American Institute of Mathematical Sciences

Advanced
2007, 4(4): 595-607. doi: 10.3934/mbe.2007.4.595

On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China

Nicolas Bacaër 1, , Xamxinur Abdurahman 2, , Jianli Ye 3, and  Pierre Auger 1,

1. 

Institut de Recherche pour le Développement (I.R.D.), 32 avenue Henri Varagnat, 93143 Bondy cedex, France
2. 

College of Mathematics and System Sciences, Xinjiang University, 14 Shengli Road, Urumqi, 830046, China
3. 

National Center for Women and Children's Health, Department of Information Management, 13 Dong Tu Cheng Street, Chang Yang District, Beijing, 100013, China

Received  April 2007 Revised  August 2007 Published  August 2007

Heterogeneity in sexual behavior is known to play an important role in the spread of HIV. In 1986, a mathematical model based on ordinary differential equations was introduced to take into account the distribution of sexual activity. Assuming proportionate mixing, it was shown that the basic reproduction number $R_0$ determining the epidemic threshold was proportional to $M+V/M$, where $M$ is the mean and $V$ the variance of the distribution. In the present paper, we notice that this theoretical distribution is different from the one obtained in behavioral surveys for the number of sexual partnerships over a period of length $\tau$. The latter is a ''mixed Poisson distribution'' whose mean $m$ and variance $v$ are such that $M=m/\tau$ and $V=(v-m)/\tau^2$. So $M+V/M=(m+v/m-1)/\tau$. This way, we improve the link between theory and data for sexual activity models of HIV/AIDS epidemics. As an example, we consider data concerning sex workers and their clients in Yunnan, China, and find an upper bound for the geometric mean of the transmission probabilities per partnership in this context.
Keywords: basic reproduction number, HIV, mixed Poisson distribution..
Mathematics Subject Classification: 92D3.
Citation: Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595-607. doi: 10.3934/mbe.2007.4.595
[1]

Jie Zhang, Yuping Duan, Yue Lu, Michael K. Ng, Huibin Chang. Bilinear constraint based ADMM for mixed Poisson-Gaussian noise removal. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020071
[2]

Hao Wang. Uniform stability estimate for the Vlasov-Poisson-Boltzmann system. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 657-680. doi: 10.3934/dcds.2020292
[3]

Yolanda Guerrero–Sánchez, Muhammad Umar, Zulqurnain Sabir, Juan L. G. Guirao, Muhammad Asif Zahoor Raja. Solving a class of biological HIV infection model of latently infected cells using heuristic approach. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020431
[4]

A. M. Elaiw, N. H. AlShamrani, A. Abdel-Aty, H. Dutta. Stability analysis of a general HIV dynamics model with multi-stages of infected cells and two routes of infection. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020441
[5]

Claudianor O. Alves, Rodrigo C. M. Nemer, Sergio H. Monari Soares. The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field. Communications on Pure & Applied Analysis, 2021, 20 (1) : 449-465. doi: 10.3934/cpaa.2020276
[6]

Yi-Long Luo, Yangjun Ma. Low Mach number limit for the compressible inertial Qian-Sheng model of liquid crystals: Convergence for classical solutions. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 921-966. doi: 10.3934/dcds.2020304
[7]

Huiying Fan, Tao Ma. Parabolic equations involving Laguerre operators and weighted mixed-norm estimates. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5487-5508. doi: 10.3934/cpaa.2020249
[8]

Juan Pablo Pinasco, Mauro Rodriguez Cartabia, Nicolas Saintier. Evolutionary game theory in mixed strategies: From microscopic interactions to kinetic equations. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2020051
[9]

Denis Bonheure, Silvia Cingolani, Simone Secchi. Concentration phenomena for the Schrödinger-Poisson system in $ \mathbb{R}^2 $. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020447
[10]

Mehdi Badsi. Collisional sheath solutions of a bi-species Vlasov-Poisson-Boltzmann boundary value problem. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2020052
[11]

Ahmad Z. Fino, Wenhui Chen. A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5387-5411. doi: 10.3934/cpaa.2020243
[12]

Shenglan Xie, Maoan Han, Peng Zhu. A posteriori error estimate of weak Galerkin fem for second order elliptic problem with mixed boundary condition. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020340

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (18)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences