Disease-emergence dynamics and control in a socially-structured wildlife species

Abstract

Once a pathogen is introduced in a population, key factors governing rate of spread include contact structure, supply of susceptible individuals and pathogen life-history. We examined the interplay of these factors on emergence dynamics and efficacy of disease prevention and response. We contrasted transmission dynamics of livestock viruses with different life-histories in hypothetical populations of feral swine with different contact structures (homogenous, metapopulation, spatial and network). Persistence probability was near 0 for the FMDV-like case under a wide range of parameter values and contact structures, while persistence was probable for the CSFV-like case. There were no sets of conditions where the FMDV-like pathogen persisted in every stochastic simulation. Even when population growth rates were up to 300% annually, the FMDV-like pathogen persisted in <25% of simulations regardless of transmission probabilities and contact structure. For networks and spatial contact structure, persistence probability of the FMDV-like pathogen was always <10%. Because of its low persistence probability, even very early response to the FMDV-like pathogen in feral swine was unwarranted while response to the CSFV-like pathogen was generally effective. When pre-emergence culling of feral swine caused population declines, it was effective at decreasing outbreak size of both diseases by ≥80%.

Figure 1

Schematic showing how group dynamics (A) and contact structure (B) were modeled. (A) Family groups consist of females and juveniles. Young males disperse together at reproductive maturity and eventually exist independently. Reproductively active, younger females disperse to form new family groups when a group reaches carrying capacity. (B) Homogenous –individuals contact other individuals with equal probability. Metapopulation – groups contact other groups with equal probability. Spatial contact structures are the same as their non-spatial counterparts but are limited to contacts within a fixed distance of their home range centroids. Network – groups only contact groups they are connected to as described by network connections. Contact structure within all groups is homogenous.

Figure 2. Outcome of disease dynamics for the FMDV-like (closed circles) and CSFV-like viruses (open triangles).

Parameters used in sensitivity analysis were fixed at: maxK = 40, Initial density = 15, Dispersal = 3 km, within-group contact rate = 0.1, between-group contact rate = 0.1, q = 0 (density-dependent transmission). Points are the mean of 100 replicate simulations, error bars are the standard deviation of the means. Simulations were run for 4 years. A single infectious individual was seeded at 1.5 years. Parameters were as in Table 1 except that the following parameters were fixed at realistic/permissive values: scaling factor on conception probability (1 which is equivalent to an annual population growth of 120% following the index case), dispersal distance (3 km), maximum family group size (40 feral swine), initial density (15 feral swine/km²), within-group transmission rate (0.1/feral swine/day), between-group transmission rate (0.1/feral swine/day), and disease-induced mortality (FMDV-like virus – 0%, CSFV-like virus -50%). Network properties were mean degree 3 and global transitivity 0.76 (light blue) and mean degree 6 and global transitivity 0.74 (dark blue). Other contact structures were: homogenous (H), metapopulation (M), spatial homogenous (SH) and spatial metapopulation (SM).

Figure 3. Relationship of within- and between-group transmission rates on outcome.

(A) Heat maps of the proportion of simulations (N = 50) where infectious individuals continue to transmit after 2.5years. (B) The mean number of total cases in simulations where total cases were >10 (i.e., arbitrary criterion for an “outbreak”). Each column of plots are results for either the FMDV-like or CSFV-like viruses (labeled on top). Each plot shows results form a particular between-group contact structure (labeled in white in the plot). Heat map response values were averages across all sets of parameters in the sensitivity analysis. Table 1 gives the ranges of variable and fixed parameters. Network properties were mean degree 3 and global transitivity 0.76. Parameters were as in Table 1.

Figure 4. Effects of host population growth rate on disease transmission.

(A) The proportion of simulations (N = 50) where infectious individuals continue to transmit after 2.5years. (B) The mean persistence in days for simulations that fade out before 2.5 years. (C) The proportion of simulations (N = 50) that have >10 total cases (i.e., arbitrary criterion for an “outbreak”). (D) The mean number of total cases for simulations that “outbreak”. X-axis represents the percent population growth in the 2.5 years following introduction of a virus. Left column of plots are for FMDV-like parameters; right column are for CSFV-like parameters. Error bars are standard deviations of the mean for all simulations with X-axis parameter values. Table 1 gives the ranges of variable and fixed parameters. Colors correspond to different between-group contact structures: Homogenous (black), Metapopulation (grey), Spatial homogenous (red), Spatial metapopulation (dark red), Network with mean degree 3 and global transitivity 0.76 (blue). Parameters were as in Table 1.

Figure 5. Effects of dispersal distance on outcome under spatial contact structure.

(A) The proportion of simulations (N = 50) where infectious individuals continue to transmit after 2.5years. (B) The mean number of total cases for simulations that “outbreak”. X-axis represents distance of dispersal for both males at reproductive maturity and females that disperse when family groups reach carrying capacity. Left column of plots are for FMDV-like parameters; right column are for CSFV-like parameters. Error bars are standard deviations of the mean for all simulations with X-axis parameter values. Table 1 gives the ranges of variable and fixed parameters. Colors correspond to different between-group contact structures: Spatial homogenous (red), Spatial metapopulation (dark red). Parameters were as in Table 1.

Figure 6. Pre-outbreak population management.

Number of individuals culled per event (X-axis) corresponded to 0.9, 1.7, 4.4, 8.7, 17.4, 35.8% of the population during the initial culling occasions. Top: spatial metapopulation contact structure, Bottom: Network with degree = 3. Colors indicate the proportion of reduction in cases due to culling; i.e., (mean without culling-mean with culling)/mean without culling. Data in the plots were derived from the mean of 100 replicate simulations for each set of culling conditions. Numbers in white show the mean proportional reduction across all culling conditions in the plot (top) and the mean standard deviation across all standard deviations in the plot (bottom). Standard deviation plots are shown in Figure S3. Parameters were as in Table 1 except that the following parameters were fixed at realistic/permissive values: scaling factor on CP (1 which is equivalent to an annual population growth of 120% following the index case in the absence of culling), dispersal distance (3 km), maximum family group size (40 feral swine), initial density (15 feral swine/km²), within-group transmission rate (0.1/feral swine/day), between-group transmission rate (0.1/feral swine/day), and disease-induced mortality (FMDV-like virus –0%, CSFV-like virus −20% & 80%).

Figure 7. Post-outbreak response.

Number of individuals culled per day (X-axis) ranged from 0.5–10% of the population at the time of disease introduction. Y-axis indicates the day daily culling begins after disease introduction. Top: spatial metapopulation contact structure, Bottom: Network with degree = 3. Colors indicate the proportion of reduction in cases due to culling; i.e., (mean without culling-mean with culling)/mean without culling. Data in the plots were derived from the mean of 100 replicate simulations for each set of culling conditions. Numbers in white show the mean proportional reduction across all culling conditions in the plot (top) and the mean standard deviation across all standard deviations in the plot (bottom). Standard deviation plots are shown in Figure S6. Parameters were as in Table 1 except that the following parameters were fixed at realistic/permissive values: scaling factor on CP (1 which is equivalent to an annual population growth of 120% following the index case in the absence of culling), dispersal distance (3 km), maximum family group size (40 feral swine), initial density (15 feral swine/km²), within-group transmission rate (0.1/feral swine/day), between-group transmission rate (0.1/feral swine/day), and disease-induced mortality (FMDV-like virus – 0%, CSFV-like virus −20 & 80%).