Relapse and delay-induced dynamics in human-to-human Nipah virus transmission: a mathematical modeling study

Abstract Nipah virus (NiV) exhibits complex transmission dynamics shaped by infection-to-transmission delays, relapse, and delayed-onset neurological complications following recovery. The epidemiological consequences of these temporal processes, particularly how they jointly shape NiV dynamics, remain poorly characterized. We develop a delay differential equation model for human-to-human NiV transmission incorporating an effective population-level infection-to-transmission delay, immediate relapse, and delayed encephalitis relapse. We derive the transmission threshold ℛ h and establish a unique feasible endemic equilibrium when ℛ h > 1. The disease-free equilibrium is unstable whenever ℛ h > 1, with a forward transcritical bifurcation at ℛ h = 1. Delays can destabilize the endemic equilibrium, inducing sustained oscillations through Hopf bifurcation under hypothetical regimes. Calibration to Bangladesh incidence data (2001-2024) yielded ℛ h ≈ 0.83 (95% bootstrap CI 0.74-1.03), with profile-likelihood regions spanning 0.67-0.95 and 96% of replicates subcritical. Relapse rates were not practically identifiable from annual incidence data; as the gradient of ℛ h is nearly orthogonal to the weak parameter direction, subcriticality is unaffected and relapse contributions are interpreted as effective replenishment. The model generated recurrent incidence through relapse and delay feedback; projected resurgence applies only within the proposed framework. Sensitivity analyses show an oblique ℛ h = 1 contour within the model: a 30% increase in immediate relapse lowers the required transmission increase from 21% to 10%. Immediate relapse most strongly shapes post-peak burden, while the infection-to-transmission delay controls epidemic timing and magnitude. Delays and relapse-mediated feedback can generate transient waves even when ℛ h < 1, underscoring the importance of monitoring recovered individuals.