Table 1 Description of various Structural Equation Models (SEM) used in this study.

From: Estimation of foot-and-mouth disease virus sero-prevalence rates using novel computational approach for the susceptible bovine population in India during the period 2008–2021

Sl. no.

Name

Models

Co-variates

1

Model 1

\({p}_{t}={\alpha }_{0}+{\alpha }_{1}{O}_{t}+{\varepsilon }_{t}\)

Current outbreak

2

Model 2

\({p}_{t}={\alpha }_{0}+{\alpha }_{1}{O}_{t}+{{\alpha }_{2}{O}_{t-1}+\varepsilon }_{t}\)

Current outbreak, outbreak (1 year lag)

3

Model 3

\({p}_{t}={\alpha }_{0}+{\alpha }_{1}{O}_{t}+{{\alpha }_{2}{O}_{t-1}+{\alpha }_{3}{O}_{t-2}+\varepsilon }_{t}\)

Current outbreak, outbreak (1 and 2 year lags)

4

Model 4

\({p}_{t}={\alpha }_{0}+{\alpha }_{1}{O}_{t}+{{\alpha }_{2}{O}_{t-1}+{\beta }_{1}{p}_{t-1}+\varepsilon }_{t}\)

Current outbreak, outbreak (1 year lag), previous positive rate

5

Model 5

\({p}_{t}={\alpha }_{0}+{\alpha }_{1}{O}_{t}+{{\alpha }_{2}{O}_{t-1}+{\alpha }_{3}{O}_{t-2}+{\beta }_{1}{p}_{t-1}++\varepsilon }_{t}\)

Current outbreak, outbreak (1 year lag), DIVA positive rate (1 year lag)

6

Model 6

\({p}_{t}={\alpha }_{0}+{\alpha }_{1}{O}_{t}+{{\alpha }_{2}{O}_{t-1}+{\beta }_{1}{p}_{t-1}+{\beta }_{2}{p}_{t-2}+\varepsilon }_{t}\)

Current outbreak, outbreak (1 year lag), DIVA positive rate (1 year lag), DIVA positive rate (2 year lags)

7

Model 7

\({p}_{t}={\alpha }_{0}+{\alpha }_{1}{O}_{t}+{{\alpha }_{2}{O}_{t-1}+{\alpha }_{3}{O}_{t-2}+{\beta }_{1}{p}_{t-1}+{\beta }_{2}{p}_{t-2}+\varepsilon }_{t}\)

Current outbreak, outbreak (1 year lag), outbreak (2 year lags), DIVA positive rate (1 year lag), DIVA positive rate (2 year lags)

8

Model 8

\({p}_{t}={\alpha }_{0}+{\alpha }_{1}{O}_{t}+{{\alpha }_{2}{O}_{t-1}+{\alpha }_{3}{O}_{t-2}+{\beta }_{1}{p}_{t-1}+{\beta }_{2}{p}_{t-2}+{NADCP}_{t}+I({sample}_{t}+{pop}_{t})+\varepsilon }_{t}\)

Current outbreak, outbreak (1 year lag), outbreak (2 year lags), DIVA positive rate (1 year lag), DIVA positive rate (2 year lags), NADCP program. Sample and population size

  1. Model 1–8: Structural Equation Models; \({p}_{t}, {p}_{t-1}, {p}_{t-2}\): Estimated DIVA positive rates for tth, (t-1)th, and (t-2)th year respectively; \({O}_{t}, {O}_{t-1}, {O}_{t-2}\): Field FMDV outbreaks at tth , (t-1)th, and (t-2)th year respectively; \({\alpha }_{0}:\) intercept term; \({\alpha }_{i} \; {\text{and}} \; {\beta }_{i}\): co-efficient terms; \(\varepsilon_{t}:\) error.
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