Estimation of the basic reproduction number for Streptococcus equi spp. equi outbreaks by meta-analysis of strangles outbreak reports.

BACKGROUND: Streptococcus equi spp. equi (S. equi), the cause of strangles in horses, is considered a highly contagious pathogen affecting equines and the equine industry worldwide. Fundamental epidemiological characteristics of outbreaks, such as the basic reproduction number (R0 ), are not well described. OBJECTIVES: Estimate R0 for S. equi in equine populations from outbreak data. STUDY DESIGN: Systematic review and meta-analysis of published and unpublished data. METHODS: A literature search for outbreak reports was carried out. Depending on data available in the reports, the early epidemic growth rate or final attack rate (AR) approach was used to estimate the basic reproduction number for that outbreak. Other recorded outbreak characteristics were the type of housing (group vs. individual). An overall estimate for R0 was computed by meta-analysis. RESULTS: Data from eight outbreaks were extracted from peer-reviewed publications. Data from two additional, non-published outbreaks was also included in the meta-analysis. A conservative estimate for R0 was 2.2 (95% confidence interval [CI] 1.9-2.5). A less conservative estimate, including outbreaks with a 100% AR for which a lower limit R0 was estimated, was 2.7 (95% CI 2.1-3.3). MAIN LIMITATIONS: Few papers describing longitudinal incidence data were found so most estimates were based on the outbreaks' final size. Several outbreaks had a 100% attack rate and could therefore only be included as a lower limit estimate in the meta-analysis. The reported result therefore may be an underestimation. CONCLUSIONS: This estimate for R0 for S. equi informs parameters for future mathematical modelling, quantifies desired preventive vaccine coverage and helps evaluate the effect of prevention strategies through future modelling studies.

Data-driven dynamical modelling of the transmission of African swine fever in a few places in China.

Since the outbreak of African swine fever (ASF) in Shengyang, it has continued spreading in China. In the early stage of the epidemic, multi-point and concentrated outbreaks were mainly in the swill feeding areas. In this paper, we developed compartmental models to investigate the transmission of ASF in several raising units including Guquan, Jinba and Liancheng. Using the data collected from these three infected premises, we calibrated the models to estimate that the average incubation period was between 8 and 11 days, the onset period was about 2-3 days and the basic reproductive number was about 4.83-11.90. We also estimated the infection on the day before culling to be 45.24% (Guquan), 89.20% (Jinba) and 16.35% (Liancheng), respectively. The infection rate of Guquan could reach about 74.8% if culling were postponed by 2 days. We found that the infection was significantly higher than the morbidities (22.11% (Guquan), 49.35% (Jinba) and 12.94% (Liancheng)) calculated by actual statistical data. Besides, we simulated and compared the control effect of stopping transport, disinfecting, stopping swill and culling. Our findings suggest that any single measure was not enough to prevent the spread of ASF on a regional level but the combined measures is the key. Under the current situation, fully culling was recognized as most effective in controlling the epidemic, despite the culling of uninfected pigs.

An Embedded Multiscale Modelling to Guide Control and Elimination of Paratuberculosis in Ruminants.

In recent years, multiscale modelling approach has begun to receive an overwhelming appreciation as an appropriate technique to characterize the complexity of infectious disease systems. In this study, we develop an embedded multiscale model of paratuberculosis in ruminants at host level that integrates the within-host scale and the between-host. A key feature of embedded multiscale models developed at host level of organization of an infectious disease system is that the within-host scale and the between-host scale influence each other in a reciprocal (i.e., both) way through superinfection, that is, through repeated infection before the host recovers from the initial infectious episode. This key feature is demonstrated in this study through a multiscale model of paratuberculosis in ruminants. The results of this study, through numerical analysis of the multiscale model, show that superinfection influences the dynamics of paratuberculosis only at the start of the infection, while the MAP bacteria replication continuously influences paratuberculosis dynamics throughout the infection until the host recovers from the initial infectious episode. This is largely because the replication of MAP bacteria at the within-host scale sustains the dynamics of paratuberculosis at this scale domain. We further use the embedded multiscale model developed in this study to evaluate the comparative effectiveness of paratuberculosis health interventions that influence the disease dynamics at different scales from efficacy data.

