Vaccination of cattle only is sufficient to stop FMDV transmission in mixed populations of sheep and cattle

Summary

We quantified the transmission of foot-and-mouth disease virus in mixed cattle-sheep populations and the effect of different vaccination strategies. The (partial) reproduction ratios (R) in groups of non-vaccinated and vaccinated cattle and/or sheep were estimated from (published) transmission experiments. A 4 × 4 next-generation matrix (NGM) was constructed using these estimates. The dominant eigenvalue of the NGM, the R for a mixed population, was determined for populations with different proportions of cattle and sheep and for three different vaccination strategies. The higher the proportion of cattle in a mixed cattle-sheep population, the higher the R for the mixed population. Therefore the impact of vaccination of the cattle is higher. After vaccination of all animals R = 0·1 independent of population composition. In mixed cattle-sheep populations with at least 14% of cattle, vaccination of cattle only is sufficient to reduce R to < 1.

INTRODUCTION

Foot-and-mouth disease (FMD) is a viral disease in cloven-hoofed animals caused by foot-and-mouth disease virus (FMDV). Transmission of FMDV is difficult to control. The magnitude of transmission of any infection is assessed using the reproduction ratio R [1, 2]. R is defined as the average number of new cases arising from a typical infected individual during its whole infectious period in a fully susceptible population. An infectious agent is able to cause major outbreaks only if R is > 1 [3]. For FMDV, R has been quantified using field data [4] and experimental data [5–12]. Using experimental data, R has been quantified for both vaccinated and non-vaccinated sheep-to-sheep transmission [7, 11] and for vaccinated and non-vaccinated cattle-to-cattle transmission [9, 10] (and in Bravo de Rueda et al., unpublished observations). In addition, a partial R for non-vaccinated sheep to non-vaccinated cattle [13] has been quantified; however, this estimate alone is not sufficient to assess the magnitude of transmission of FMDV in a mixed population of cattle and sheep. In order to understand the transmission of FMDV in field conditions where different species co-exist, it is necessary to quantify R for heterogeneous populations (i.e. consisting of sheep and cattle).

Vaccination against FMDV has been recognized as an important tool for the control of FMDV. Vaccination against FMDV can prevent transmission of the virus both in field conditions [14–16] and experimentally [5, 7, 9–11, 17, 18]. In mainland Europe, FMDV was eradicated by prophylactic vaccination of cattle only [15]. In parts of South America, FMDV was successfully eradicated by vaccination of cattle only [16]. For example, in Uruguay, where cattle and sheep, mingle freely and where (before 2002) the proportion of sheep in the population was slightly higher than that of cattle, vaccination of cattle only was sufficient to eradicate FMDV [16, 19]. In the European Union, emergency vaccination of (all) susceptible species is an option during an FMDV outbreak (EU directive 2003/85). The Netherlands used emergency vaccination in the 2001 outbreak with vaccination of all FMDV-susceptible animals. However, it is unclear whether emergency vaccination of all susceptible species is necessary to control an epidemic or if targeting vaccination to certain species (e.g. only cattle) could be sufficient.

In the current study we developed a method to determine R for mixed populations consisting of cattle and sheep by using experimental transmission data and a technique known as the next-generation matrix (NGM) [20]. The method allows analysis of different vaccination strategies in different mixed populations consisting of cattle and sheep.

METHODS

Data source from experimental studies

Data available from direct contact transmission studies [7, 9–11, 13] (and in Bravo de Rueda et al. unpublished observations) were used. These data were collected from three cattle-to-cattle transmission studies (26 experimental groups), two sheep-to-sheep transmission studies (24 experimental groups) and one sheep-to-cattle transmission study (10 experimental groups). These transmission studies were selected because the raw data on the number of susceptible, infectious, and recovered animals were readily available, and because comparable methods were used in the experiments. The donors in all these studies were inoculated via the intranasal route using either FMDV O/NET/2001 or Asia-1 TUR/11/2000. Five of these six studies also contained data on transmission of FMDV after vaccination, using either FMDV O Manisa or FMDV Asia-1 Shamir as vaccine strains.

