Abstract
In this paper, we first present a stochastic model of the proportion of the population infected with HIV against total population, and prove the existence and uniquess of its solution. Through computer simulation, we forecast the proportion of the population infected with HIV against the total population in the transmission course of AIDS in China in next 20 years. Especially, we study the control index of the transmission rate β to obtain its effect on the epidemic trend of AIDS when it fluctuates. As such, we present a strategy to adjust β to reach a certain control aim based on the analysis of the mean value and variance of the proportion.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Haynatzka, V.R., Gani, J., Rachevn, S.T.: The spread of AIDS among interactive transmission. Biosystems 73(3), 157–161 (2004)
Castillo, C.C., et al.: The role of long incubation periodic in the dynamics of acquired immunodeficiency syndrome—Single population models. Math. Biol. 7, 373–398 (1989)
Blythe, S.P., Anderson, R.M.: Distributed incubation and infections periods in models of transmission dynamics of human immunodeficiency virus (HIV). IMA J. Math. Appl. Med. Biol. 1–19 (1988)
Blythe, S.P., Anderson, R.M.: Variable infectiousness in HIV transmission models. IMA. Math. Appl. Med. Biol. 5, 181–200 (1988)
Blythe, S.P., Anderson, R.M.: Heterogeneous sexual activity models of HIV transmission in male homosexual populations. IMA J. Math. Appl. Med. Biol. 5, 237–260 (1988)
Jacquez, J.A., Simon, C.P., Koopman, J.S.: Structured mixing: Heterogeneous mixing by the definition of activity groups. In: Castillo-Chavez, C. (ed.) Mathematical and Statistical Approaches to AIDS Epidemiology. Lecture Notes in Biomath., pp. 301–315. Springer, Heidelberg (1989)
Jacquez, J.A., Simon, C.P., Koopman, J.S.: The reproduction number in deterministic models of contagious disease. Comments Theor. Biol. 2, 159–209 (1988)
Greenhalgh, D., Doyle, M., Lewis, F.: A mathematical model of AIDS and condom use. IMA J. Math. Appl. Med. Biol. 18, 225–262 (2001)
Roberts, M.G., Saha, A.K.: The asymptotic behavior of a logistic epidemic model with stochastic disease transmission. Applied Mathematics Letters 12, 37–41 (1999)
Friedman, A.: Stochastic Differential Equations and Their Applications. Academic Press, New York (1976)
Okesendel, B.: Stochastic Differential Equations. Springer, Heidelberg (1985)
Kloeden, P.E., Platen, E.: Numerical solution of stochastic differential equations. Springer, Heidelberg (1992)
Saito, Y., Higham, T.: Stability analysis of numerical scheme for stochastic differential equations. SIAM, Numer. Anal. 33, 2254–2267 (1996)
Higham, D.J.: Mean-square and asymptotic stability of the stochastic theta method. SIAM, Numer. Anal. 38(3), 753–769 (2000)
Ryden, T., Wiktorsson, M.: On the simulation of iterated Ito integrals. Stochastic Processes and their Applications 91(1), 116–151 (2001)
Burrage, K., Burrage, P., Mitsui, T.: Numerical solutions of stochastic differential equations-implementation and stability issues. Computational and Applied Mathematics 125, 171–182 (2000)
Slominski, L.: Euler’s approximations of solutions of SDEs with reflecting boundary. Stochastic Processes and their Applications 94(2), 317–337 (2001)
Liu, M.X., Zhou, Y.C.: An age-structured dynamic model of HIV. Journal of North China Institute of Technology 25(2), 25–30 (2004)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Xu, M., Ding, Y., Hu, L. (2007). A Stochastic Model for Prevention and Control of HIV/AIDS Transmission Dynamics. In: Li, K., Li, X., Irwin, G.W., He, G. (eds) Life System Modeling and Simulation. LSMS 2007. Lecture Notes in Computer Science(), vol 4689. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74771-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-74771-0_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74770-3
Online ISBN: 978-3-540-74771-0
eBook Packages: Computer ScienceComputer Science (R0)