Stochastic models for the spread of HIV in a mobile heterosexual population

Mathematical Biosciences

Volumn 208, Issue 1, 2007, Pages 98-124

  Sani, A ^a,b   Kroese, D P ^a   Pollett, P K ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

^b HALU OLEO UNIVERSITY   (Indonesia)

Author keywords

Density dependent Markov process; Diffusion approximation; Epidemiology; HIV AIDS; Mobility; Multiple patches

Indexed keywords

DISEASES; MARKOV PROCESSES; NUMERICAL METHODS; POPULATION DYNAMICS; STOCHASTIC MODELS; SYSTEM STABILITY;

DENSITY DEPENDENT MARKOV PROCESS; DIFFUSION APPROXIMATION; HETEROSEXUAL POPULATION; MULTIPLE PATCHES;

EPIDEMIOLOGY;

ACQUIRED IMMUNE DEFICIENCY SYNDROME; DISEASE SPREAD; DISEASE TRANSMISSION; EPIDEMIOLOGY; HUMAN IMMUNODEFICIENCY VIRUS; MOBILITY; POPULATION MODELING; POPULATION SIZE; STOCHASTICITY;

ARTICLE; DISEASE TRANSMISSION; FEMALE; HETEROSEXUALITY; HUMAN; HUMAN IMMUNODEFICIENCY VIRUS INFECTION; MALE; MATHEMATICAL MODEL; POPULATION SIZE; PROBABILITY; STOCHASTIC MODEL;

ALGORITHMS; COMPUTER SIMULATION; ENDEMIC DISEASES; FEMALE; HETEROSEXUALITY; HIV INFECTIONS; HUMANS; MALE; MARKOV CHAINS; MODELS, BIOLOGICAL; POPULATION DENSITY; POPULATION DYNAMICS; STOCHASTIC PROCESSES; SURVIVAL RATE;

EID: 34249277378     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2006.09.024     Document Type: Article

References (32)

1. Allen L.J.S. An Introduction to Stochastic Processes with Applications to Biology (2003), Pearson Education
2. Arino J., and van den Driessche P. A multi-city epidemic model. Math. Popul. Stud. 10 3 (2003) 175
3. Arrigoni F. Deterministic approximation of a stochastic metapopulation model. Adv. Appl. Probab. 35 3 (2003) 691
4. Barbour A.D. Quasi-stationary distributions in Markov population processes. Adv. Appl. Probab. 8 (1976) 296
5. Cazelles B., and Chau N.P. Using the kalman filter and dynamic models to assess the changing HIV/AIDS epidemic. Math. Biosci. 140 2 (1997) 131
6. Clancy D. A stochastic SIS infection model incorporating indirect transmission. J. Appl. Probab. 42 3 (2005) 726
7. Clancy D., O'Neill P.D., and Pollett P.K. Approximations for the long-term behavior of an open-population epidemic model. Methodol. Comput. Appl. Probab. 3 (2001) 75
8. 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28 4 (1990) 365
9. Dietz K. On the transmission dynamics of HIV. Math. Biosci. 90 (1988) 397
10. Huang W., Cooke K.L., and Castillo-Chavez C. Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission. SIAM J. Appl. Math. 52 (1992) 835
11. G. Hugo, Indonesia, internal and international population mobility: implications for the spread of HIV/AIDS. Technical report, University of Adelaide, Australia, November 2001.
12. J.M. Hyman, T. LaForce, Modeling the spread of influenza among cities. In Bioterrorism, volume 28 of Frontiers Appl. Math., p. 211. SIAM, Philadelphia, PA, 2003.
13. Hyman J.M., and Li J. The reproductive number for an HIV model with differential infectivity and staged progression. Linear Algebra Appl. 398 (2005) 101
14. Hyman J.M., Li J., and Stanley E.A. Modeling the impact of random screening and contact tracing in reducing the spread of HIV. Math. Biosci. 181 1 (2003) 17
15. Hyman J.M., and Stanley E.A. Using mathematical models to understand the AIDS epidemic. Math. Biosci. 90 (1988) 415
16. Isham V. Mathematical modelling of the transmission dynamics of HIV infection and AIDS: a review. J. Roy. Statist. Soc. Ser. A 151 (1988) p. 5, 44, with discussion
17. Kremer M., and Morcom C. The effect of changing sexual activity on HIV prevalence. Math. Biosci. 151 (1998) 99
18. Kurtz T.G. Solutions of ordinary differential equations as limits of pure jump Markov processes. J. Appl. Probab. 7 (1970) 49
19. Kurtz T.G. Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. J. Appl. Probab. 8 (1971) 344
20. Lloyd A.L., and Jansen V.A.A. Spatiotemporal dynamics of epidemics: synchrony in metapopulation models. Math. Biosci. 188 (2004) 1
21. R.M. May, R.M. Anderson, A.R. McLean, Possible demographic consequences of HIV/AIDS epidemics. II. Assuming HIV infection does not necessarily lead to AIDS. In: Mathematical Approaches to Problems in Resource Management and Epidemiology (Ithaca, NY, 1987), vol. 81, Lecture Notes in Biomath., Springer, Berlin, 1989, p. 220.
22. Mode C.J., and Sleeman C.K. A new design of stochastic partnership models for epidemic of sexually transmitted diseases with stages. Math. Biosci. 156 (1999) 95
23. Mode C.J., and Sleeman C.K. Stochastic Processes in Epidemiology, HIV/AIDS, Other Infectious Diseases and Computers (2000), World Scientific Press, Singapore
24. Pollett P.K. On a model for interference between searching insect parasites. J. Austral. Math. Soc. Ser. B 32 (1990) 133
25. Ross S.M. Stochastic Processes (1996), John Wiley
26. Sattenspiel L., and Dietz K. A structured epidemic model incorporating geographic mobility among regions. Math. Biosci. 123 (1995) 71
27. Tan W.Y., and Xiang Z. A state space model for the HIV epidemic in homosexual populations and some applications. Math. Biosci. 152 (1998) 29
28. Tan W.Y., and Zhu X. A stochastic model for the HIV epidemic in homosexual populations involving age and race. Math. Comput. Model. 24 (1996) 67
29. Tan W.Y., and Zhu X. A stochastic model of the HIV epidemic for heterosexual transmission involving married couples and prostitutes: I. the probabilities of HIV transmission and pair formation. Math. Comput. Modelling 24 (1996) 47
30. Tan W.Y., and Zhu X. A stochastic model of the HIV epidemic for heterosexual transmission involving married couples and prostitutes: II. the chain multinomial model of the HIV epidemic. Math. Comput. Model. 26 11 (1997) 17
31. van den Driessche P., and Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180 (2002) 29 John A. Jacquez memorial volume
32. S. Woods (Ed.), Report on the Global AIDS Epidemic: 4th Global Report. Joint United Nations Programme on HIV/AIDS (UNAIDS), 2004.