Quantification of (partial) R values by using experimental data

The SIR model [21] was used for the quantification of R cattle to cattle (R _c–c), sheep to sheep (R _s–s), and partial R sheep to cattle (partial R _s–c) for non-vaccinated animals and of R ^vac _c–c and R ^vac _s–s for vaccinated animals. The animals from the direct contact transmission studies [7, 9–11, 13] (and in Bravo de Rueda et al., unpublished observations) were classified as susceptible, infectious, or recovered (S-I-R, respectively), at the start (S₀, I₀) and at the end (S_t, R_t) of the experiment. It was assumed that the animals were infectious if they tested positive by virus isolation (on secondary lamb kidney cells) or if they developed infection specific antibodies (detected by NS-ELISA). Contact animals were considered infected if they tested positive for FMDV or FMDV-specific antibodies during the experiment. Animals that were infectious during the experiment were considered as recovered at the end of the experiment (R_t). Data originating from experiments with the same donor species and same contact animal species were pooled for the calculation of the reproduction ratio R.

The recorded data as S₀, I₀, S_t and R_t and the frequencies at which they occurred (see Tables 1 and 2), were used to estimate the reproduction ratio R [22] for non-vaccinated and/or vaccinated groups by using the final size method [23, 24]. The R _c–c, R ^vac _c–c, R _s–s, R ^vac _s–s and partial R _s–c, and their 95% confidence intervals (CI) were calculated from the final sizes using the maximum likelihood estimation and exact confidence bounds [25] in Mathematica^® (http://www.wolfram.com/mathematica/).

Table 1. Final outcome from the transmission experiments with non-vaccinated animals

S₀ and S_t represent the number of susceptible animals at the start and at the end of the experiment; I₀ represents the number of infectious animals at the start of the experiment; and R_t represents the number of recovered animals at the end of the experiment. Frequency represents the number of experimental groups with the same outcome. Dashed lines separate the experimental groups of animals.

Table 2. Final outcome from the transmission experiments with vaccinated animals

S₀ and S_t represent the number of susceptible animals at the start and at the end of the experiment; I₀ represents the number of infectious animals at the start of the experiment; and R_t represents the number of recovered animals at the end of the experiment. Frequency represents the number of experimental groups with the same outcome. Dashed lines separate the experimental groups of animals.

The null hypothesis that no difference existed between the estimates of R _c–c and R _s–s, R _s–s and partial R _s–c, and R _c–c and partial R _s–c was tested by using a two-sided test with a significance level of 0·05 [25].

Estimation of relative infectivities, susceptibilities and the unknown (partial) R values by using the separable mixing assumption

We built a 4 × 4 table using the (partial) R's between non-vaccinated/vaccinated cattle and non-vaccinated/vaccinated sheep. In this 4 × 4 table only five out of the possible 16 values were quantified using the experimental data. By assuming separable mixing, i.e. assuming that the (partial) R's are the product of a relative infectivity f _i [where i is either non-vaccinated cattle (nc), vaccinated cattle (vc), non-vaccinated sheep (ns), or vaccinated sheep (vs)] and a relative susceptibility g _i [where i is either non-vaccinated cattle (nc), vaccinated cattle (vc), non-vaccinated sheep (ns), or vaccinated sheep (vs)], we calculated the missing values in the table. Without loss of generality we chose non-vaccinated cattle to have a susceptibility of 1. Further, we assumed the relative susceptibility of vaccinated animals also to be 1, the same as the relative susceptibility of non-vaccinated animals. This assumption might seem counterintuitive, but local virus replication is often detected in vaccinated animals after challenge [26], indicating that vaccinated animals are still susceptible. In our calculations, the value is only necessary for filling the table. It does not influence the results on the diagonal, which are the only numbers that will be used (as will be explained below) in the calculation of the R values for the different strategies. Note that the reduction in transmission due to vaccination is now assumed to be due to the lower infectivity of the vaccinated and then infected animals (Table 3).

Table 3. (Partial) R values as estimated from infected non-vaccinated (NV) or vaccinated (V) animals to non-vaccinated (NV) or vaccinated (V) contact animals

The values in bold were estimated from experimental data using the final size method. The other R values were based on the product of the relative infectivity (f _i ) and relative susceptibility (g _j ). We assumed that the relative susceptibility of both non-vaccinated and vaccinated cattle and sheep are equal. Without any loss of generality we took non-vaccinated cattle to have susceptibility equal to 1. Note: this table is not yet the NGM as the proportion of the different animal species and the proportion of vaccinated animals are still missing.

