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

Abstract

BackgroundHerpes 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.ResultsIn 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 ℜ0 and prove that if ℜ0≤1, then the disease-free equilibrium is globally asymptotically stable, whereas if ℜ0>1, then the endemic equilibrium is so. Based on this global stability result, we estimate ℜ0 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 ℜ0 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.ConclusionsThrough 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.

A sexually transmitted infection model with long-term partnerships in homogeneous and heterogenous populations

“…Note that we only modeled infectiousness reduction due to condom use, not including HSV-2 suppression treatment. Also, the condom reduction value used for the MSM calculation is only estimated from the well studied WSM-MSW values (Abu-Raddad et al., 2008; Schiffer, Mayer, Fong, Swan, & Wald, 2014; Wang et al., 2017), but studies (Turner et al., 2003) suggest that the reduction to be low. Thus the long-term partnerships do not significantly increase the reproduction number for MSM for durations of less than 4 years past the tipping point, R0<1.…”

Dynamics of HSV-2 in the Presence of Optimal Counseling and Education among Prisoners

“…ese studies, indeed, produced useful results and we utilize some of the results to develop and analyze our framework. Several mathematical epidemiological models have been presented and analyzed to probe the HSV-2 transmission dynamics and their control (see [29][30][31][32][33][34][35][36][37]). Podder and Gumel [29] formulated and analyzed a deterministic mathematical epidemiological model for HSV-2, which considered disease transmission by the infected individuals in the dormant state and an imperfect vaccine for HSV-2.…”

“…A case study on HSV-2 was carried out, with the major aim of understanding the transmission dynamics of an infectious disease. An SVIRI multigroup epidemic model for HSV-2 was then developed and analyzed, which considered infection relapse, waning vaccine immunity, and the effects of vaccination [37].…”