Multiscale modeling to explore Ebola vaccination strategies

The power to assess potential outcomes and intervention strategies is critical for epidemic preparedness. But emerging and mutated pathogens always challenge our current knowledge, pleading for fresh approaches to explore their epidemic potentials up front. This paper coupled a within-host viral dynamics model and a between-host network model of Ebola virus (EBOV) infection showing that its transmission characteristics can be faithfully recapitulated. Based on this multiscale model, EBOV’s incubation period is predicted in the range from 2.6 to 12.4 days, while infected subjects can remain infectious until day 17. The predicted basic reproductive number (R0) differs by age-groups: the overall is 1.4 and the highest is 4.7 for the 10-14 years old. Random vaccination strategies can reduce R0 and case-fatality rate, eliminate the possibility of large outbreaks, but the effect depends on timing and coverage. A random vaccination program can reduce R0 below one if 85% coverage is achieved, and if it was conducted during the period from five months before to one week after the start of an epidemic. A vaccination coverage of 33% can reduce the epidemic size by ten to hundred times compared to a non-intervention scenario. Altogether, infection characteristics and epidemic mitigation approaches could be assessed using experimental data. An early, age-group specific, and high coverage vaccination program is the most beneficial.

The power to assess potential outcomes and intervention strategies is critical for epidemic preparedness. But emerging and mutated pathogens always challenge our current knowledge, pleading for fresh approaches to explore their epidemic potentials up front.
This paper coupled a within-host viral dynamics model and a between-host network model of Ebola virus (EBOV) infection showing that its transmission characteristics can be faithfully recapitulated.
Based on this multiscale model, EBOV's incubation period is predicted in the range from 2.6 to 12.4 days, while infected subjects can remain infectious until day 17. The predicted basic reproductive number (R0) differs by age-groups: the overall is 1.4 and the highest is 4.7 for the 10-14 years old. Random vaccination strategies can reduce R0 and case-fatality rate, eliminate the possibility of large outbreaks, but the effect depends on timing and coverage.
A random vaccination program can reduce R0 below one if 85% coverage is achieved, and if it was conducted during the period from five months before to one week after the start of an epidemic. A vaccination coverage of 33% can reduce the epidemic size by ten to hundred times compared to a non-intervention scenario. Altogether, infection characteristics and epidemic mitigation approaches could be assessed using experimental data. An early, age-group specific, and high coverage vaccination program is the most beneficial.
1. Introduction 1 Epidemics of infectious diseases are listed among the potential catastrophes and can be potentially 2 misused as mass destruction weapons [1]. Overwhelming research efforts have been developed 3 to early predict the danger of the epidemics but their crisis nature left scientists no better option 4 than learning from the past [1,2]. However, confronting outbreaks of emerging infections requires 5 swift responses and thus the ability to evaluate quickly and early potential outcomes [1]. As such, 6 computer simulations of epidemic models undoubtedly hold the potential as the first-aid toolbox 7 for decision making amid the crisis [1,3]. 8 A majority of epidemic modelling studies has exclusively relied on the availability of outbreak 9 data [4][5][6]. This approach requires that sufficient incidence data are available; for example, data 10 at the end of an epidemic or at least until its peak [7]. As such, it has limited applicability to 11 newly emerging epidemics. Moreover, mechanistic models based on outbreak data are often 12 oversimplified [8]. For example, the effective transmission probability [6] has been usually 13 simplified as a single parameter that reflects collective effects of the contact rate with the 14 infectious, the infectivity of the infectious, and the susceptibility of the susceptible. As a result, 15 these key processes in the disease transmission are lost, especially the transient nature of the 16 infection course [9]. In reality, the within-host infection process determines key parameters in replication and immune responses race with each other that eventually determines an individual infectivity, for example, his symptoms and possibly behaviours. At the between hosts level, infected individuals make contact(s) with susceptible individual(s) that eventually lead to a transmission, depending on both the infectivity of the infectious and the susceptibility of the susceptible. 17 the disease transmission [9][10][11][12][13]. In an infected subject, interactions between the viruses and In particular, we embedded a within-host infection model of EBOV infection directly into a 31 network transmission model at population level to simulate epidemic trajectories. Both the used 32 models were derived based on empirical data of EBOV infection and human contact networks. 33 Parameters obtained from simulations were then compared to those estimated based on actual 34 outbreak data and empirical observations. The results showed that using with-host infection 35 model not only uncovered faithful estimate of the transmission parameters, but also allowed 36 the evaluations of realistic vaccination effects. In that capacity, epidemic consequences can be 37 evaluated ahead of time once within-host viral dynamics are available. 38 Material and Methods 39 In an EBOV-infected subject, different immune systems components dynamically evolve in 40 response to the viral replication dynamic. As a result, a series of events is triggered determining 41 infection outcomes such as infectious status, symptoms, recovery, or death [24][25][26]. Therefore, 42 the EBOV replication dynamics within a host were used in this paper to infer transmission 43 parameters. 44 Within-host model 45 Using viral dynamics and immune responses data within a host, mathematical relations can be 46 defined to test hypothesized infection mechanisms [12,27]. In this context, non-human primates (NHPs) are the standard animal model for developing EBOV's therapeutics and vaccines in 48 humans [28,29] which recently has been used to develop an effective vaccine against EBOV 49 [30]. Epidemiological and pharmacological studies reported that a viral load higher than 50 10 6 copies/mL [29,31] is associated with a higher mortality rate, whereas observations on 51 experimental data in NHPs showed that a viral load level higher than 10 6 TCID 50 was fatal 52 [24,25]. Here the viral load dynamics were simulated based on the model as follows [13]: where r V , K V and In denote the replication rate, the host's carrying capacity, and a constraint 55 threshold expressing the lag-phase growth of the virus. The parameter K Ab represents the 56 strength of the immune system at which the antibody titre inhibits the viral net growth rate [13].

