MAP is difficult to eradicate from a herd, because the pathogen persists in the environment for a long time. Upon infection with MAP, cattle undergo an asymptomatic period which can last for years. As the disease advances, an infected cow eventually becomes overtly symptomatic with decreased milk production, persistent diarrhea, and despite having no changes in appetite, the affected animal will exhibit progressive wasting and death if not culled. The very slow progression of JD and the difficulty in identifying infected animals due to imperfect diagnostic tests contribute to the difficulty in conducting MAP control measure studies. Accurate and detailed data from testing animals throughout their lifespan and at slaughter are often not available. As a result, researchers have relied on mathematical and statistical models to study transmission dynamics of MAP. Infectious disease modeling and simulation can also be used to determine the effects of control policies and to identify the risk factors contributing to disease spread. Although between-pen cattle movement is an important factor in the spread of infectious diseases, vertical grow racks it has been largely ignored in the modeling and analysis of various infectious diseases of farmed ruminants.
Many studies include a diffusion term to capture the cattle movement, however, these models assume random movement of cattle throughout the farm rather than the purposeful movement of cattle between pens for management reasons. In addition, recent studies have used network data to study the dynamic of cattle trade movements. However, most of network models only investigate the mobility patterns of individual animals among farms and ignore between-pen cattle movements within each farm. Without considering between- pen cattle movements it would be difficult to provide meaningful inferences pertaining to within and between-pen disease transmission dynamics. The objective of this study was to create a nested compartmental model for MAP transmission which accounts for progression of the disease and also the movement of cattle between pens on a dairy. Using the numerical simulations of the model we identified the most optimal intervention combinations yielding the greatest reduction of JD incidence and prevalence on a dairy.Cattle movements between pens can modify the contact rates between MAP in the environment, susceptible and infected cattle.
The changes in cattle population and contact patterns are more complicated than concept of random mixing assumed in most infectious disease models. In practice, the continuous management-based changes in pen populations on a dairy can strongly influence MAP transmission dynamics and the effects of MAP control measures. Thus, an NC model for MAP transmission on a dairy farm was constructed by considering the states of MAP infection in dairy cattle as well as the frequency and patterns of cattle movements between pens on a dairy. The Cattle Movement model is a compartmental model formulated with a set of Ordinary Differential Equations and acts as the shell or outer layer of the NC model. The CM model represents different pens on a dairy and within each pen type, a compartmental MAP transmission model is embedded according to the age of cattle in the respective pen.The CM model encompasses the different production stages common to large dairy herds which represented 47% of US dairies in 2007. The CM model was constructed by dividing the dairy into pen types that closely represent cattle housing on a dairy. The pens include the calf nursery, growing and breeding pens, post-calving , high and low milk production, and non-milking cow pens for a total of 14 pen types. Table 1 lists the pen types, descriptions and the expected residence times per given animal. Fig 1 is a flowchart of the CM model depicting the dynamics of moving dairy cattle between pens on a dairy.
Although several dairy farms may have different pen structures, the illustrated flowchart is widely accepted among researchers and practitioners. Moreover, the flowchart represents the pen types, and there can be multiple pens of each type. Calves born to nulliparous females also known as springers in pen 5, are transported to the pre-weaned calf hutches, collectively identified here, pen 1. Also, calves born to parous females in pen 14, which are either uniparous or multiparous , are transported to pen 1. Once calves are weaned they are moved to pen 2, post-weaned group pens. On a dairy that raises female heifers for breeding, heifer calves are moved to pen 3 at breeding age and to pen 4 when pregnant. As the pregnant heifer approach calving they are moved to the springers pen, where they calve; or, depending on the dairy’s management, may be moved to an individual or group maternity pen. Because it is common for springers to calve in the closeup pens, the CM model was designed as such. The recently calved females, now first lactation dams, are then moved to pen 6 after calving. Pen 6 houses only recently calved first lactation cows separated from multiparous cows. This is a common management practice since older cows tend to be more dominant and may limit the younger smaller uniparous females’ access to feed. Furthermore, depending on the dairy’s management, pen 6 may also serve as a hospital pen to facilitate segregation of colostrum and milk produced in the first few days post-calving since both are not saleable for human consumption and hence are not milked into the bulk tank on the dairy. Pen 8 houses high producing cows. When milk production begins to decline, first lactation cows are moved to the low-production pen 9. Later in lactation and as milking cows approach calving, they will undergo dry-off, an industry term referring to the voluntary cessation of milking approximately 60 days prior to calving, a period necessary to replenish a cow’s body reserves and initiation of colostrum production in preparation for the new born calf. Dry-off cows are moved to pen 12 until before calving when they are then moved to the close-up pen and fed a different ration. Cows that start calving are moved to the calving pen 14 and once calved they are moved to pen 7, the fresh/hospital pen.Data from four California dairies was accessed retrospectively through their dairy herd improvement software . Records from varying intervals of time between January 2011, to June 2015 were used to estimate rates of moving cows between pens. Dairy 1 contributed pen movement data from two different time periods demarcated by the dairy herd’s transition from an all Holstein to a mixed breed essentially acting as two dairies and hence bringing the total to five herds. Herd managers and veterinarians were interviewed to identify the pen types and pen population demographics including age, production and reproductive status. Although 14 pen types were identified, cattle of the same age, production, or reproductive state were housed in one or more physical pens. Hence cow movement rates were estimated for pen type and not for each pen. Pen population records from the study dairies were examined by programming a Matlab code. The code employs the optimization toolbox to estimate the time intervals and calculate each cow’s unique residence time in a pen. To account for the possibility that a cow may have been moved into a pen before the record extraction date, 5 days were added to the beginning and end of each cow’s unique record date, respectively. Subsequently, indoor grow lights shelves the rates of moving cows between pens were estimated as the inverse of the pen residence times for each dairy farm.Specifically, the Susceptible animals in pen i can be exposed to the infection by direct host-to-host contact, or indirectly by contacting the contaminated pen environment or the general environment . The host-to-host contact occurs when susceptible individuals come into contact with infectious individuals including super-shedders.
