Dynamic modeling and analysis of sexually transmitted diseases on heterogeneous networks

• Correlation coefficients about degrees are defined.
• We proposed an SIS mean-field dynamical model of STDs.
• We analyzed the basic reproduction number of the model.
• Influences of homosexual and heterosexual transmissions on STDs are studied.

Considering homosexual contacts and heterosexual contacts in the course of sexual contacts, double degrees which describe the numbers of homosexual contacts and heterosexual contacts are introduced, correlation coefficients about degrees based on the joint probability distribution are given, and an SIS mean-field model about sexually transmitted diseases is presented when degrees are uncorrelated. The basic reproduction number of diseases is studied by the method of next generation matrix. Results show that, when homosexual contacts and heterosexual contacts all exist, once the disease is epidemic in the interior of male (female) population which is caused by male (female) homosexual transmissions, or the disease is epidemic between the two species which is caused by heterosexual transmissions, the disease must be epidemic in the whole population. Numerical simulations confirm the theoretical results.