitted Diseases, SIAM Journal of Applied. Mathematics. 56(2):494-508. [PDF]
A basic result on the integral for birth-death Markov processes (Carlos M. Hernández-Suárez, Carlos Castillo-Chavez);. Mathematical Biosciences; May 1999. [PDF]
 

2000

Aparicio J., A. Capurro and C. Castillo-Chavez, Transmission and Dynamics of Tuberculosis on Generalized Households (2000). Journal of Theoretical Biology (2000) 206, 327-341. [PDF]
Hernández-Suárez C. M. and C. Castillo-Chavez, Urn models and vaccine efficacy estimation (2000). Statistics in Medicine. Volume 19: 827-835. [PDF]
 

2001

Aparicio, J., A. Capurro and C. Castillo-Chavez, Markers of disease evolution: the case of tuberculosis, Journal of Theoretical Biology (accepted). [PDF]
Feng, Z. W. Huang and C. Castillo-Chavez, On the role of variable latent periods in mathematical models for tuberculosis. Journal of Dynamics and Differential Equations, Vol. 13, No. 2, 2001 pp425-452, 2001. [PDF]
Castillo-Chavez C. and A. Yakubu, Dispersal, disease and life history evolution Dispersal, Disease and Life-History Evolution, Math. Biosc. 173, 35-53 (2001). [PDF]
 

2002

Aparicio, J., A. Capurro and C. Castillo-Chavez, On the long-term dynamics and re-emergence of tuberculosis. In: Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, IMA Volume 125, 351-360, Springer-Veralg, Berlin-Heidelberg-New York. Edited by Carlos Castillo-Chavez with Pauline van den Driessche, Denise Kirschner and Abdul-Aziz Yakubu.[PDF]
Heiderich, K. R., W. Huang and C. Castillo-Chavez. Nonlocal response in a simple epidemiological model, In: Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, IMA Volume 125, 129-151, Springer-Veralg, Berlin-Heidelberg-New York. Edited by Carlos Castillo-Chavez with Pauline van den Driessche, Denise Kirschner and Abdul-Aziz Yakubu. [PDF]
Castillo-Chavez C., Z. Feng and W. Huang. On the computation Ro and its role on global stability, In: Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, IMA Volume 125, 229-250, Springer-Veralg, Berlin-Heidelberg-New York. Edited by Carlos Castillo-Chavez with Pauline van den Driessche, Denise Kirschner and Abdul-Aziz Yakubu. [PDF]
Huang W. and C. Castillo-Chavez, Age-structured Core Groups and their impact on HIV dynamics. In: Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods and Theory, IMA Volume 126, 261-273, Springer-Veralg, Berlin-Heidelberg-New York. Edited by Carlos Castillo-Chavez with Pauline van den Driessche, Denise Kirschner and Abdul-Aziz Yakubu. [PDF]
Baojun Song, C. Castillo-Chavez and J. A. Aparicio, Tuberculosis Models with Fast and Slow Dynamics: The Role of Close and Casual Contacts, Mathematical Biosciences, (accepted). [PDF]
Aparicio, J., A. Capurro and C. Castillo-Chavez, Frequency Dependent Risk of Infection and the Spread of Infectious Diseases. In: Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, IMA Volume 125, 341-350, Springer-Veralg, Berlin-Heidelberg-New York. Edited by Carlos Castillo-Chavez with Pauline van den Driessche, Denise Kirschner and Abdul-Aziz Yakubu. [PDF]
Castillo-Chavez C. and A. Yakubu, Intra-specific competition, dispersal and disease dynamics in discrete-time patchy environments. In: Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, IMA Volume 125, 165-181, Springer-Veralg, Berlin-Heidelberg-New York. Edited by Carlos Castillo-Chavez with Pauline van den Driessche, Denise Kirschner and Abdul-Aziz Yakubu. [PDF]
Castillo-Chavez, C., A-A Yakubu, H. Thieme and M. Martcheva, Nonlinear mating models for populations with discrete generations. In: Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, IMA Volume 125, 251-268, Springer-Veralg, Berlin-Heidelberg-New York. Edited by Carlos Castillo-Chavez with Pauline van den Driessche, Denise Kirschner and Abdul-Aziz Yakubu. [PDF]
Castillo-Chavez C. and Abdul Aziz Yakubu, Discrete-time S-I-S models with simple and complex dynamics. In: Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, IMA Volume 125, 153-163, Springer-Veralg, Berlin-Heidelberg-New York, Edited by Carlos Castillo-Chavez with Pauline van den Driessche, Denise Kirschner and Abdul-Aziz Yakubu. [PDF]
Song, B., C. Castillo-Chavez and J. Aparicio, Global dynamics of tuberculosis models with density dependent demography. In: Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods and Theory, IMA Volume 126, 275-294, Springer-Veralg, Berlin-Heidelberg-New York. Edited by Carlos Castillo-Chavez with Pauline van den Driessche, Denise Kirschner and Abdul-Aziz Yakubu. [PDF]
Best, J., C. Castillo-Chavez and A. Yakubu, A. Hierarchical competition in discrete time models with dispersal, Fields Institute Communications, (accepted). [PDF]
M. Nuño, Z. Feng, M. Martcheva, C. Castillo-Chavez. Dynamics of Two-Strain Influenza with Isolation and Cross-Immunity,Technical Report BU-1606-M of BSCB department, Cornell University (submitted to Math. Biosc.) . [PDF]
Carlos Castillo-Chavez and Baoun Song. An overview of Mathematical Models of Tuberculosis. Technical Rport BU-1606-M of BSCB department, Cornell University. [PDF]
Baojun Song, Carlos Castillo-Chavez, Juan Pablo Aparicio. Tuberculosis Models with Fast and Slow Dynamics: The Role of Close and Casual Contacts. Mathematical Biosciences 180 (2002) 187-205. [PDF]

More publications...

