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Sex-biased prevalence in infections with heterosexual, direct, and vector-mediated transmission: a theoretical analysis

1. Dipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14,38123 Povo (TN), Italy
2. School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 85281, USA
3. Instituto de Matemáticas, Universidad Nacional Autónoma de México (UNAM), Ciudad Universitaria 04510, Ciudad de Mexico, Mexico

Three deterministic Kermack-McKendrick-type models for studying the transmission dynamics of an infection in a two-sex closed population are analyzed here. In each model it is assumed that infection can be transmitted through heterosexual contacts, and that there is a higher probability of transmission from one sex to the other than vice versa. The study is focused on understanding whether and how this bias in transmission reflects in sex differences in final attack ratios (i.e. the fraction of individuals of each sex that eventually gets infected). In the first model, where the other two transmission modes are not considered, the attack ratios (fractions of the population of each sex that will eventually be infected) can be obtained as solutions of a system of two nonlinear equations, that has a unique solution if the net reproduction number exceeds unity. It is also shown that the ratio of attack ratios depends solely on the ratio of gender-specific susceptibilities and on the basic reproductive number of the epidemic $ \mathcal{R}_0 $, and that the gender-specific final attack-ratio is biased in the same direction as the gender-specific susceptibilities. The second model allows also for infection transmission through direct, non-sexual, contacts. In this case too, an analytical expression is derived from which the attack ratios can be obtained. The qualitative results are similar to those obtained for the previous model, but another important parameter for determining the value of the ratio between the attack ratios in the two sexes is obtained, the relative weight of direct vs. heterosexual transmission (namely, ρ). Quantitatively, the ratio of final attack ratios generally will not exceed 1.5, if non-sexual transmission accounts for most transmission events (ρ ≥ 0.6) and the ratio of gender-specific susceptibilities is not too large (say, 5 at most).

The third model considers vector-borne, instead of direct transmission. In this case, we were not able to find an analytical expression for the final attack ratios, but used instead numerical simulations. The results on final attack ratios are actually quite similar to those obtained with the second model. It is interesting to note that transient patterns can differ from final attack ratios, as new cases will tend to occur more often in the more susceptible sex, while later depletion of susceptibles may bias the ratio in the opposite direction.

The analysis of these simple models, despite their lack of realism, can help in providing insight into, and assessment of, the potential role of gender-specific transmission in infections with multiple modes of transmission, such as Zika virus (ZIKV), by gauging what can be expected to be seen from epidemiological reports of new cases, disease incidence and seroprevalence surveys.

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Keywords Epidemic model; heterosexual transmission; vector transmission; sex-biased prevalence; Zika epidemic model

Citation: Andrea Pugliese, Abba B. Gumel, Fabio A. Milner, Jorge X. Velasco-Hernandez. Sex-biased prevalence in infections with heterosexual, direct, and vector-mediated transmission: a theoretical analysis. Mathematical Biosciences and Engineering, 2018, 15(1): 125-140. doi: 10.3934/mbe.2018005

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