Basic reproduction number of African swine fever in wild boars (Sus scrofa) and its spatiotemporal heterogeneity in South Korea.

BACKGROUND: African swine fever (ASF) is a hemorrhagic fever occurring in wild boars (Sus scrofa) and domestic pigs. The epidemic situation of ASF in South Korean wild boars has increased the risk of ASF in domestic pig farms. Although basic reproduction number (R0) can be applied for control policies, it is challenging to estimate the R0 for ASF in wild boars due to surveillance bias, lack of wild boar population data, and the effect of ASF-positive wild boar carcass on disease dynamics. OBJECTIVES: This study was undertaken to estimate the R0 of ASF in wild boars in South Korea, and subsequently analyze the spatiotemporal heterogeneity. METHODS: We detected the local transmission clusters using the spatiotemporal clustering algorithm, which was modified to incorporate the effect of ASF-positive wild boar carcass. With the assumption of exponential growth, R0 was estimated for each cluster. The temporal change of the estimates and its association with the habitat suitability of wild boar were analyzed. RESULTS: Totally, 22 local transmission clusters were detected, showing seasonal patterns occurring in winter and spring. Mean value of R0 of each cluster was 1.54. The estimates showed a temporal increasing trend and positive association with habitat suitability of wild boar. CONCLUSIONS: The disease dynamics among wild boars seems to have worsened over time. Thus, in areas with a high elevation and suitable for wild boars, practical methods need to be contrived to ratify the control policies for wild boars.

Modeling the transmission dynamics of foot and mouth disease in Amhara region, Ethiopia.

Foot and mouth disease (FMD) is contagious, acute viral disease of all cloven-hoofed animals. The disease is endemic in Ethiopia and causes multiple outbreak every year all over the country. While it is important to understand to the transmission dynamics of FMD outbreaks for appropriate control intervention, no such study has been done in Ethiopia. Thus, the aims of this study were to estimate the basic reproduction number (R0) of FMD and simulate FMD transmission dynamics of FMD in Amhara region of Ethiopia. Basic reproduction number (R0) was estimated from age stratified sero-prevalence data through maximum likelihood estimation. A stochastic SIR (susceptible-infectious-recovered) compartmental FMD model was formulated and parameterized using literature and age stratified sero-prevalence field data. The R0 of FMD in the region was estimated to be 1.27 (95%CI: 1.20-1.34). The simulation of the SIR model showed only 24% (95% CI: 16-32%) of the infection introduced in the region caused major outbreaks. Out of the major outbreaks 25% of them tend to persist in the region. Major outbreaks cause 38.9% (95% CI: 38.8-39.1%) morbidity and 0.0019% (95% CI: 0.0018-0.0020%) mortality in cattle and the outbreaks stayed for an average of 690 days (95%CI: 655-727). Validation of the model prediction with farmer's field experience indicated a fairly similar result especially for the predicted morbidity caused by outbreaks. This study revealed low transmission of FMD within the Amhara region cattle population indicating not very high vaccination coverage is needed, if control through vaccination is envisaged at regional level. However, owing to several simplified assumptions made during the modeling, this conclusion should be taken cautiously.

Using the basic reproduction number to assess the risk of transmission of lumpy skin disease virus by biting insects.