The Evolution of Age-Structured Marriage Functions: It Takes Two to Tango (Castillo-Chavez, C., and Hsu Schmitz, S.) Structured-Population Models in Marine, Terrestrial, and Freshwater Systems. Tuljapurkar and Caswell(eds.), Chapman & Hall, N.Y., 533-553, 1977.

In prior work, we characterized two-sex marriage functions for socially structured populations as multiplicative perturbations of heterosexually random/proportionate mixing. These perturbations were expressed in terms of the preferences/affinities of males for females and vice versa. Male and female preferences/affinities are obviously not independent as they depend on the availability fo male and female behavioral "genotypes". We show that knowledge of the preferences/affinities of one gender can characterize the preferences/affinities of both genders in socially-structured populations; in other words, it takes two to tango. This is the basic content of the T3 Theorem. In this chapter, we revise our results for socially structured populations and extend them to situations where the population is characterized by continuous variables such as age. It is shown that different sets of preferences/affinities, that is, distinct behavioral "genotypes", bay give rise to identical mixing/mating probabilities, the determinants of the behavioral "phenotypes". Hence, different sets fo individual decisions can lead to identical social dynamics - a fact well established in genetics. The importance of the incorporation of mating systems at the population level is a neglected but central area in evolutionary biology.

Demographic Recruitment In Sexually Transmitted Disease Models (Brauer, F., and Glythe, S.P., and Castillo-Chavez, C.), Mathematical Biology and Medicine 5:1438-1457, 1996. (Keywords: risk behavior, sexually-transmitted disease, autonomous response, non-linear incidence, HIV/AIDS.)

Models of STD dynamics customarily comprise a series of stages through which individuals may pass (susceptible, infected, infectious, recovered, or dead, for example). Unless these models try to incorporate some aspects of age-structure (so that there are birth rates), the population considered is to be effectively that of sexually active adults, into which individuals are recruited at some given rate g. In the case of AIDS models, for example, g is almost invariably taken to be a constant; the implication is that the population to be modeled is part of a larger meta-population, and the effects of infection within the population do not influence the demograhic processes in the meta-population. It is of interest, however, to consider what happens if potential recruits from the meta-population are influenced by the knowledge of disease prevalence-as in the case of AIDS of gonorrhea. This knowledge may influence who enters the population as well as who returns to the meta-population. For example, fewer recruits may decide to enter the population when prevalence becomes large, or susceptible or recovered may return to the meta-population (effects on internal recruitment). We approximate these behavioral demographic effects by making g a funtion of the population variables: g may be a decreasing function of the total number of infected, or of the fraction of the population infected. In this paper we address, in as simple a setting as possible, the effects of information on the size of the group.

The Effects of Females' Susceptibility on the Coexistence of Multiple Pathogen Strains of Sexually Transmitted Diseases (Castillo-Chavez, C., Huang, W., and Li, J.), J. Math.Biol. 35:503-522, 1997. (Keywords: sexually trasnmitted disease, pathogen strains, coexistence.)

We study the dynamics of sexually transmitted pathogens in a heterosexually active population, where females are divided into two different groups based on their susceptibility to two distinct pathogenic strains. It is assumed that a host cannot be invaded simultaneously by both disease agents and that when symptoms appear - a function of the pathogen, strain, virulence, and an individual's degree of susceptibility - then individuals are treated and/or recover. Heterogeneity in susceptibility to the acquisition of infection and/or in variability in the length of the infection period of the female subpopulations is incorporated. Pathogens' coexistence is highly unlikely on homogeneously mixing female and male populations with no heterogeneity among individuals of either gender. Variability in susceptibility in the female subpopulation makes coexistence possible albeit under a complex set of circumstances that must include differences in contact/mixing rates between the groups of females and the male population as well as the differences in the lengths of their average periods of infectiousness for the three groups.

To Treat or Not to Treat: The Case of Tuberculosis (Castillo-Chavez, C., and Feng, Z.), Journal of Mathematical Biology 35: 629-656, 1997. (Keywords: tuberculosis, antibiotic resistance, epidemiology, co-existence, dynamical systems.)

Incomplete treatment of patients with infectious tuberculosis (TB) may not only lead to relapse but also to the development of antibiotic resistant TB - one of the most serious health problems facing society today. In this article, we formulate one-strain and two-strain TB models to determine possible mechanisms that may allow for the survival and spread of naturally resistant strains of TB as well as antibiotic-generated resistant strains of TB. Analysis of our models shows that non-antibiotic co-existence is possible but rare for naturally resistant strains, while co-existence is almost the rule for strains that result from the lack of compliance with antibiotic treatment by TB infected individuals.

Other Publications
State Dept. Stops Free Speech At The Border, Carlos Castillo-Chavez; The New York Times; October 12, 1994

 

Last Update: Feb 22, 2005
Comments to:
Reynaldo.Castro@asu.edu