| Citation: |
Peng Wu, Hongyong Zhao. MODELING AND DYNAMICS OF HIV TRANSMISSION AMONG HIGH-RISK GROUPS IN GUANGZHOU CITY, CHINA[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1561-1587. doi: 10.11948/20190252
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MODELING AND DYNAMICS OF HIV TRANSMISSION AMONG HIGH-RISK GROUPS IN GUANGZHOU CITY, CHINA
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Abstract
In this paper, a multicompartmental model is formulated to study how HIV is transmitted among different HIV high-risk groups, including MSM (men who have sex with men), FRs (foreigner residents), FSWs (female sex workers), and IDUs (injection drug users). The explicit expression for the basic reproduction number is obtained via the next generation matrix approach. We show that the disease free equilibrium is locally as well as globally asymptotically stable (the disease goes to extinction) when the basic reproduction number is less than unity, and the disease is always present when the basic reproduction number is larger than unity. As an illustration of our theoretical results, we conduct numerical simulations. We also conduct a case study where model parameters are estimated from the demographic and epidemiological data from Guangzhou. Using the parameter estimates, we predict the HIV/AIDS trend for each high-risk group. Furthermore, our study suggests that reducing the transmission routes of the disease and increasing condom use will be useful for control of HIV transmission.-
Keywords:
- Basic reproduction number /
- HIV high-risk groups /
- permanence /
- sensitivity analysis
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References
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Peng Wu, Hongyong Zhao. MODELING AND DYNAMICS OF HIV TRANSMISSION AMONG HIGH-RISK GROUPS IN GUANGZHOU CITY, CHINA[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1561-1587. doi: 10.11948/20190252
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Figure 1. The flow diagram of model
$ (2.1) $ , the incidence rate from$ I_1 $ to$ S_3 $ is$ \frac{\alpha_{13}I_1}{N_3} $ (red imaginary line), the incidence rate from$ I_3 $ to$ S_1 $ is$ \frac{\alpha_{31}I_3}{N_1} $ (orange imaginary line), the incidence rates from$ I_2 $ to$ S_1 $ ,$ S_3 $ are$ \frac{\alpha_{21}I_2}{N_1} $ and$ \frac{\alpha_{23}I_2}{N_3} $ (purple imaginary line). Red solid lines show the moving rate from$ S_1, \ S_3 $ to$ S_4 $ and green solid lines show the moving rate from$ S_4 $ to other susceptible groups -
Figure 2. The stable disease-free equilibrium
$ E_0 $ of system ($ 2.1) $ with$ r_i = 1.25 $ , other parameters are the same as Table 8,$ R_0 < 1 $ -
Figure 3. The existence of endemic equilibrium and persistence of system, parameters are shown in Table 8,
$ R^{1}_0 > 1, \ R^{2}_0 > 1 $ , and$ R^{3}_0 > 1 $ -
Figure 4. (a) The proportion of injecting drugs among drug users from 2005 to 2008 in Guangzhou
$ (\%) $ [19], (b) The prevalence of HIV in drug users reported by 6 sentinel points from 2005 to 2008 in Guangzhou$ (\%) $ [19] - Figure 5. The fitting curves of the total population of MSM, FRs and IDUs. Other parameters are the same as Table 8
- Figure 6. The fitting curves of new HIV/AIDS infected FSWs, IDUs, FRs and MSM in Guangzhou from 2008 to 2017
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Figure 7. The PRCC of
$ R^3_0 $ -
Figure 8. (a), (b):
$ R^{1}_0 $ trends in regard to some parameters of model$ (2.1) $ , (c), (d):$ R^{2}_0 $ trends in regard to some parameters of model$ (2.1) $ , other parameters are the same as Table 8 -
Figure 9.
$ R^{3}_0 $ trends in regard to some parameters of model$ (2.1) $ , the other parameters are the same as Table 8. -
Figure 10. The value of
$I_T(t)+A_T(t)$ in time and with respect to the recruitments of different compartments$\Lambda_{i}\ (i=1, 2, 3, 4)$ being all varied in the interval [0, 4000], other parameters are the same as Table 8. - Figure 11. Different parameters influence on HIV infected among MSM. Other parameters are the same as Table 8