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Simulated subject-specific infection course 62 To simulate subject-specific infection course, the antibody response strength K Ab was varied 63 from a normal level approximately 10 2.5 [25,32] to the highest observed level of 10 4.5 [25].

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This value was assumed to vary based on individual's age, i.e., a U-shaped function of age with larger values for the infant and the elderly [15]. As infective dose can alter the course of

Measure Definition
A Incubation period the interval between exposure to a pathogen and initial occurrence of symptoms [4] was defined from the infection time to the first time the viral load crosses over the detectable threshold (Fig. S2). B Time from symptom onset to recovery [4] defined as the interval between the first day of detectable viral load and the first day the viral load goes undetectable (Fig. S2). C Time from symptom onset to death [4] defined as the interval between the first day with detectable viral load and the day the area under the viral load curve (AUC) crosses the reference threshold AU C 7 (Fig. S2). D Basic reproductive number (R0) calculated based on the network of infected subjects at the end of an epidemic. In terms of network models, this equals the mean degree distribution of the infected network, considering a directed network without loops (e.g., Fig. S3). The R0 by age-group was also calculated in the same fashion based on the assigned age-attribute. Note that in epidemics with intervention, the R0 is called the effective reproductive number (Re). E Final infected fraction the proportion of infected nodes at the end of the epidemic simulations. infected subjects were assumed recovered once the viral load was no longer detectable (Fig. S2).

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Depending on the infective dose and the adaptive immune response strength, an infection will 80 manifest different viral dynamics. Based on that, we defined the transmission parameters as in 81   Table 1A-C.

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The network model 83 The European's contact patterns survey data [35] were used to generate a network model 84 reflecting the number of contacts, the mixing patterns among age-groups, and a specific 85 population age-structure. The age-distribution of the city Freetown in Sierra Leon was used as 86 the reference [36]. A detailed description of the implementation can be found in Supplemental 1.

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Because EBOV spreads through direct contacts with infectious subjects [33], and that the highest 88 risk of infection is contacting with blood, faeces, and vomit [37], we used only the data of physical 89 contacts and excluded those contacts with a duration less than five minutes. To account for the 90 transmission route through funeral practices in EBOV outbreaks [2], we considered deceased 91 EBOV-infected subjects infectious until they were buried. During the last epidemics in Sierra 92 Leone, the time from death to burial was one to two days on average but can be a week [38].

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This number was randomly assigned using a truncated normal distribution at zero and seven 94 with unit mean and variance.  Basic reproductive number (R0) 118 Simulation results showed that the overall estimate of the R0 was 1.43 (Fig. 3). However, the 119 estimates differed by age-groups with the highest of 4.7 for the group of 10-14 years of age.

