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Dive into the research topics where Baojun Song is active.

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Featured researches published by Baojun Song.


Bellman Prize in Mathematical Biosciences | 2002

Tuberculosis models with fast and slow dynamics: the role of close and casual contacts

Baojun Song; Carlos Castillo-Chavez; Juan P. Aparicio

Models that incorporate local and individual interactions are introduced in the context of the transmission dynamics of tuberculosis (TB). The multi-level contact structure implicitly assumes that individuals are at risk of infection from close contacts in generalized household (clusters) as well as from casual (random) contacts in the general population. Epidemiological time scales are used to reduce the dimensionality of the model and singular perturbation methods are used to corroborate the results of time-scale approximations. The concept and impact of optimal average cluster or generalized household size on TB dynamics is discussed. We also discuss the potential impact of our results on the spread of TB.


Siam Journal on Applied Mathematics | 2010

ROLE OF PREY DISPERSAL AND REFUGES ON PREDATOR-PREY DYNAMICS ∗

Faina S. Berezovskaya; Baojun Song; Carlos Castillo-Chavez

We explore the population dynamics of predator-prey systems when their interac- tions are mediated by a prey population with access to a refuge. The emphasis is in situations when differences in prey abundance between refuge and nonrefuge habitats are the drivers of prey disper- sal. It is shown that as dispersal between the prey-refuge and the predator-prey habitats increase, the system typically experiences transitions from predator extinction (for all initial conditions) to predator-prey oscillatory coexistence, to predator-prey nonoscillatory coexistence (outcomes depend on initial conditions). The possibility of bistability and tristability all leading to distinct outcomes is discussed. We argue that the impact of evolution is enhanced by the availability of refuges, the dis- persal of fragile prey populations (strong Allee effect), and the existence of habitat-specific predators. Differential outcomes (highly distinct joint predator-prey dynamics) turn out to be purely a function of the initial conditions. That is, the analyses in this paper show that diversity in predator-prey life- history dynamics must not necessarily be the result of sophisticated intrinsic biological mechanism like, for example, those responsible for genotypic differences. The variability may in fact be the result of random variation on the initial conditions of a system.


Archive | 2002

Global Dynamics of Tuberculosis Models with Density Dependent Demography

Baojun Song; Carlos Castillo-Chavez; Juan P. Aparicio

Mathematical models for Tuberculosis with linear and logistic growth rates are considered. The global dynamic structure for the logistic recruitment model is analyzed with the help of a strong version of the Poincare-Bendixson Theorem. The nature of the global dynamics of the same model with a linear recruitment rate is established with the use of explicit threshold quantities controlling the absolute and relative spread of the disease and the likelihood of extinction or persistence of the total population. The classification of planar quadratic systems helps rule out the existence of closed orbits (limit cycles).


Mathematical Biosciences and Engineering | 2004

DYNAMICAL MODELS OF TUBERCULOSIS AND THEIR APPLICATIONS

Carlos Castillo-Chavez; Baojun Song


Mathematical Biosciences and Engineering | 2008

MATHEMATICAL ANALYSIS OF THE TRANSMISSION DYNAMICS OF HIV/TB COINFECTION IN THE PRESENCE OF TREATMENT

Oluwaseun Sharomi; Chandra N. Podder; Abba B. Gumel; Baojun Song


Mathematical Biosciences and Engineering | 2004

A Simple Epidemic Model with Surprising Dynamics

Berezovsky F; Karev G; Baojun Song; Carlos Castillo-Chavez


Mathematical Biosciences and Engineering | 2005

Raves, clubs and ecstasy: the impact of peer pressure

Baojun Song; Melissa Castillo-Garsow; Karen R. Ríos-Soto; Marcin Mejran; Leilani Henso; Carlos Castillo-Chavez


Archive | 2010

Models for the transmission dynamics of fanatic behaviors

Carlos Castillo-Chavez; Baojun Song


Mathematical Biosciences and Engineering | 2008

Existence of multiple-stable equilibria for a multi-drug-resistant model of mycobacterium tuberculosis

Abba B. Gumel; Baojun Song


Archive | 2003

An Epidemic Model with Virtual Mass Transportation: The Case of Smallpox in a Large City

Carlos Castillo-Chavez; Baojun Song; Juan Zhang

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Abba B. Gumel

Arizona State University

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Ariel Cintrón-Arias

North Carolina State University

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Azizeh Jabbari

Arizona State University

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Christopher Kribs Zaleta

University of Texas at Arlington

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