Abstract:
Epidemiological surveillance data collected during the early stage of an outbreak are rarely free of doubt: case counts are revised, contact-tracing records are incomplete, and a share of reports remain formally unclassified, a pattern documented explicitly during the 2014–2016 West Africa Ebola outbreak, when the World Health Organization stopped consistently reporting probable and suspected case counts because of high reclassification rates. Fuzzy and intuitionistic fuzzy differential equations model vagueness in such parameters but cannot separately track how much of the uncertainty is indeterminate rather than simply "false." This paper develops a Susceptible–Infected–Recovered (SIR) epidemic model in which the transmission rate and the recovery rate are represented as single-valued triangular neutrosophic numbers, so that truth, indeterminacy, and falsity in the parameter estimates are carried independently through the dynamics. We recall the algebra of triangular neutrosophic numbers and their (α,β,γ)-cuts, define the model through the generalized Hukuhara neutrosophic derivative, prove existence and uniqueness for the resulting family of classical systems, and prove in closed form that the epidemic peak and the final attack rate are monotonic in the transmission and recovery rates, which is what rigorously justifies reading the computed cut families as genuine bounds. A corner-point (α, β, γ)-cut solution procedure is proposed and solved with an adaptive Runge–Kutta scheme on parameters grounded in published country-level reproduction-number estimates from the West Africa Ebola outbreak. Truth-, indeterminacy-, and falsity-cut families are all computed numerically, showing how the epidemic peak, its timing, the final attack rate, and the effective reproduction number widen or narrow independently along each of the three membership dimensions, and that the indeterminacy- and falsity-cut bounds diverge from one another even at matched confidence levels a distinction no fuzzy or intuitionistic fuzzy model can represent. The results indicate that the neutrosophic formulation keeps the full three-way structure of the uncertainty in the surveillance data while remaining computationally no more demanding than a comparable fuzzy model, and that it collapses to the classical deterministic SIR model at the maximal-confidence limit of every cut, giving a consistent basis for comparison with existing crisp and fuzzy epidemic models.
Keywords:
neutrosophic differential equations; neutrosophic numbers; (α,β,γ)-cut; generalized Hukuhara derivative; SIR epidemic model; epistemic uncertainty.,
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