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Generally, the age-groups with a higher contact rate had also a higher R0. Simulations of 121 epidemics with varied intervention strategies showed that the Re can be reduced below one 122 if the vaccination program with 85% coverage were deployed as far as five months before the introduction of the index case (time zero) or as late as one week after that (Fig. S4). This coverage 124 threshold was tested as it is the highest vaccine coverage currently achieved worldwide for some 125 diseases, e.g. Hepatitis B, measles, and polio [39]. Late initiations of similar interventions from 126 one to five months after the time zero gradually shift the Re to the outbreak domain.

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A lower vaccination coverage of 33% appeared not protective and posed a potential of 128 outbreak regardless the time of vaccination program (Fig. S4). This coverage was tested as it is a 129 theoretical protective threshold, i.e., 1-1/R0 [40]. Note that the tested time window of five months 130 before the appearance of the index case was chosen based on the windows of opportunity for 131 EBOV vaccination [13]. As of now, no data are available on the secondary antibody responses to 132 EBOV; it was assumed that secondary responses are similar to the primary responses.

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Case-fatality rate 134 Simulations showed that the case-fatality rate in the absence of intervention is 90.93% (Fig. S5) 135 which falls in the range of literature estimates of 0.4 to 0.91 [4]. Furthermore, simulation results

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showed that all the intervention strategies mentioned previously can reduce the case-fatality rate.

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These results highlight a benefit of vaccination programs even they are late, i.e., they can reduce Theoretical analyses of epidemic models showed when the R0 is larger than one, the final 143 size of an epidemic will converge to a two points distribution: either the epidemic dies out 144 with a small number of infected cases or the epidemic takes off and converges to a normal 145 distribution [40]. Simulation results confirmed this epidemic behavior (Fig. 4). The results showed 146 that without intervention, EBOV had approximately 50% to infect more than half the population.

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The introduction of vaccination programs at both the coverage thresholds previously mentioned 148 and at any vaccination time points under assessments were able to scale down the epidemic A synthetic population of ten thousand individuals was generated. One thousand simulations were run to simulate the epidemic in the time course of one year. Each time, one individual was chosen randomly as the index case. Circles, diamonds, and connected lines are median. Filled areas are the corresponding non-parametric densities estimates [41].
Two median values are presented for multi-modal density estimates, determining by inflection points. size (Fig. 4). The two points epidemics size distribution gradually converged to a uni-modal Epidemic modelling aims to obtain generalized solutions to questions such as whether or not a 164 substantial population fraction is getting infected? how large would the outbreak spread? and 165 how can the outbreak be mitigated with certain intervention approaches [6,40]. Answering those 166 questions requires the use of assumptive parameters as well as actual outbreak data [6,14,22,   Estimates of the incubation period suggest a contact tracing period of three weeks for Ebola 170 epidemics, matching the current WHO's recommendation of 21 days [42]. Estimates of the delay 171 distributions agreed that EBOV infected subjects can be infectious from day 3 up to three weeks 172 post infection [4]. Understanding of these delay distributions is critical in both clinical and epidemiological perspectives [43]. These distributions, however, are most often only partially 174 observed in practice: it is difficult to know the exact time of exposure to the pathogen or 175 to have complete outbreak data [5,44]. As such, parameter estimation of these distributions have been relied on testing and comparing different distributional assumptions [44]. In this 177 paper, mechanistically generated transmission characteristics using viral dynamics remarkably 178 resemble literature estimates of Ebola. This approach is thus promising and practical given the 179 accumulating experimental data on varieties of pathogens, notably, the one that as yet unknown 180 in epidemic contexts.

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To determine infection outcomes, the threshold AUC 7 was chosen based on suggestions from 182 empirical data in humans [34] and non-human primates [24,25]. Simulations of the epidemics 183 using this threshold revealed faithful estimates of the EBOV case-fatality rate (Fig. S5), supporting 184 the use of the total viral load (AUC) as a criterion for determining infection outcomes. Although 185 a more precise threshold criterion is desirable, it might not be feasible to obtain in practice 186 considering inherent ethical reasons. Thus a similar criterion could be considered when adapting 187 this approach to other infectious diseases, but ideally with dedicated experimental data.

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Different classes of network models have been proposed, but they cannot reproduce properties 189 observed in real world networks [45]. Thus, a network model obeying empirical data provides a