Mathematical modeling of climate-driven ToLCNDV transmission in cucurbits with dynamic farmer adoption

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\begin{abstract}\textbf{Background:} Tomato leaf curl New Delhi virus (ToLCNDV) is an emerging threat to global cucurbit production, with transmission strongly influenced by climatic conditions and farmer management decisions. However, existing mathematical models rarely integrate environmental forcing, vector--host epidemiology, and adaptive farmer behavior within a unified framework. This study develops a coupled climate--epidemiological--socio-economic model to investigate how these interacting mechanisms shape ToLCNDV transmission and control. \textbf{Main findings:} The epidemiological component employs an SEIR structure for cucurbit plants and an SI structure for the whitefly vector. Temperature and relative humidity are incorporated explicitly through nonlinear response functions governing vector recruitment, transmission efficiency, mortality, and disease progression. Farmer adaptation is represented by an evolutionary game-theoretic replicator equation, with adoption of climate-smart practices enhancing rogueing and vector-control rates. We derive a climate- and behavior-dependent basic reproduction number, $\mathcal{R}_0(T_0, H_0, x_a^*)$, and establish positivity, boundedness, and well-posedness of the model. A Lyapunov analysis proves global asymptotic stability of the disease-free equilibrium for $\mathcal{R}_0 < 1$, while bifurcation analysis demonstrates a forward transcritical bifurcation at $\mathcal{R}_0 = 1$ and excludes backward bifurcation. PRCC analysis identifies farmer adoption as the strongest negative driver of $\mathcal{R}_0$. Seasonal simulations reveal climate-driven epidemic waves and a dynamic feedback whereby disease pressure increases farmer adoption, subsequently reducing epidemic peaks. \textbf{Conclusions:} The results demonstrate that climate-smart interventions can generate reinforcing socio-epidemiological feedbacks that enhance disease suppression. Policies that reduce the economic barriers to adoption may therefore promote sustained, community-driven control of ToLCNDV under climatic variability.\end{abstract}