Control Model of the HIV/AIDS Epidemic Based on Kinetic Equation


The corresponding dynamics equation model of HIV/AIDS was given based on the popular situation of HIV/AIDS in recent years. We studied the stability of the equilibrium point, discussed the threshold of epidemic, and carried on the numerical simulation based on the different persuade rate P, the different disease mortality α and the different infection rate β. The HIV/AIDS epidemic disease can pop in city at R0 > 1. We suggested that more persuade should be increased in addition to strengthening routine work according to the characteristics of R0 in the prevented and the controlled work of HIV/AIDS, which could more effectively reduce the number of HIV/AIDS patients. It provided the theoretical guidance, the beneficial reference on the prevented and the controlled work of HIV/AIDS.

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C. Xiong, Y. Zhou, C. Yu and H. Mei, "Control Model of the HIV/AIDS Epidemic Based on Kinetic Equation," World Journal of AIDS, Vol. 3 No. 2, 2013, pp. 79-84. doi: 10.4236/wja.2013.32011.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] R. Kandwal, P. K. Garg and R. D. Garg, “Health GIS and HIV/AIDS Studies: Perspective and Retrospective,” Journal of Biomedical Informatics, Vol. 42, No. 4, 2009, pp. 748-755. doi:10.1016/j.jbi.2009.04.008
[2] E. J. Singer, M. Valdes-Sueiras, D. Commins and A. Levine, “Neurologic Presentations of AIDS,” Neurologic Clinics, Vol. 28, No. 1, 2010, pp. 253-275. doi:10.1016/j.ncl.2009.09.018
[3] R. Arnab and S. Singh, “Randomized Response Techniques: An Application to the Botswana AIDS Impact Survey,” Journal of Statistical Planning and Inference, Vol. 140, No. 4, 2010, pp. 941-953. doi:10.1016/j.jspi.2009.09.019
[4] Z. Mukandavire, C. Chiyaka, G. Magombedze, G. Musuka and N. J. Malunguza, “Assessing the Effects of Homosexuals and Bisexuals on the Intrinsic Dynamics of HIV/AIDS in Heterosexual Settings,” Mathematical and Computer Modelling, Vol. 49, No. 9-10, 2009, pp. 1869-1882. doi:10.1016/j.mcm.2008.12.012
[5] P. van den Driessche and J. Watmough, “Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission,” Mathematical Biosciences, Vol. 180, No. 1-2, 2002, pp. 29-48. doi:10.1016/S0025-5564(02)00108-6
[6] J. M. Hyman and J. Li, “An Intuitive Formulation for the Reproductive Number for the Spread of Diseases in Heterogeneous Populations,” Mathematical Biosciences, Vol. 167, No. 1, 2000, pp. 65-86.
[7] W. Z. Huang, K. L. Cook and C. C. Carlos, “Stability and Bifurcation for a Multiple Group Model for the Dynamics of HIV/AIDS Transmission,” SIAM Journal on Applied Mathematics, Vol. 52, No. 3, 1992, pp. 835-854. doi:10.1137/0152047
[8] S. M. Moghadas and A. B. Gumel, “Stability of a TwoStage Epidemic Model with Generalized Nonlinear Incidence,” Mathematics and Computers in Simulation, Vol. 60, No. 1-2, 2002, pp. 107-118. doi:10.1016/S0378-4754(02)00002-2
[9] R. Naresh, A. Tripathi and D. Sharma, “Modelling and Analysis of the Spread of AIDS Epidemic with Immigration of HIV Infectives,” Mathematical and Computer Modelling, Vol. 49, No. 5-6, 2009, pp. 880-892. doi:10.1016/j.mcm.2008.09.013
[10] H. Ying and S. P. Sheu, “The Effect of the Density-Dependent Treatment and Behavior Change on the Dynamics of HIV Transmission,” Journal of Mathematical Biology, Vol. 43, No. 1, 2001, pp. 69-80. doi:10.1007/s002850100087

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