×

Transmission dynamics of a two-sex model for herpes simplex virus type 2. (English) Zbl 1209.92040

Summary: 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 by the authors in IMA J. Appl. Math. 75, No. 1, 75–107 (2010; Zbl 1193.37136)] 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.

MSC:

92C60 Medical epidemiology
93C95 Application models in control theory
34D20 Stability of solutions to ordinary differential equations
65C20 Probabilistic models, generic numerical methods in probability and statistics
37N25 Dynamical systems in biology
34D23 Global stability of solutions to ordinary differential equations

Citations:

Zbl 1193.37136
PDFBibTeX XMLCite