Nonlinear modelling and simulation of climate-sensitive malaria transmission with imported infections and real data

This study develops a climate-sensitive neural-mechanistic modelling framework for modelling weekly malaria transmission in Tak Province, Thailand. A new human-mosquito compartmental model is formulated by extending a vaccination and infected-immigration malaria system to include rainfall- and temperature-dependent transmission rates, climate-sensitive mosquito recruitment and mortality, imported infections, normalized host-vector infection terms, and cumulative incidence for comparison with reported cases. The mathematical properties of the proposed model are analysed by proving positivity of solutions and well-posedness in a biologically feasible region. The model is then applied to 2025 weekly malaria surveillance data and NASA POWER climate data for Tak Province. The calibrated mechanistic model reproduced the timing of the main seasonal peak, with both observed and predicted cases peaking in week 24, and achieved a full-year NRMSE of 0.1572. Several artificial neural network models were then evaluated, including climate-only, climate plus lagged-cases, and ODE-ANN residual-correction models. The climate plus lagged-cases ANN achieved the best direct validation performance, with validation NRMSE =0.2852. To retain biological interpretability, an ANN was also embedded inside the ODE system as a bounded multiplicative correction to the human infection transmission rate β_H(t). The validation-aware embedded model selected by lowest validation error reduced validation NRMSE from 0.5504 to 0.5442, with correction factors remaining close to one; averaged over twenty random initializations, however, validation NRMSE was 0.5515, indicating that the embedded correction did not consistently improve held-out performance. Because the analysis rests on a single year of 52 weekly observations, this work is presented as an exploratory, proof-of-concept study rather than a validated forecasting system: the reported metrics characterise in-sample calibration and held-out behaviour within one transmission season, and are not intended as estimates of operational forecast skill. Within this scope, the results show that mechanistic epidemiological modelling can be combined with neural-network-based computing while preserving biological interpretability under limited real-world surveillance data.