Potential impact of sexual transmission of Ebola virus on the epidemic in West Africa

Sexual transmission of Ebola virus disease (EVD) 6 months after onset of symptoms has been recently documented, and Ebola virus RNA has been detected in semen of survivors up to 9 months after onset of symptoms. As countries affected by the 2013–2015 epidemic in West Africa, by far the largest to date, are declared free of Ebola virus disease (EVD), it remains unclear what threat is posed by rare sexual transmission events that could arise from survivors. We devised a novel mathematical model that includes sexual transmission from convalescent survivors: a SEICR (susceptible-exposed-infectious-convalescent-recovered) transmission model. We fitted the model to weekly incidence of EVD cases from the 2014–2015 epidemic in Sierra Leone. Sensitivity analyses and Monte Carlo simulations showed that a 0.1% per sex act transmission probability and a 3-month convalescent period (the two key unknown parameters of sexual transmission) create very few additional cases, but would extend the epidemic by 83 days [95% CI: 68–98 days] (p < 0.0001) on average. Strikingly, a 6-month convalescent period extended the average epidemic by 540 days (95% CI: 508–572 days), doubling the current length, despite an insignificant rise in the number of new cases generated. Our results show that current recommendations for abstinence and condom use should reduce the number of sporadic sexual transmission events, but will not reduce the length of time the public health community must stay vigilant. While the number of infectious survivors is expected to greatly decline over the coming months, our results show that transmission events may still be expected for quite some time as each event results in a new potential cluster of non-sexual transmission. Precise measurement of the convalescent period is thus important for planning ongoing surveillance efforts.

researchers have warned that it should be considered in epidemiological models that are 82 used to predict the trajectory of an outbreak [11]. To this end, we devised a novel 83 mathematical model for EVD transmission: SEICR (susceptible-exposed-infectious- who maintain active Ebola virus replication (Fig. 1). The resulting SEICR model has five 98 states: susceptible, S, exposed, E, symptomatic and infectious, I, convalescent, C, fully 99 recovered and immune, R, and dead, D. The model is represented by the following set of 100 ordinary differential equations (ODEs): 101 (1) 102 where N = S + E + I + C + R denotes the total population size. We assumed the non-103 sexual transmission rate, β(t), to be initially constant (β 0 ) before it starts to decay 104 exponentially due to the effect of control interventions and behavior change after timeτ: 105 β(t) = β 1 + (β 0 -β 1 )e -k(t-τ) [12]. The sexual transmission parameter, β s , can be described as 106 the product of two parameters (β s = ηq) that we will consider separately: η is the per sex 107 act transmission probability of Ebola virus from convalescent men, and q is the daily rate 108 at which they engage in sexual intercourse. The number of convalescent individuals are 109 scaled by p, which is the proportion of convalescent survivors who are sexually active 110 men. 1/σ and 1/γ represent the average durations of incubation and symptomatic 111 infection, respectively. f is the case fatality rate. The average duration after which 112 convalescent patients recover completely and shed no further replicating Ebola virus from their body is given by 1/α. We assumed that sexual transmission is frequency-dependent 114 [3,15,16], i.e., the probability that the sexual partner of a convalescent man is susceptible 115 is given by S/N . The basic reproductive number, R 0 , for the SEICR model can be calculated using the 120 next-generation matrix method [17,18] and is given by 121 where S 0 is the initial number of susceptible individuals (see Supplementary Material 123 Appendix S1). When α goes to infinity or either β s = 0 or p = 0, the equation reduces to   Fig. S1). The data set was extended with 131 weekly incidence from the situation report for the most recent weeks when no data was 132 available in the patient database. In order to account for variability in the accuracy of 133 reporting, we assumed that the number of reported cases follows a negative binomial 134 distribution with mean as predicted by the model and dispersion parameter [20]. We  Deterministic model and sensitivity analysis. We solved the system of ODEs 149 numerically using the function ode from the deSolve package in the R software 150 environment for statistical computing [29]. We compared the following response 151 variables of the model: the epidemic peak number of exposed, E, acute, I, and 152 convalescents, C, cases; the cumulative number of EVD cases, deaths, and recoveries; the 153 date at the epidemic peak; the daily and cumulative incidence of sexual transmission; and 154 the date at which the last symptomatic case either died or entered into convalescence 155 ("day of last case"). We defined the day of last case as the time when the number of 156 symptomatic and infectious individuals, I, dropped below 0.5. We considered the 157 following parameters for the sensitivity analysis: the per sex act transmission probability 158 of Ebola virus from convalescent men (η), the proportion of convalescent survivors who 159 are sexually active men (p), the rate at which they engage in sexual intercourse (q), and 160 the rate at which convalescent patients recover completely and shed no further replicating 161 Ebola virus from their body (α). The sensitivity of the response variables to changes in R 0 162 was explored simultaneously as a comparison. We generated 1000 parameter 163 combinations from the uniform ranges, log-transformed [0.5x -2x] for the parameter 164 values for η, p, q, and α, given in Table 1

