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## Simple Summary

## Abstract

_{0}, was 10 (95% HPD: 1.1 to 30). Our estimates of the basic reproductive number R

_{0}were greater than estimates of R

_{0}for ASF reported previously. The results presented in this study may be used to estimate the number of pigs expected to be showing clinical signs at a given number of days following an estimated incursion date. This will allow sample size calculations, with or without adjustment to account for less than perfect sensitivity of clinical examination, to be used to determine the appropriate number of pigs to examine to detect at least one with the disease. A second use of the results of this study would be to inform the equation-based within-herd spread components of stochastic agent-based and hybrid simulation models of ASF.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Population and Data Collection

#### 2.2. Model Structure

A frequency-dependent continuous time stochastic susceptible-exposed-infectious-removed model was developed (Figure 1) using the Gillespie algorithm [23,24]. The model was designed to estimate changes in the prevalence of infectious pigs as a function of the number of days following the onset of clinical signs of the assigned index case in the herd. Expressions defining the number of pigs transitioning out of the susceptible state into the exposed, infectious, and removed states as a function of time are shown in Equations 1 to 4, respectively.

**Figure 1.**Schematic diagram of the susceptible-exposed-infectious-removed (SEIR) model described in the text. Sojourn times in the exposed I and infectious (I) states were split into 4 sub-compartments, effectively following Erlang distributions with shape parameter k = 4.

. The rate at which pigs transitioned from the exposed to infectious state was dependent on σ such that the average latent period was equal to 1/σ. The rate at which individuals transition to the removed state was dependent on γ, defined as the inverse of the average duration of infectiousness [16]. The length of time individuals remained in the exposed (E), and infectious (I) states were assumed to follow Erlang distributions with a shape parameter k=4

#### 2.3. Model Parameters

, σ, and γ (Table 1) for the process that generated the available dataset. The bounds of the uniform prior distributions used in the ABC-SMC were set at values that encompassed the range of plausible values. These were based on a review of published literature from studies that reported on epidemiological parameters from field observations of African swine fever outbreaks (see Table 1), where possible, confined to estimates based only on within-farm transmission. The viral strains circulating in Vietnam at the time of the outbreak belonged to genotype II (p72 and p54 genes), serogroup 8 (CD2v gene), and CVR I – which share 100% identity with previously reported Vietnamese ASF viral isolates and those reported in China, Georgia, Korea, and Russia [30]. In order to perform an exhaustive exploration of the parameter space, the minimum and maximum limits of our prior distributions included parameter estimates derived from observational studies across different regions. The ABC SMC algorithm involved sampling combinations of β, σ, and γ values (i.e., particles) until n = 2000 particles were retained at each step, based on a distance function. The distance function was estimated as the difference between the observed data and three summary statistics for a simulation run on each particle: the number of days to reach the outbreak peak, the peak outbreak size, and the sum of epidemic curve residuals (i.e., the sum of the magnitude of the differences between the simulated and observed epidemic curve, by day). In the first step, particles were accepted if their distance from the observed data was within predefined tolerances, set to capture the peak within ± 4 days and ±4 cases, and an epidemic curve residual sum of ≤40 cases. The tolerance was progressively narrowed in sequential steps of the SMC algorithm to the 75th percentile of the distance from the observed data of the retained particles from the previous step, per summary statistic. The ABC-SMC algorithm was coded in R [31] and run until there was limited further gain with additional steps, in this case, for 18 steps. An estimate of the basic reproductive number (R0), defined as the expected number of new infectious individuals that one infectious individual will produce during its period of infectiousness in a fully susceptible population [16], was obtained as a calculated output by dividing β by γ

**Table 1.**Description of model parameters and prior distributions used in the ABC-SMC, based on published information from empirical observations of within-farm spread of African swine fever.

## 3. Results

**Figure 2.**Frequency histogram showing counts of animals showing clinical signs and counts of animals that died as a function of calendar date.

