Table 1.
Brief description of model variables.
Table 2.
Parameters used in the simulations.
Figure 1.
A) Ratios used to describe the JD iceberg phenomenon. Infections underneath are not detectable while those that are above are visible. However, the extent of the depth of disease beneath is difficult to predict. B) Conceptual framework illustrating interactions between cattle and the environment, and the flow of cattle between the susceptible, exposed (silent), subclinical, and clinical compartments. Solid black lines represent the movement of cattle between classes. Dashed magenta, red, and black lines represent interactions between the subclinical, clinical, and the environment with susceptible cattle, respectively . Dotted black arrows represent MAP bacteria shedding by subclinical and clinical infected cattle, while red solid lines denote cattle deaths and clearance of environmental contamination.
Figure 2.
A), An illustration of MAP transmission in a farm when incubation, , for the silent stage is varied from 4 months to 12 months in steps of 2 months. Qualitatively similar simulations are achieved with different combinations of parameters as long as
. At any given time
. B) Comparative analysis of cattle population at different disease stages in different time regions (see Table 3 for ratios in different regions). Simulations were carried out using parameters given in Table 2 with
(cattle natural death rate).
Figure 3.
Percentages and ratios of animals in each sub-class.
A) Frequency (or percentage) compositions of cattle within the exposed, subclinical, and clinical classes over the course of the disease. B) Simulated exposed, subclinical and clinical cattle ratios over the course of the disease. Ratios in each category were calculated relative to cattle in the exposed class. Parameters used are given in Table 2.
Table 3.
Approximate ratios for animal populations in different stages of JD under different time regions.
Figure 4.
Simulations demonstrating the iceberg phenomenon when or
for a cattle life span of 20 years. Whenever the above inequality fails, the Iceberg phenomenon is not observable. In A,
was varied between 0.02 and 0.05 in steps of 0.01. Simulations were generated using the parameters
,
,
,
, and the rest as given in Table 2.
Figure 5.
Fitted and predicted prevalence.
Fitted prevalence assuming A) cattle life span of five years (farm setting), and B) cattle life span of 20 years (average cattle natural life span). C) and D) Predict disease prevalence over 50 years in the absence of control programs for cattle life spans of 5 and 20 years, respectively.
Figure 6.
Predicted JD dynamics with estimated parameters
. Predicted disease dynamics using parameters estimated through fitting model to prevalence with A) cattle life span of 5 years, and B) cattle life span of 20 years.
Table 4.
Parameters estimated by fitting the ODE model to prevalence data.
Table 5.
Approximate ratios for animal populations in different stages of JD under different time regions (Figure 6 A).
Figure 7.
What the model predicts and suggests the iceberg phenomenon should be like in JD.
Simulation results presented in Figures 2, 3, and 6, and Tables 3 and 5 demonstrate that there are always fewer cattle in the silent stage compared to the subclinical and clinical stages. We do not dispute that there are potentially more undiagnosed cases but suggests that the majority of these cases should be subclinical cases instead of cases in the silent stage.
Figure 8.
Sensitivity analysis of model output variables predicated that disease transmission dynamics when duration (,
,
), transmission (
,
,
) and environmental control (
) parameters are varied within ranges given in Table 5. The output variability shows high likelihood of environmental contamination whenever cattle are shedding MAP. Variation of
to
and
to
ratios are shown to be consistent with observations in Tables 3 and 5, and Figures 3 and 6.
Table 6.
Sensitivity ranks of parameters used in the model in relation to predicated model outputs.
Table 7.
Model parameter partial rank correlation coefficients (PRCCs) that cause significant model output variability.
Figure 9.
A) Varying the time delay before exposed cattle (in the silent stage) move into the subclinical stage does not cause any significant change to the dynamics of the disease. B: Varying the delay
associated with time spent in the subclinical stage contributes to variable disease transmission dynamics and different levels of environmental contamination. With
varied from 2 years to 10 years in steps of 2 years.