In recent years, lumpy skin disease virus (LSDV) has emerged as a major threat to cattle outside Africa, where it is endemic. Although evidence suggests that LSDV is transmitted by the bites of blood sucking arthropods, few studies have assessed the risk of transmission posed by particular vector species. Here this risk is assessed by calculating the basic reproduction number (R0 ) for transmission of LSDV by five species of biting insect: the stable fly, Stomoxys calcitrans, the biting midge, Culicoides nubeculosus, and three mosquito species, Aedes aegypti, Anopheles stephensi, and Culex quinquefasciatus. Parameters relating to mechanical transmission of LSDV were estimated using new analyses of previously published data from transmission experiments, while vector life history parameters were derived from the published literature. Uncertainty and sensitivity analyses were used to compute R0 for each species and to identify those parameters which influence its magnitude. Results suggest that S. calcitrans is likely to be the most efficient at transmitting LSDV, with Ae. aegypti also an efficient vector. By contrast, C. nubeculosus, An. stephensi, and Cx. quinquefasciatus are likely to be inefficient vectors of LSDV. However, there is considerable uncertainty associated with the estimates of R0 , reflecting uncertainty in most of the constituent parameters. Sensitivity analysis suggests that future experimental work should focus on estimating the probability of transmission from insect to bovine and on the virus inactivation rate in insects.

How much does direct transmission between pigs contribute to Japanese Encephalitis virus circulation? A modelling approach in Cambodia.

Japanese Encephalitis (JE) is the most important cause of human encephalitis throughout Asia and the Pacific. Although JE is a vector-borne disease, it has been demonstrated experimentally that transmission between pigs can occur through direct contact. Whether pig-to-pig transmission plays a role in the natural epidemiological cycle of JE remains unknown. To assess whether direct transmission between pigs may occur under field conditions, we built two mathematical models of JE transmission incorporating vector-borne transmission alone or a combination of vector-borne and direct transmission. We used Markov Chain Monte Carlo (MCMC) techniques to estimate the parameters of the models. We fitted the models to (i) two serological datasets collected longitudinally from two pig cohorts (C1 and C2) during two periods of four months on a farm on the outskirts of Phnom-Penh, Cambodia and to (ii) a cross-sectional (CS) serological survey dataset collected from 505 swine coming from eight different provinces of Cambodia. In both cases, the model incorporating both vector-borne and direct transmission better explained the data. We computed the value of the basic reproduction number R0 (2.93 for C1, 2.66 for C2 and 2.27 for CS), as well as the vector-borne reproduction number Rpv and the direct transmission reproduction number Rpp. We then determined the contribution of direct transmission on R0 (11.90% for C1, 11.62% for C2 and 7.51% for CS). According to our results, the existence of pig-to-pig transmission is consistent with our swine serological data. Thus, direct transmission may contribute to the epidemiological cycle of JE in Cambodia. These results need to be confirmed in other eco-climatic settings, in particular in temperate areas where pig-to-pig transmission may facilitate the persistence of JE virus (JEV) during cold seasons when there are no or few mosquitoes.

Estimating the between-farm transmission rates for highly pathogenic avian influenza subtype H5N1 epidemics in Bangladesh between 2007 and 2013.

Highly Pathogenic Avian Influenza (HPAI) is classified by the World Organization for Animal Health as one of the notifiable diseases. Its occurrence is associated with severe socio-economic impacts and is also zoonotic. Bangladesh HPAI epidemic data for the period between 2007 and 2013 were obtained and split into epidemic waves based on the time lag between outbreaks. By assuming the number of newly infected farms to be binomially distributed, we fit a Generalized Linear Model to the data to estimate between-farm transmission rates (ß). These parameters are then used together with the calculated infectious periods to estimate the respective basic reproduction numbers (R0 ). The change in ß and R0 with time during the course of each epidemic wave was explored. Finally, sensitivity analyses of the effects of reducing the delay in detecting infection on a farm as well as extended infectiousness of a farm beyond the day of culling were assessed. The point estimates obtained for ß ranged from 0.08 (95% CI: 0.06-0.10) to 0.11 (95% CI: 0.08-0.20) per infectious farm per day while R0 ranged from 0.85 (95% CI: 0.77-1.02) to 0.96 (95% CI: 0.72-1.20). Sensitivity analyses reveal that the estimates are quite robust to changes in the assumptions about the day in reporting infection and extended infectiousness. In the analysis allowing for time-varying transmission parameters, the rising and declining phases observed in the epidemic data were synchronized with the moments when R0 was greater and less than one, respectively. From an epidemiological perspective, the consistency of these estimates and their magnitude (R0  ≈ 1) indicate that the effectiveness of the deployed control measures was largely invariant between epidemic waves and the trend of the time-varying R0 supports the hypothesis of sustained farm-to-farm transmission that is possibly initiated by a few unique introductions.