The exposed animals in pen i are infected, but yet to be infectious, hence are latent and denoted by Li. As infection progresses the latently infected cattle in pen i become infectious and eventually may become super-shedders . Fig 2depicts the MAP transmission model in preweaned calves in pen 1 of the CM model, which distinguishes between three classes: Susceptible , Latent , Environment here onwards referred to as the SLE model and the corresponding system of ODEs is given in S3 Appendix. Intrauterine transmission from infected dams to their calves while rare, occurs even when a dam is subclinical. This process has been considered in SLE model , where a is the proportion of the newborn calves that are born latently infected and 1-a is the remaining susceptible proportion. Although calves are presumably more susceptible to MAP infection compared to adult cattle, it is very difficult to identify infected calves due to the disease’s prolonged latent period. Furthermore, studies suggest that MAP infected pre-weaned calves do not commonly shed the bacterium and the disease in this age group may not necessarily include an infectious state. Hence, the SLE model assumes that the number of shedding calves is either negligible or the amount of shedding does not sustainably influence the transmission dynamics of JD . Furthermore, animals may show no clinical symptoms of disease for years after infection and diagnostic tests are not sensitive enough to identify infected animals in this latent stage. Therefore, susceptible preweaned calves may progress to the latent stage but may not contaminate the pen environment = 0 for all t = 0. For SLIE and SLICE models, the main assumption is that a susceptible host can become infected after direct contact with contaminated environment, an infectious host or a supershedder. Infected cattle shed the MAP bacilli into their feces and hence the pen environment, which contaminates the general environment; that infection also spreads due to the cattle moving dynamics, further exposing susceptible cattle on the dairy farm. The primary transmission route for the disease is fecal-oral. Free-living MAP can survive more than a year in the environment . In addition, MAP has been found in milk and colostrum, semen, blood and saliva. The SLIE model is considered in pens i = 1, . . ., 6 with the assumption that calves and heifer MAP transmission do not include the super-shedding stage of MAP infection due to their younger age . The SLICE model is considered in pens i = 7, . . ., 14, which includes supper-shedders. See S3 Appendix for the set of ODEs corresponding to the SLIE model.The progression of MAP infection at various stages of infection was incorporated within each pen of the CM model. Calf population in pen 1 is divided into susceptible and latent individuals, with disease dynamics based on the SLE model. In Fig 1, the rates m1 and b1 represent the mean culling/all-cause mortality rate, and purchase/birth rate, respectively. A proportion a1 of newborn calves are born latently infected and the rest are susceptible. The coefficient β1G represents the transmission rate due to exposure to MAP in the general environment including due to recycled lagoon water from the entire dairy and used to flush below the calf hutches, and 1/r is the duration of pathogen survival. Use of fresh water to flush is recommended, however recycled lagoon water collected from the parlor and flush from adult pens is sometimes used exposing calves to MAP from the remaining herd.The control measures are the strategies to control or reduce the occurrence of MAP as reflected by the basic reproduction number of the NC model. In the NC model, R0 has 63 parameters. To understand how R0 is affected by these parameters, we completed a global uncertainty analysis. A total of 27 combined or individual control strategies were designed and each was simulated 50,000 times to examine their effects on prevalence and incidence of MAP infection and R0 value on a dairy farm of 10,000 susceptible cows with a super shedder and an infectious cow introduced to the farm. Specifically, using the range of parameter values in using the parameter values in Table 3, Tables B and C , the numerical simulations of the NC model were carried out to estimate R0 values and MAP incidence and prevalence. The simulation randomly picked numbers within the given ranges for each parameter used to calculate R0. For each case of control strategy, 50,000 calculations of R0 values, minimum, maximum, mean, 95% confidence intervals , and risk of MAP occurrence were calculated. The risk was calculated as the fraction of the simulation iterations, where R0 was greater than 1. Table 3 includes the range parameter values used in the model simulations. In addition to S2 Appendix, details of parameter estimations are provided in the rest of this section.