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Results on the dynamics for models for the sexual transmission of the human immunodeficiency virus. (English) Zbl 0703.92022

Summary: We report on the formulation and mathematical analysis of single and multiple group models for the spread of the human immuno-deficiency virus (HIV), which is the etiological agent for the acquired immunodeficiency syndrome (AIDS). Results on the robustness of a single group model are stated for specific and arbitrary survivorship functions. In addition, we provide results that show that multiple group models can have multiple endemic equilibria.

MSC:

92D30 Epidemiology
45J05 Integro-ordinary differential equations

References:

[1] Anderson, R. M.; May, R. M.; Medley, G. F.; Johnson, A., A Preliminary Study of the Transmission Dynamics of the Human Immunodeficiency Virus (HIV), the Causative Agent of AIDS, IMA J. Math. Med. Biol, 3, 229-263 (1986) · Zbl 0609.92025
[2] Anderson, R. M.; May, R. M., Transmission Dynamics of HIV Infection, Nature, 326, 137-142 (1987)
[3] Blythe, S. P.; Anderson, R. M., Distributed Incubation and Infectious Periods in Models of the Transmission Dynamics of the Human Immunodeficiency Virus (HIV), IMA J. Math. Med. Biol, 5, 1-19 (1988) · Zbl 0686.92015
[4] S.P. Blythe, and C. Castillo-Chavez, Like-with-Like Preference and Sexual Mixing Models; S.P. Blythe, and C. Castillo-Chavez, Like-with-Like Preference and Sexual Mixing Models · Zbl 0679.92017
[5] C. Castillo-Chavez, K. Cooke, W Huang, and S.A. Levin, “The Role of Long Periods of Infectiousness in the Dynamics of Acquired Immunodeficiency Syndrome (AIDS), in Mathematical Approaches to Problems in Resource Management and Epidemiology,” Springer-Verlag, (in press).; C. Castillo-Chavez, K. Cooke, W Huang, and S.A. Levin, “The Role of Long Periods of Infectiousness in the Dynamics of Acquired Immunodeficiency Syndrome (AIDS), in Mathematical Approaches to Problems in Resource Management and Epidemiology,” Springer-Verlag, (in press). · Zbl 0682.92013
[6] C. Castillo-Chavez, K. Cooke, W Huang, and S.A. Levin, On the Role of Long Incubation Periods in the Dynamics of Acquired Immunodeficiency Syndrome (AIDS), Part 1. Single Population Models; C. Castillo-Chavez, K. Cooke, W Huang, and S.A. Levin, On the Role of Long Incubation Periods in the Dynamics of Acquired Immunodeficiency Syndrome (AIDS), Part 1. Single Population Models · Zbl 0715.92029
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[8] W. Huang, C. Castillo-Chavez, K. Cooke, and S.A. Levin, “On the role of Long Incubation Periods in the Dynamics of Acquired Immunodeficiency Syndrome (AIDS), Part 2, Multiple Group Models, in Mathematical and Statistical Approaches to AIDS Epidemiology,” Springer-Verlag, to appear.; W. Huang, C. Castillo-Chavez, K. Cooke, and S.A. Levin, “On the role of Long Incubation Periods in the Dynamics of Acquired Immunodeficiency Syndrome (AIDS), Part 2, Multiple Group Models, in Mathematical and Statistical Approaches to AIDS Epidemiology,” Springer-Verlag, to appear. · Zbl 0705.92018
[9] W. Huang, C. Castillo-Chavez, K. Cooke, and S.A. Levin, Multiple Group Models for the Dynamics of HIV/AIDS Transmission with Proportionate Mixing and Multiple Endemic Equilibria; W. Huang, C. Castillo-Chavez, K. Cooke, and S.A. Levin, Multiple Group Models for the Dynamics of HIV/AIDS Transmission with Proportionate Mixing and Multiple Endemic Equilibria
[10] Hyman, J. M.; Stanley, E. A., A Risk Base Model for the Spread of the AIDS virus, Math. Biosci., 90, 415-473 (1988) · Zbl 0727.92025
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