Estimating the Basic Reproductive Number for African Swine Fever Using the Ukrainian Historical Epidemic of 1977.

In 1977, Ukraine experienced a local epidemic of African swine fever (ASF) in the Odessa region. A total of 20 settlements were affected during the course of the epidemic, including both large farms and backyard households. Thanks to timely interventions, the virus circulation was successfully eradicated within 6 months, leading to no additional outbreaks. Detailed report of the outbreak's investigation has been publically available from 2014. The report contains some quantitative data that allow studying the ASF-spread dynamics in the course of the epidemic. In our study, we used this historical epidemic to estimate the basic reproductive number of the ASF virus both within and between farms. The basic reproductive number (R0 ) represents the average number of secondary infections caused by one infectious unit during its infectious period in a susceptible population. Calculations were made under assumption of an exponential initial growth by fitting the approximating curve to the initial segments of the epidemic curves. The R0 both within farm and between farms was estimated at 7.46 (95% confidence interval: 5.68-9.21) and 1.65 (1.42-1.88), respectively. Corresponding daily transmission rates were estimated at 1.07 (0.81-1.32) and 0.09 (0.07-0.10). These estimations based on historical data are consistent with those using data generated by the recent epidemic currently affecting eastern Europe. Such results contribute to the published knowledge on the ASF transmission dynamics under natural conditions and could be used to model and predict the spread of ASF in affected and non-affected regions and to evaluate the effectiveness of different control measures.

Experimental pig-to-pig transmission dynamics for African swine fever virus, Georgia 2007/1 strain.

African swine fever virus (ASFV) continues to cause outbreaks in domestic pigs and wild boar in Eastern European countries. To gain insights into its transmission dynamics, we estimated the pig-to-pig basic reproduction number (R 0) for the Georgia 2007/1 ASFV strain using a stochastic susceptible-exposed-infectious-recovered (SEIR) model with parameters estimated from transmission experiments. Models showed that R 0 is 2·8 [95% confidence interval (CI) 1·3-4·8] within a pen and 1·4 (95% CI 0·6-2·4) between pens. The results furthermore suggest that ASFV genome detection in oronasal samples is an effective diagnostic tool for early detection of infection. This study provides quantitative information on transmission parameters for ASFV in domestic pigs, which are required to more effectively assess the potential impact of strategies for the control of between-farm epidemic spread in European countries.

Empirical Estimation of R0 for Unknown Transmission Functions: The Case of Chronic Wasting Disease in Alberta.

We consider the problem of estimating the basic reproduction number R0 from data on prevalence dynamics at the beginning of a disease outbreak. We derive discrete and continuous time models, some coefficients of which are to be fitted from data. We show that prevalence of the disease is sufficient to determine R0. We apply this method to chronic wasting disease spread in Alberta determining a range of possible R0 and their sensitivity to the probability of deer annual survival.

Transmission dynamics and control for a brucellosis model in Hinggan League of Inner Mongolia, China.

Brucellosis is one of the major infectious and contagious bacterial diseases in Hinggan League of Inner Mongolia, China. The number of newly infected human brucellosis data in this area has increased dramatically in the last 10 years. In this study, in order to explore effective control and prevention measures we propose a deterministic model to investigate the transmission dynamics of brucellosis in Hinggan League. The model describes the spread of brucellosis among sheep and from sheep to humans. The model simulations agree with newly infected human brucellosis data from 2001 to 2011, and the trend of newly infected human brucellosis cases is given. We estimate that the control reproduction number Rc is about 1.9789 for the brucellosis transmission in Hinggan League and compare the effect of existing mixed cross infection between basic ewes and other sheep or not for newly infected human brucellosis cases. Our study demonstrates that combination of prohibiting mixed feeding between basic ewes and other sheep, vaccination, detection and elimination are useful strategies in controlling human brucellosis in Hinggan League.