Construction of a NGM

A NGM allows the analysis of the effect of different categories of individuals on the overall transmission, i.e. in a mixed population [27]. In our case, R for a mixed population of cattle and sheep depends on the proportion of each animal species in the population. In the matrix p _c is the proportion of cattle (i.e. the total number of cattle divided by the total number of cattle and sheep in a population) and 1 – p _c is the proportion of sheep in the same population. In the matrix the proportion of vaccinated animals per species are indicated by pv_c and pv_s, where pv_c and pv_s represent the proportion of vaccinated cattle and the proportion of vaccinated sheep, respectively. The relative infectivity f _i and relative susceptibility g _i from the above 4 × 4 table were added to the NGM. Thus, the elements of our matrix are functions of the relative infectivity (f _i ), relative susceptibility (g _i ), the proportion of cattle (p _c), and the proportion of vaccinated cattle and that of sheep (pv_c or pv_s).

Evaluation of the influence of different proportions of cattle (p _c) and sheep (1 – p _c)

We studied the influence of different proportions of cattle and sheep on the transmission of FMDV in our NGM. To illustrate this we used five different populations: (1) a population consisting of cattle only, (2) a population with a higher number of cattle than sheep, (3) a population with a relatively similar number of cattle and sheep, (4) a population with a higher number of sheep than cattle, and (5) a population consisting of sheep only. For defining the different mixed populations consisting of cattle and sheep we used proportions of known livestock populations from the FAOSTAT database [28]. In 2011 these p _c values were: 0·78 in The Netherlands (for population 2), 0·61 in Uruguay (for population 3), and 0·24 in New Zealand (for population 4). The proportions of the population of cattle (p _c per population) were included in the NGM. Finally, the dominant eigenvalue of the NGM, i.e. the reproduction ratio for the mixed populations, was determined for all five populations.

Evaluation of the effect of different vaccination strategies

We used the five above-mentioned populations to evaluate the effect of three different vaccination strategies for the control of FMD transmission. These strategies were: (1) vaccinating both species equally, thus pv_c = pv_s, (2) vaccinating all cattle with additional vaccination of sheep (pv_c = 1 and pv_s ≠ 0) and, (3) vaccinating all sheep with additional vaccination of cattle (pv_c ≠ 0 and pv_s = 1). The obtained results were plotted for each strategy. Because R depends on p _c, pv_c and pv_s, we calculated the proportion of animals that has to be vaccinated (or has to be present in a population) at which R reached the value of 1.

RESULTS

Quantification of (partial) R values by using experimental data

In groups where no vaccination was applied, R _c–c was estimated as 5·3 (95% CI 3·0–42) and R _s–s was estimated as 1·1 (95% CI 0·44–2·4). The partial R _s–c was estimated as 0·87 (95% CI 0·20–2·9) (bold values in Table 3). R _c–c was found to be significantly higher than R _s–s (P = 0·002). Moreover, R _c–c was significantly higher than partial R _s–c (P = 0·005). R _s–s was not significantly different from partial R _s–c (P = 0·56) and therefore based on these results the susceptibility of cattle and sheep are considered similar.

In groups where vaccination was applied, the R ^vac _c–c was estimated as 0·13 (95% CI 0·0032–0·83) and R ^vac _s–s was estimated as 0·098 (95% CI 0·0026–0·65). The estimated relative infectivities (f _i ), relative susceptibilities (g _i ), and the (partial) R's are shown in Table 3.

Construction of the NGM

Equation (1) shows the 4 × 4 NGM in which the proportions of cattle and sheep and the proportion of vaccinated animals are included. In our matrix, because of the assumption of separable mixing, the dominant eigenvalue equals the sum of the elements on the diagonal (from top left to bottom right) which is called the trace of the matrix [27]. This dominant eigenvalue is the R for the mixed population described by the NGM [20, 27]. Thus

$$\eqalign{ R\left( {\,p_{\rm c}, p{\rm v}_{\rm c}, p{\rm v}_{\rm s}} \right) &= p_{\rm c} \left( {\left( {1-p{\rm v}_{\rm c}}\right)f_{\rm c} g_{\rm c} + p{\rm v}_{\rm c} f_{\rm vc} g_{\rm vc}} \right) \cr &\quad + \left( {1-p_{\rm c}} \right)\left( {\left( {1-p{\rm v}_{\rm s}} \right)f_{\rm s} g_{\rm s} + p{\rm v}_{\rm s} f_{\rm vs} g_{\rm vs}} \right).} $$

For example, for a population consisting of non-vaccinated cattle only, the dominant eigenvalue of that matrix is R(1, 0, 0) = f _c g _c = R _c–c and, for a population consisting of only vaccinated cattle, the dominant eigenvalue of that matrix is R(1, 1, 0) = f _vc g _vc = R ^vac _c–c.

