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

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 in existing models. 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 human-to-human transmission threshold \(R_h\) and establish a unique biologically feasible endemic equilibrium when \(R_h > 1\). Local stability of the disease-free equilibrium is governed by the full linearized delay system; the disease-free equilibrium is unstable whenever \(R_h > 1\), and the model exhibits a forward transcritical bifurcation at \(R_h = 1\). Delays can destabilize the endemic equilibrium and induce sustained oscillations through Hopf bifurcation under hypothetical parameter regimes. Calibration to Bangladesh NiV incidence data (2001-2024) yields $R_h\approx0.81$, though uncertainty admits values on both sides of unity, and projections through 2030 suggest later resurgence driven by relapse and delay mechanisms. A relapse contribution fraction shows that relapse increasingly contributes to infectious-compartment replenishment as the recovered population accumulates. Sensitivity analyses identify transmission and immediate relapse as dominant determinants of \(R_h\): a 30\% increase in immediate relapse rate lowers the transmission-rate increase required to cross \(R_h = 1\) from 24\% to 15\%. 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 therefore generate transient waves even when \(R_h < 1\), underscoring the importance of monitoring recovered individuals.