The evolutionary consequences of alternative types of imperfect vaccines.

The emergence and spread of mutant pathogens that evade the effects of prophylactic interventions, including vaccines, threatens our ability to control infectious diseases globally. Imperfect vaccines (e.g. those used against influenza), while not providing life-long immunity, confer protection by reducing a range of pathogen life-history characteristics; conversely, mutant pathogens can gain an advantage by restoring the same range of traits in vaccinated hosts. Using an SEIR model motivated by equine influenza, we investigate the evolutionary consequences of alternative types of imperfect vaccination, by comparing the spread rate of three types of mutant pathogens, in response to three types of vaccines. All mutant types spread faster in response to a transmission-blocking vaccine, relative to vaccines that reduce the proportion of exposed vaccinated individuals becoming infectious, and to vaccines that reduce the length of the infectious period; this difference increases with increasing vaccine efficacy. We interpret our results using the first published Price equation formulation for an SEIR model, and find that our main result is explained by the effects of vaccines on the equilibrium host distribution across epidemiological classes. In particular, the proportion of vaccinated infectious individuals among all exposed and infectious hosts, which is relatively higher in the transmission-blocking vaccine scenario, is important in explaining the faster spread of mutant strains in response to that vaccine. Our work illustrates the connection between epidemiological and evolutionary dynamics, and the need to incorporate both in order to explain and interpret findings of complicated infectious disease dynamics.

The network level reproduction number for infectious diseases with both vertical and horizontal transmission.

A wide range of infectious diseases are both vertically and horizontally transmitted. Such diseases are spatially transmitted via multiple species in heterogeneous environments, typically described by complex meta-population models. The reproduction number, R0, is a critical metric predicting whether the disease can invade the meta-population system. This paper presents the reproduction number for a generic disease vertically and horizontally transmitted among multiple species in heterogeneous networks, where nodes are locations, and links reflect outgoing or incoming movement flows. The metapopulation model for vertically and horizontally transmitted diseases is gradually formulated from two species, two-node network models. We derived an explicit expression of R0, which is the spectral radius of a matrix reduced in size with respect to the original next generation matrix. The reproduction number is shown to be a function of vertical and horizontal transmission parameters, and the lower bound is the reproduction number for horizontal transmission. As an application, the reproduction number and its bounds for the Rift Valley fever zoonosis, where livestock, mosquitoes, and humans are the involved species are derived. By computing the reproduction number for different scenarios through numerical simulations, we found the reproduction number is affected by livestock movement rates only when parameters are heterogeneous across nodes. To summarize, our study contributes the reproduction number for vertically and horizontally transmitted diseases in heterogeneous networks. This explicit expression is easily adaptable to specific infectious diseases, affording insights into disease evolution.

Modeling the spatial spread of Rift Valley fever in Egypt.

Rift Valley fever (RVF) is a severe viral zoonosis in Africa and the Middle East that harms both human health and livestock production. It is believed that RVF in Egypt has been repeatedly introduced by the importation of infected animals from Sudan. In this paper, we propose a three-patch model for the process by which animals enter Egypt from Sudan, are moved up the Nile, and then consumed at population centers. The basic reproduction number for each patch is introduced and then the threshold dynamics of the model are established. We simulate an interesting scenario showing a possible explanation of the observed phenomenon of the geographic spread of RVF in Egypt.

Epidemic characterization and modeling within herd transmission dynamics of an "emerging trans-boundary" camel disease epidemic in Ethiopia.