Equation 1: NGM with non-vaccinated and vaccinated animals. f _c and f _s correspond to the infectivity of cattle and of sheep, respectively. g _c and g _s correspond to the susceptibility of cattle and of sheep, respectively. The proportion of the population of cattle p _c and of sheep 1 – p _c depends on the characteristics of a mixed population. pv_c represents the proportion of vaccinated cattle and pv_s, the proportion of vaccinated sheep:

$$\eqalign{& \left[ {\matrix{ {{\,f_{\rm c}}{g_{\rm c}}{\,p_{\rm c}}(1 - P{{\rm v}_{\rm c}})} & {{\,f_{\rm s}}{g_{\rm c}}{\,p_{\rm c}}(1 - P{{\rm v}_{\rm c}})} \cr {{\,f_{\rm c}}{g_{\rm s}}(1 - {\,p_{\rm c}})(1 - p{v_{\rm s}})} & {{\,f_{\rm s}}{g_{\rm s}}(1 - {\,p_{\rm c}})(1 - p{v_{\rm s}})} \cr {{\,f_{\rm c}}{g_{{\rm vc}}}{\,p_{\rm c}}p{v_{\rm c}}} & {{\,f_{\rm s}}{g_{{\rm vc}}}{\,p_{\rm c}}p{v_{\rm c}}} \cr {{\,f_{\rm c}}{g_{{\rm vs}}}(1 - {\,p_{\rm c}})p{v_{\rm s}}} & {{\,f_{\rm c}}{g_{{\rm vs}}}(1 - {\,p_{\rm c}})p{v_{\rm s}}} \cr } } {\matrix{ {{\,f_{{\rm vc}}}{g_{\rm c}}{\,p_{\rm c}}(1 - p{v_{\rm c}})} & {{\,f_{{\rm vs}}}{g_{\rm c}}{\,p_{\rm c}}(1 - p{v_{\rm c}})} \cr \hskip6pt{{\,f_{vc}}{g_s}(1 - {\,p_c})(1 - p{v_{\rm s}})} & {{\,f_{{\rm vs}}}{g_{\rm s}}(1 - {\,p_{\rm c}})(1 - p{v_{\rm s}})} \cr {{\,f_{{\rm vc}}}{g_{{\rm vc}}}{\,p_{\rm c}}p{v_c}} & {{\,f_{{\rm vs}}}{g_{{\rm vc}}}{\,p_{\rm c}}p{v_{\rm c}}} \cr {{\,f_{{\rm vc}}}{g_{{\rm vs}}}(1 - {\,p_{\rm c}})p{v_{\rm s}}} & {{\,f_{{\rm vs}}}{g_{{\rm vs}}}(1 - {\,p_{\rm c}})p{v_{\rm s}}} } } \right]} $$

Evaluation of the influence of different proportions of cattle (p _c) and sheep (1 – p _c)

In the different non-vaccinated mixed populations, for populations with 0%, 24%, 61%, 78% and 100% cattle, R was estimated to be 1·1, 2·1, 3·7, 4·4 and 5·3, respectively.

Evaluation of the effect of different vaccination strategies

Strategy 1: vaccination of both cattle and sheep

In Figure 1a we show the effect of vaccination when we vaccinate (the same proportion of) both cattle and sheep (so when pv = pv_c = pv_s) for populations consisting of cattle or sheep in different proportions. The R for a fully vaccinated mixed population with 0%, 24%, 61%, 78% and 100% cattle was 0·1, 0·11, 0·12, 0·12 and 0·13, respectively, i.e. always <1.

Fig. 1. The effect of different vaccination strategies on the reduction of R in mixed populations. (a) The effect of vaccination of both cattle and sheep (in equal proportions) on the reduction of R in different mixed populations with cattle and sheep. (b) The effect of vaccination of all cattle and additional vaccination of sheep on the reduction of R in different mixed populations with cattle and sheep. (c) The effect of vaccination of all sheep and additional vaccination of cattle on the reduction of R in different mixed populations with cattle and sheep. p _c represents the proportion of cattle of the mixed population. The threshold value of R = 1 is indicated by a grey line. The percentage of the population of (a) cattle and sheep, (b) sheep, or (c) cattle that needs to be (additionally) vaccinated to reach the threshold value of 1 is indicated.

The percentage of the population that has to be vaccinated to achieve R = 1 is: 14%, 56%, 75%, 79% and 83% for populations with 0%, 24%, 61%, 78% and 100% cattle, respectively.