Effect of sexual transmission parameters on epidemic dynamics. The two key unknown 194
parameters of sexual transmission are the per sex act transmission probability, η, and the 195 rate at which convalescent survivors fully recover, α. Both parameters were found to have 196 very small effects on the peak number of infected or exposed patients ( Fig. 2A; Fig. 3A; 197 Figs. 4A, 4B, 4C; Fig. S2; Fig. S3). The duration of the convalescent period has a large 198 impact on the peak number of convalescent individuals, while η does not (compare Fig.  199 2A and Fig. 3A). The total number of recovered individuals is reached more slowly the 200 longer the convalescent period (Fig. 2B), which is not an effect caused by η (Fig. 3b).  The number of sexual transmission events expected from the baseline scenario (η = 0.001 218 and 1/ α = 3 months) is 31.2, the majority of which will occur around the peak of the 219 epidemic ( Fig. 2C and Fig. 3D) and thus likely go undetected. Doubling either η or 1/ α 220 results in nearly equal increases in the incidence and cumulative number of sexual 221 transmission events (Fig. 2C, 2D and Fig. 3C, 3D), with either leading to roughly double 222 the number of sexually transmitted cases over the course of the whole epidemic (> 60 223 cases). It should be noted that the total number of cases increases more than by simply the  new potential cluster of non-sexual transmission. The day of last case is affected more by 226 the convalescent period than the per sex act transmission probability (represented by 227 vertical lines in Fig. 2A and Fig. 3A), a result confirmed by the sensitivity analysis (see 228 Supplementary Material, Fig. S3A). The tail of the epidemic will depend on a small 229 number of events that are likely to be affected by stochastic processes, thus we used 230 Monte Carlo simulations to explore this behaviour. (two years) after the start of the epidemic (Fig. 4H). Strikingly, when the convalescent 250 period was extended from 3 months to 6 months, the projected length of the epidemic 251 increased to a mean of 1088 days (+/-15.5), with 84.0% of the 538 sustained epidemics 252 taking over two years to end (Fig. 4F, 4I). However, the average number of new cases

Discussion 261
Our study shows that the length of the convalescent period will determine whether or not 262 sexual transmission of Ebola virus from recovering patients will have a profound effect 263 on the length of time it will take for the epidemic to completely fade. For Sierra Leone,264 we found that an average convalescent period of 3 months, and a per sex act transmission 265 probability of 0.1%, could extend the EVD epidemic in Sierra Leone by an average of 83 266 days (95% CI: 68-98 days). Such a scenario would be consistent with the occurrence of a 267 small number of sexual transmission events during the end-phase of the epidemic. 268 However, assuming an average convalescent period of 6 months led to simulated 269 epidemics whose tails were much more variable, and much longer, despite a lack of 270 significant increase in the total number of cases. So far, the reported cases of sexual 271 Example stochastic run Sexual transmission event Each stochastic run Mean of stochastic runs Standard error Sierra Leone data    West Africa has been estimated to have high substitution rates [26,44,45]. This rapid 308 evolution detected throughout the current outbreak zone suggests that within-or between-309 host adaptation of the virus leading to pro-longed persistence in the seminal fluids is 310 possible. However, evolution of sexual transmission becoming the primary route of 311 spread is highly unlikely. 312 313 Awareness of the potential for sexual transmission has led to WHO issuing 314 recommendations that ask convalescent men to abstain from sexual activity as much as 315 possible and to use condoms for up to 6 months after the onset of symptoms [28].
convalescence should have an impact on the per sex act transmission probability (η) and 318 the frequency of sex acts (q), respectively. Our results show that condom use should 319 reduce the number of sporadic sexual transmission events during the tail of the epidemic 320 and after discharge of all remaining symptomatic individuals. However, the time during 321 which the public health community must stay vigilant is not reduced because these 322 interventions will not affect the time during which convalescent survivors can shed 323 infectious virus (1/α). This is especially poignant since adherence to these 324 recommendations will never be 100%. Thus, our results suggest that the current 325 requirement for declaring a region free from EVD (42 days following either death or a 326 second negative RT-PCR test of the blood from the last known patient), officially 327 declared in Sierra Leone on 7 November 2015 [46], may be premature. 328

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As more data about the convalescent survivors of EVD becomes available, this and future 330 mathematical modeling studies will help to better understand the potential 331 epidemiological consequences of sexual transmission on the EVD epidemic in West 332 Africa. Precise estimates are important for providing convalescent survivors with sound 333 advice that balances protection of the community with the harm that could come from 334 unnecessary stigmatization [47][48][49]. 335