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<p>Nipah virus (NiV) is a highly lethal zoonotic pathogen causing severe respiratory distress and encephalitis, with case fatality rates exceeding 70% in South Asia. The absence of approved therapies for Nipah virus&#xa0;(NiV) and its persistently high mortality across South and Southeast Asia make rigorous mathematical modelling an essential tool for outbreak preparedness. This study introduces a six-compartment <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {S}\mathcal {E}\mathcal {I}_{R}\mathcal {I}_{E}\mathcal {H}\mathcal {R}\)</EquationSource> </InlineEquation> epidemic model under the Atangana-Baleanu-Caputo&#xa0;(<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {ABC}\)</EquationSource> </InlineEquation>) fractional derivative with a non-singular Mittag–Leffler kernel, explicitly separating the infectious stage into respiratory distress&#xa0;(<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal {I}_{R}\)</EquationSource> </InlineEquation>) and encephalitis&#xa0;(<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal {I}_{E}\)</EquationSource> </InlineEquation>) compartments with distinct hospitalization pathways and waning immunity, a clinically motivated structure absent from prior NiV models. The Natural Transform Method derives iterative series solutions, and existence, uniqueness of the solutions is rigorously established via Lipschitz conditions and the Banach fixed-point theorem. The basic reproduction number <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\textsf{R}_{0} = 1.4428\)</EquationSource> </InlineEquation>, computed by the next-generation matrix method, confirms active epidemic spread. Local and global asymptotic stability at both equilibria are proved using Lyapunov functions and the Routh-Hurwitz criterion, and Ulam-Hyers stability is verified to ensure numerical robustness. PRCC sensitivity analysis identifies the transmission rate&#xa0;<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\beta\)</EquationSource> </InlineEquation> as the dominant driver of epidemic risk. Numerical simulations via an Adams-type predictor-corrector (PC) algorithm show that stronger memory effects (lower <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation>) delay outbreak peaks and prolong the outbreak duration relative to the classical ODE model. For the first time in NiV fractional modelling, solutions are cross-validated against Physics-Informed Neural Networks&#xa0;(PINNs), achieving <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(R^{2}&gt;0.99\)</EquationSource> </InlineEquation> across all six compartments. The results provide actionable strategies: prioritizing isolation of respiratory distress cases and implementing long-term, memory aware public health measures. The model serves as a validated tool for optimizing Nipah virus elimination strategies, particularly in resource-limited settings, while highlighting directions for future refinement.</p>

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Mathematical modeling of Nipah virus transmission dynamics using Atangana-Baleanu Caputo fractional derivatives and physics-informed neural networks

  • 期刊论文

  • 发表日期：

    2026年7月9日

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  • Nivetha Rathinasamy,
  • Arul Joseph Gnanaprakasam

摘要

Nipah virus (NiV) is a highly lethal zoonotic pathogen causing severe respiratory distress and encephalitis, with case fatality rates exceeding 70% in South Asia. The absence of approved therapies for Nipah virus (NiV) and its persistently high mortality across South and Southeast Asia make rigorous mathematical modelling an essential tool for outbreak preparedness. This study introduces a six-compartment \(\mathcal {S}\mathcal {E}\mathcal {I}_{R}\mathcal {I}_{E}\mathcal {H}\mathcal {R}\) epidemic model under the Atangana-Baleanu-Caputo ( \(\mathcal {ABC}\) ) fractional derivative with a non-singular Mittag–Leffler kernel, explicitly separating the infectious stage into respiratory distress ( \(\mathcal {I}_{R}\) ) and encephalitis ( \(\mathcal {I}_{E}\) ) compartments with distinct hospitalization pathways and waning immunity, a clinically motivated structure absent from prior NiV models. The Natural Transform Method derives iterative series solutions, and existence, uniqueness of the solutions is rigorously established via Lipschitz conditions and the Banach fixed-point theorem. The basic reproduction number \(\textsf{R}_{0} = 1.4428\) , computed by the next-generation matrix method, confirms active epidemic spread. Local and global asymptotic stability at both equilibria are proved using Lyapunov functions and the Routh-Hurwitz criterion, and Ulam-Hyers stability is verified to ensure numerical robustness. PRCC sensitivity analysis identifies the transmission rate  \(\beta\) as the dominant driver of epidemic risk. Numerical simulations via an Adams-type predictor-corrector (PC) algorithm show that stronger memory effects (lower \(\alpha\) ) delay outbreak peaks and prolong the outbreak duration relative to the classical ODE model. For the first time in NiV fractional modelling, solutions are cross-validated against Physics-Informed Neural Networks (PINNs), achieving \(R^{2}>0.99\) across all six compartments. The results provide actionable strategies: prioritizing isolation of respiratory distress cases and implementing long-term, memory aware public health measures. The model serves as a validated tool for optimizing Nipah virus elimination strategies, particularly in resource-limited settings, while highlighting directions for future refinement.