Strategy 2: vaccination of all cattle with additional vaccination of sheep

When in the populations no sheep, but only all cattle (thus 100% of the cattle) are vaccinated, R was 1·1, 0·90, 0·52, 0·35 and 0·13 for populations with 0%, 24%, 61%, 78% and 100% cattle, respectively (see Fig. 1b ). The percentage of cattle in the population that has to be present to reach R = 1 (when all cattle are vaccinated) was 14%.

Strategy 3: vaccination of all sheep with additional vaccination of cattle

When in the populations no cattle, but only all sheep (thus 100% of the sheep) are vaccinated, R was 0·1, 1·4, 3·3, 4·1 and 5·3 for populations with 0%, 24%, 61%, 78% and 100% cattle, respectively (see Fig. 1c ).

The additional percentage of the cattle population that has to be vaccinated to reach R = 1 was 0%, 29%, 72% and 78% and 83%, respectively, for populations with 0%, 24%, 61%, 78%, and 100% cattle, respectively.

DISCUSSION

In the current study we quantified the transmission of FMDV in mixed cattle-sheep populations and evaluated the effect of different vaccination strategies. The evaluation of different vaccination strategies was based on the transmission estimates from experimental transmission studies. The higher the proportion of cattle in a mixed cattle-sheep population, the higher the R for the mixed population is. Thus, the impact of vaccination of the cattle is higher. When the whole population is vaccinated, R < 1 regardless of the population composition. In mixed cattle-sheep populations with at least 14% of cattle, vaccination of cattle only is sufficient to reduce R to <1. The strategy of vaccinating cattle only for eradication purposes has been used in the past in continental Europe [15] and South America [16, 19] with success. Previous studies using mathematical modelling also predicted that for emergency vaccination, targeting cattle only is much more efficient than using other vaccination strategies [29]. Therefore, this strategy will be more cost-effective in countries with mixed populations of cattle and sheep where prophylactic vaccination is applied [30], as it would mean a reduction in the number of vaccine doses needed and in required manpower. Moreover, when using it as an emergency vaccination strategy, it would also mean a reduction in the time needed to immunize all the animals.

While our conclusions are valid for mixed cattle-sheep populations, different results might be expected for mixed populations where other FMDV-susceptible species are present. For instance, in The Netherlands, where routine annual vaccination of cattle only was used from 1953 to 1991, FMD outbreaks occurred between 1961 and 1967 in mixed cattle and pig farms. At that time, additional vaccination of pig herds was used effectively to control the outbreaks [31]. Additionally, in Asian countries, where the Asian buffalo (Bubalus bubalis) is a host of epidemiological importance [32], a vaccination strategy that includes (additional) vaccination of the Asian buffalo is probably advisable. Thus depending on the different species and percentages of these species in a population, different vaccination strategies might be needed. When quantitative data of transmission of FMDV for other animal species are known, this could be included in the NGM and then similar analyses can be performed for other heterogeneous populations.

In our analysis, we used data from transmission studies in which good quality vaccines, containing >6 PD₅₀ per dose, were used. Experience in South America [33] shows that the strategy of vaccinating cattle only is only effective when good quality vaccines are used. The use of good quality vaccines is of course a prerequisite when using vaccination to control a disease. We used data from within-pen transmission studies in which cattle and/or sheep were mingling in one animal room, thus within-pen transmission occurred. However, in many situations, cattle and sheep within a population will have less intensive contact. Other studies show that transmission between pens is in general lower than within a pen [12, 34] and that between-herd transmission will be even lower [35]. Thus, the effect of targeting vaccination towards cattle will probably be even better under these circumstances than predicted in the current study. In the current study, we used a mathematical approach to calculate which vaccination strategies would be effective. In field situations, other aspects, e.g. vaccine quality, might influence the results. However, even if the quality of the vaccine batch is low, it is probably better to use it in cattle only than spread the available capacity over both species. Although we did use different serotypes in the current study, which produced similar results, there might be a different outcome for other virus strains. Moreover, our approach looks only at the scenario where eradication of FMDV is the goal, there may be an interest to consider scenarios where intermediate situations (FMDV still endemic) have also to be considered, but this has not been studied here.

We developed an NGM that can be used to evaluate the transmission of FMDV for mixed populations of cattle and sheep and we analysed the effect of a targeted vaccination strategy. We conclude that vaccination of cattle only in mixed populations consisting of sheep and cattle will in most cases be sufficient for controlling FMDV epidemics.