**Figure 3.**Line plots showing rectal temperature for individual pigs as a function of the number of days 15 March 2019. On each plot, the days on which pigs were showing clinical signs of ASF are shown in black. The days on which blood samples were taken from individual pigs are marked on each plot as inverted triangles, with shading indicating the PCR Ct value.

, the average latent period σ−1, the average duration of infectiousness γ−1 and the basic reproductive number R0 are presented in Table 2. Figure 4 shows the uniform prior distributions assigned to β, σ, and γ and the approximate posterior distributions estimated by the ABC-SMC algorithm, along with the calculated approximate posterior distribution for R0

**Figure 4.**Prior (dashed lines) and posterior (solid lines) distributions for (

**a**) the transmission coefficient β

**b**) the inverse of the average latent period σ; (

**c**) the inverse of the average duration of infectiousness γ; (

**d**) the basic reproductive number, R

_{0}which was a calculated output and (being a ratio) is presented on a logged horizontal axis.

**Figure 5.**Line plot showing the number of infectious pigs as a function of the number of days since the onset of signs in the first affected pig (black line). Superimposed on this plot are the predicted median (grey line) number of infectious pigs per day. The dark and light shaded areas show the 50% and 95% quantiles around these estimates.

**Table 2.**Descriptive statistics of the posterior distributions of the transmission coefficient β

, the average latent period (days) σ−1, the average duration of infectiousness (days) γ−1 and the basic reproductive number R0

## 4. Discussion

(10; 95% HPD: 1.1 to 30) in this study is comparable to the 5 to 12 range reported by Schulz et al. [40] in a study that summarized within-herd R0 estimates across two observational studies [35,36]. Our median estimate of R0 is also within the 4.92 and 24.2 range estimated under experimental conditions [41]. Estimates from field observations from an outbreak in 1977 in Ukraine [35] presented a lower range, from 6 to 9, while an analysis of a recent outbreak in Uganda, where the farming system is likely to differ markedly from Vietnam, was from 1.6 to 3.2 [38]. Differences in estimates of R0 across studies arise from the properties of different virus isolates (e.g., virulence and infectivity), the frequency of contacts between pigs within a herd (influenced by herd structure and management), and the analytical method used [40]. A strength of this study is that empirical data were used to simultaneously estimate β, σ, and γ using ABC methods as opposed to the more commonly used and potentially biased technique that involves estimation of β

_{0}is high and comparable to that of measles in human populations [42]. Thus, the pursuit of solutions based on vaccine development must also consider well-planned vaccine deployment to achieve high levels of coverage. In the absence of a vaccine, our results suggest that herd managers should regard all animals as potentially infectious in an ASF outbreak—not just those showing clinical signs. The time series plots of the rectal temperatures as a function of outbreak day, in combination with the results of PCR testing (Figure 3), show that pigs became PCR-positive and shed the virus before the onset of pyrexia and presumably clinical signs. These results agree with the findings of de Carvalho Ferreira et al. [41] in a study investigating the transmission rate of ASF under laboratory conditions. The application of strict biosecurity measures focused on minimizing the transference of infected body tissues and fomites from infected to uninfected animals [4] should be prioritized to reduce the within- and between-herd spread of ASF. Enforcement of strict biosecurity measures to mitigate ASF in smallholder premises requires close monitoring, as it may result in increasing trading and consumption of infected animals [43], magnifying the outbreak effects [44].

, σ, and γ

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Approximate Posterior Distribution and R Code

## Appendix B. Cross-Correlations between Parameters in the Accepted Particles

**Figure A1.**Heat map of the pair-wise correlations between parameters in the approximate posterior distribution.

## Appendix C. Repeated Simulations from the Posterior Distribution Versus Empirical Data

**Figure A2.**Line plots show the number of infectious pigs as a function of the number of days since the onset of signs in the first affected pig (black line). Superimposed on this plot are the predicted median (grey line) number of infectious pigs per day based on re-simulated samples from the approximate posterior. The dark and light shaded areas show the 50% and 95% quantiles around these estimates.

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