A highly acute and contagious camel disease, an epidemic wave of unknown etiology, referred to here as camel sudden death syndrome, has plagued camel population in countries in the Horn of Africa. To better understand its epidemic patterns and transmission dynamics, we used epidemiologic parameters and differential equation deterministic modeling (SEIR/D-model) to predict the outcome likelihood following an exposure of susceptible camel population. Our results showed 45.7, 17.6, and 38.6 % overall morbidity, mortality, and case fatality rates of the epidemic, respectively. Pregnant camels had the highest mortality and case fatality rates, followed by breeding males, and lactating females, implying serious socioeconomic consequences. Disease dynamics appeared to be linked to livestock trade route and animal movements. The epidemic exhibited a strong basic reproductive number (R (0)) with an average of 16 camels infected by one infectious case during the entire infectious period. The epidemic curve suggested that the critical moment of the disease development is approximately between 30 and 40 days, where both infected/exposed and infectious camels are at their highest numbers. The lag between infected/infectious curves indicates a time-shift of approximately 3-5 days from when a camel is infected and until it becomes infectious. According to this predictive model, of all animals exposed to the infection, 66.8 % (n = 868) and 33.2 % (n = 431) had recovered and died, respectively, at the end of epidemic period. Hence, if early measures are not taken, such an epidemic could cause a much more devastative effect, within short period of time than the anticipated proportion.

Estimating spatial and temporal variations of the reproduction number for highly pathogenic avian influenza H5N1 epidemic in Thailand.

Since 2003, highly pathogenic avian influenza (HPAI) H5N1 virus has spread, causing a pandemic with serious economic consequences and public health implications. Quantitative estimates of the spread of HPAI H5N1 are needed to adapt control measures. This study aimed to estimate the variations of the reproduction number R in space and time for the HPAI H5N1 epidemic in Thailand. Transmission between sub-districts was analyzed using three different and complementary methods. Transmission of HPAI H5N1 was intense (R(t)>1) before October 2004, at which point the epidemic started to progressively fade out (R(t)<1). The spread was mainly local, with 75% of the putative distances of transmission less than 32km. The map of the mean standardized ratio of transmitting the infection (sr) showed sub-districts with a high risk of transmitting infection. Findings from this study can contribute to discussions regarding the efficacy of control measures and help target surveillance programs.

Foot and mouth disease virus transmission during the incubation period of the disease in piglets, lambs, calves, and dairy cows.

Transmission of foot and mouth disease (FMD) virus by infected animals may already occur before clinical signs are evident. Quantitative data for FMD transmission rates during this so-called high-risk period are currently lacking and would provide useful information to develop surveillance systems in which the number of new outbreaks is an outcome variable. In order to address this, we used experimental data to quantify transmission in cattle, swine and sheep during the non-clinical phase of the disease. Groups consisted of vaccinated or non-vaccinated animals of one species; half of each group was inoculated with FMDV, the other half was contact-exposed. We estimated the reproduction ratio R(nonclin) using a mathematical SIR model. R(nonclin) was defined as the average number of secondary infections caused by one infectious individual in its non-clinical phase. Animals not showing clinical signs shed lower amounts of virus than clinically affected ones. Therefore, we estimated transmission proportionally to the virus excretion. Low estimates for R(nonclin) in groups with non-vaccinated and vaccinated calves; 0.30 [0.03; 3.43] and 1.03x10(-8) [0; infinity] respectively and 0.21 [0.02; 2.48] for the non-vaccinated and 0.16 [0.009; 2.96] for the vaccinated lambs, were observed. These results indicate that only few secondary infections are to be expected from infected calves and lambs when they are not clinically affected. In groups of non-vaccinated piglets estimates were R(nonclin)=13.20 [4.08; 42.68], and in vaccinated piglets R(nonclin)=1.26 [0.18; 8.96]. The estimate for R(nonclin) for non-vaccinated dairy cows was R(nonclin)=176.65 [80.38; 388.24], whereas R(nonclin) in the vaccinated groups could not be estimated. Our findings suggest that a large number of individuals might have been infected before clinical signs are noticed, especially in non-vaccinated swine and dairy herds. These findings suggest that after clinical recognition of FMD, priority should be given to trace back contacts with swine and dairy farms, as they may already have been infectious in the herd's incubation period.