Latest News

About CAMQ

Information for Authors

Editorial Board

Browse CAMQ Online

Subscription and Pricing

CAMQ Contacts

CAMQ Home

 

Volume 17,     Number 2,     Summer 2009

 

TRANSMISSION DYNAMICS OF A TWO-SEX
MODEL FOR HERPES SIMPLEX VIRUS TYPE 2
CHANDRA N. PODDER AND ABBA B. GUMEL

Abstract. A new sex-structured deterministic model for the transmission dynamics of Herpes Simplex Virus type 2 (HSV-2) is designed and qualitatively analysed. The model has a globally-asymptotic stable (GAS) disease-free equilibrium (DFE) whenever the associated reproduction threshold is less than unity. Further, it has a unique endemic equilibrium (EEP), which is shown to be GAS for a special case, when the reproduction threshold exceeds unity. The model is extended to incorporate some anti-HSV-2 control strategies, namely an imperfect vaccine, condoms and drug treatment. The resulting model has a GAS DFE whenever its associated reproduction threshold is less than unity. Furthermore, the extended model has at least one endemic equilibrium when the threshold exceeds unity (this EEP is GAS under certain conditions). These analyses reveal that adding sex structure to the basic (single sex) HSV-2 model (considered in [40]) does not alter the (main qualitative) dynamics of the single sex model. Numerical simulations of the extended model show that, for low treatment rates, very high condom compliance will be required to effectively control the spread of the disease in the absence of vaccination. Furthermore, the combined use of the three strategies offers great prospect for the effective control of HSV-2 even for low treatment and vaccination rates. It is shown that using vaccination as a single intervention strategy, the targeted vac- cination of one sex group (only) induces an indirect benefit in the other sex group. Under such vaccine-only strategy, more new cases of females are prevented than new cases of males, regardless of which sex group is targeted for vaccination.

 

Download PDF Files
 
(Subscribers Only)

© 2006-2010 Canadian Applied Mathematics Quarterly (CAMQ)