Mathematical Biosciences and Engineering, 2008, 5(4): 713-727. doi: 10.3934/mbe.2008.5.713.

Primary: 92D40, 92D25; Secondary: 35K55, 35K57

Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Spatial spread of sexually transmitted diseases within susceptible populations at demographic steady state

1. Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287
2. Department of Mathematics, University of Louisville, Louisville, KY 40292

In this study, we expand on the susceptible-infected-susceptible (SIS) heterosexual mixing setting by including the movement of individuals of both genders in a spatial domain in order to more comprehensively address the transmission dynamics of competing strains of sexually-transmitted pathogens. In prior models, these transmission dynamics have only been studied in the context of nonexplicitly mobile heterosexually active populations at the demographic steady state, or, explicitly in the simplest context of SIS frameworks whose limiting systems are order preserving. We introduce reaction-diffusion equations to study the dynamics of sexually-transmitted diseases (STDs) in spatially mobile heterosexually active populations. To accomplish this, we study a single-strain STD model, and discuss in what forms and at what speed the disease spreads to noninfected regions as it expands its spatial range. The dynamics of two competing distinct strains of the same pathogen on this population are then considered. The focus is on the investigation of the spatial transition dynamics between the two endemic equilibria supported by the nonspatial corresponding model. We establish conditions for the successful invasion of a population living in endemic conditions by introducing a strain with higher fitness. It is shown that there exists a unique spreading speed (where the spreading speed is characterized as the slowest speed of a class of traveling waves connecting two endemic equilibria) at which the infectious population carrying the invading stronger strain spreads into the space where an equilibrium distribution has been established by the population with the weaker strain. Finally, we give sufficient conditions under which an explicit formula for the spreading speed can be found.
  Article Metrics

Keywords sexually transmitted disease; traveling wave; spreading speed; disease spread

Citation: Carlos Castillo-Chavez, Bingtuan Li. Spatial spread of sexually transmitted diseases within susceptible populations at demographic steady state. Mathematical Biosciences and Engineering, 2008, 5(4): 713-727. doi: 10.3934/mbe.2008.5.713


This article has been cited by

  • 1. Evelyn K. Thomas, Katharine F. Gurski, Kathleen A. Hoffman, Analysis of SI models with multiple interacting populations using subpopulations, Mathematical Biosciences and Engineering, 2014, 12, 1, 135, 10.3934/mbe.2015.12.135
  • 2. Jonathan James Ryder, Daria Pastok, Mary-Jo Hoare, Michael J. Bottery, Michael Boots, Robert K. Knell, David Atkinson, Gregory D.D. Hurst, Spatial variation in food supply, mating behavior, and sexually transmitted disease epidemics, Behavioral Ecology, 2013, 24, 3, 723, 10.1093/beheco/ars209
  • 3. K. E. Yong, E. Díaz Herrera, C. Castillo-Chavez, , Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases, 2016, Chapter 11, 169, 10.1007/978-3-319-40413-4_11
  • 4. Baojun Song, Zhilan Feng, Gerardo Chowell, From the guest editors, Mathematical Biosciences and Engineering, 2013, 10, 5/6, 10.3934/mbe.2013.10.5i
  • 5. A. K. MISRA, MILAN TIWARI, ANUPAMA SHARMA, SPATIO-TEMPORAL PATTERNS IN A CHOLERA TRANSMISSION MODEL, Journal of Biological Systems, 2015, 23, 03, 471, 10.1142/S0218339015500242

Reader Comments

your name: *   your email: *  

Copyright Info: 2008, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved