Modelling infectious diseases with relapse: a case study of HSV-2

BACKGROUND: Herpes Simplex Virus Type 2 (HSV-2) is one of the most common sexually transmitted diseases. Although there is still no licensed vaccine for HSV-2, a theoretical investigation of the potential effects of a vaccine is considered important and has recently been conducted by several researchers. Although compartmental mathematical models were considered for each special case in the previous studies, as yet there are few global stability results. RESULTS: In this paper, we formulate a multi-group SVIRI epidemic model for HSV-2, which enables us to consider the effects of vaccination, of waning vaccine immunity, and of infection relapse. Since the number of groups is arbitrary, our model can be applied to various structures such as risk, sex, and age group structures. For our model, we define the basic reproduction number ℜ(0) and prove that if ℜ(0)≤1, then the disease-free equilibrium is globally asymptotically stable, whereas if ℜ(0)>1, then the endemic equilibrium is so. Based on this global stability result, we estimate ℜ(0) for HSV-2 by applying our model to the risk group structure and using US data from 2001 to 2014. Through sensitivity analysis, we find that ℜ(0) is approximately in the range of 2-3. Moreover, using the estimated parameters, we discuss the optimal vaccination strategy for the eradication of HSV-2. CONCLUSIONS: Through discussion of the optimal vaccination strategy, we come to the following conclusions. (1) Improving vaccine efficacy is more effective than increasing the number of vaccines. (2) Although the transmission risk in female individuals is higher than that in male individuals, distributing the available vaccines almost equally between female and male individuals is more effective than concentrating them within the female population.