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. 2019 Nov 22;9(1):17408.
doi: 10.1038/s41598-019-53841-8.

The type-reproduction number of sexually transmitted infections through heterosexual and vertical transmission

Hiromu Ito  1   2 , Taro Yamamoto  1 , Satoru Morita  3   4
Affiliations

The type-reproduction number of sexually transmitted infections through heterosexual and vertical transmission

Hiromu Ito et al. Sci Rep. .

Abstract

Multiple sexually transmitted infections (STIs) have threatened human health for centuries. Most STIs spread not only through sexual (horizontal) transmission but also through mother-to-child (vertical) transmission. In a previous work (Ito et al. 2019), we studied a simple model including heterosexual and mother-to-child transmission and proposed a formulation of the basic reproduction number over generations. In the present study, we improved the model to take into account some factors neglected in the previous work: adult mortality from infection, infant mortality caused by mother-to-child transmission, infertility or stillbirth caused by infection, and recovery with treatment. We showed that the addition of these factors has no essential effect on the theoretical formulation. To study the characteristics of the epidemic threshold, we derived analytical formulas for three type-reproduction numbers for adult men, adult women and juveniles. Our result indicates that if an efficient vaccine exists for a prevalent STI, vaccination of females is more effective for containment of the STI than vaccination of males, because the type-reproduction number for adult men is larger than that for adult women when they are larger than one.

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Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1
Intuitive derivation of Eqs. (15), (20–22). (a) The two figures represent the processes through which daughters and sons are vertically infected by an infected adult woman, where the average production numbers of vertically infected juveniles are given by αeff and γ1−γαeff, respectively. (b) The average total number of female offspring infected vertically by a horizontally infected adult woman is derived by a geometric series with initial term αeff and geometric ratio αeff, which gives Eq. (21). (c) The average total number of male offspring infected vertically by a horizontally infected adult woman is derived similarly, giving Eq. (22).
Figure 2
Figure 2
Intuitive derivation of type-reproduction numbers: Eqs. (24), (26) and (28). (a) There are four basic processes of infection spread starting from an infected adult woman and two starting from an infected adult man. The top two processes (yellow and green) represent vertical transmission starting from a horizontally infected adult woman, where the average production numbers are calculated as in Fig. 1b,c. Note that these processes contain vertical transmission starting from a vertically infected adult woman. The middle two processes represent horizontal transmission from a horizontally (blue) or vertically (brown) infected woman. The bottom two processes represent horizontal transmission from a horizontally (purple) or vertically (red) infected man. The average production numbers are given by the product of the transmissibility (βf→m or βm→f), contact rate (cf, kf, cm or km), and duration (1/(μf' + ηf) or 1/(μm' + ηm)). (b) There are three paths starting from a horizontally infected adult woman and ending with a horizontally infected adult woman: two horizontal transmissions (HH), one vertical and two horizontal transmissions (VHH), and one vertical and one horizontal transmission (VH). Because the HH case is made up of the processes shown in blue and purple in (a), the reproduction rate RHH for the HH case is given by the product of their average production numbers. We can calculate the reproduction rates RVHH and RVH for the VHH and VH cases in the same way. Thus, the type-reproduction number for adult women is given by summing these rates: RHH + RVHH + RVH; thus, Eq. (24) is obtained. (c) The paths starting with a horizontally infected adult man and ending with a horizontally infected adult man are more complicated. The HH case (purple and blue) and the VHH case (purple, yellow, and brown) are similar to (b) (see the top two parts). The average production numbers of these cases are RHH and RVHH. In addition to these two cases, secondary infected women may vertically infect their sons, who may then infect other women (i.e., we can insert the green and red parts in the way; see the middle two parts). The average production numbers of these cases are RHHRVH and RVHHRVH. This procedure can be repeated (see the bottom two parts). Thus, the type-reproduction number for adult men is derived by a geometric series with geometric ratio RVH, and Eq. (26) is obtained. (d) The paths starting with an infected juvenile and ending with an infected juvenile are also complicated. The case through one woman is simple, and it is obvious that its reproduction rate is αeff. There are two cases through two women: One includes men infected horizontally (brown and purple), and the other includes those infected vertically (red). Inserting the blue and purple part in the way, we obtain two cases through three women. This procedure can be repeated. Considering two geometric series with geometric ratio RHH, we obtain the type-reproduction number for juveniles—Eq. (28).
Figure 3
Figure 3
Graphical analysis of the three type-reproduction numbers. (a–c) The three type-reproduction numbers (Rm, Rf, Rj) are plotted as a function of the geometric mean of the sexual transmission rates βf→mβm→f for constant vertical transmission rate (α = 0.5), and (d–i) they are plotted as a function of α for constant sexual transmission rates. The left panels (a,d,g) represent the same sexual transmission rate (βf→m = βm→f), the middle panels (b,e,h) represent the case in which the sexual transmission rate from males to females is greater than that in the opposite direction (βm→f = 10βf→m), and the right panels (c,f,i) represent the case in which the sexual transmission rate from females to males is greater than that in the opposite direction (βf→m = 10βm→f). For the case that βf→mβm→f is large (d–f), Rj is not plotted because it diverges. The other parameters are set as kf, km = 0.8, cf, cm = 20, μf, μf', μm, μm', μj, μj' = 1/50, ηf, ηm, ηj = 0, δ = 0, λ = λ′ = 1/15, then αeff = α.
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References

    1. Oriel, J. D. The Scars of Venus: A History of Venereology (Springer-Verlag, 1994).
    1. Waugh, M. History of sexually transmitted infections. In Sexually Transmitted Infections and Sexually Transmitted Diseases (eds Gross, G. & Tyring, S. K.) 3–11 (Springer-Verlag, 2011).
    1. Gewirtzman, A., Bobrick, L., Conner, K. & Tyring, S. K. Epidemiology of sexually transmitted infections. In Sexually Transmitted Infections and Sexually Transmitted Diseases (eds Gross, G. & Tyring, S. K.) 13–34 (Springer-Verlag, 2011).
    1. World Health Organization. Global Strategy for the Prevention and Control of Sexually Transmitted Infections, 2006–2015: Breaking the Chain of Transmission (WHO Press, 2007).
    1. Erbelding E, Quinn TC. The impact of antimicrobial resistance on the treatment of sexually transmitted diseases. Inf. Dis. Clin. North Am. 1997;11:889–903. doi: 10.1016/S0891-5520(05)70396-2. - DOI - PubMed

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