Communication in Biomathematical Sciences

Mathematical Modeling of Antimalarial Drug Resistance in Sub-Saharan Africa: Transmission Trajectories and Mitigation Strategies

Romain Glèlè Kakaï

Antimalarial drug resistance continues to threaten malaria control in Sub-Saharan Africa. While mathematical models of malaria transmission are well established, few have simultaneously accounted for asymptomatic reservoirs, treatment failure, and vector control within a drug-resistance framework and applied it comparatively across multiple high-burden countries. We developed a deterministic compartmental model that explicitly integrates asymptomatic and symptomatic infections, treatment pathways, treatment failure, and vector control to examine drug-resistant malaria transmission dynamics in Ghana, Burkina Faso, and Uganda from 2000 to 2023. Positivity, boundedness, and stability of the malaria-free equilibrium were established analytically. The basic reproduction number (R0) and control reproduction number (Rc) were derived using the next-generation matrix approach, and sensitivity analysis identified the main drivers of transmission, focusing on treatment failure. Model parameters were estimated using nonlinear least squares. Results revealed substantial
heterogeneity in transmission intensity across the three countries: Ghana and Burkina Faso exhibited lower transmission potential, while Uganda remained above the epidemic threshold throughout the study period. Treatment failure and asymptomatic infectivity emerged as the strongest drivers of sustained transmission. These findings highlight the need for context-specific intervention strategies that improve treatment effectiveness, target asymptomatic reservoirs, and strengthen vector control measures to reduce drug-resistant malaria transmission across the region.

A A Compartmental Model for Tuberculosis Transmission Dynamics with Control Measures

MORGAN WALICHO

Tuberculosis is a global endemic that claims millions of lives every year. Therefore,there is need for continuous research in order to understand its dynamics for effective prevention and control as recommended by WHO. The study developed a six compartmental $SVLATR$ mathematical model that incorporated TB transmission dynamics with control measures to assess their impact on TB spread . The threshold quantity called basic reproduction number $R_0$ ,that determines whether the disease persists and spreads or gets eliminated was computed using the Next Generation Matrix ($NGM$) and found to be $ R_0 \approx 1.73 > 1$ indicating persistence of the endemic. The model was used to predict future trends in TB and projected a decline in TB incidence,prevalence and mortality for the next 5 years but insufficient to fully eliminate TB. The stability properties of the system were analyzed using Jacobian matrix and eigenvalue analysis. The condition for stability of the Disease Free Equilibrium ($DFE$) is stable if $R_0 < 1$ . Since $R_0 > 1$ it was found to be unstable while Endemic Equilibrium ($EE$) is locally asymptotically stable since $R_0 >1$ . Bifurcation analysis indicated that the system is at the endemic state and measures to lower reproduction number below unity are needed to eliminate TB. The simulated results using the real world epidemiological data indicates persistence of TB under the current intervention measures. This modeling approach provides policymakers and public health stakeholders with evidence based recommendations for improving TB control.

Ensemble Learning to Predict Hospital Stay Duration from Diagnostic and Drug Consumption Information

Syarif Hidayatullah

Predicting the length of patient hospitalisation is an important challenge in hospital operational management, particularly under package-based financing schemes such as Indonesia's INA-CBGs, where reimbursement does not increase with the duration of stay. This study developed a stacking ensemble model to predict length of stay (LOS) using demographic, diagnosis, and medication data from a tertiary referral hospital in Aceh, Indonesia, comprising 43,128 inpatient visits from 29,410 patients. Five base learners (LightGBM, XGBoost, CatBoost, Random Forest, and AdaBoost) were tuned using Bayesian optimisation and combined through an XGBoost meta-model trained on out-of-fold predictions. To minimise data leakage, patient-level GroupKFold cross-validation was applied throughout the modelling process, and feature filtering was performed exclusively within the training partition of each fold. The stacked ensemble achieved an average R² of 0.853, with an RMSE of 2.180 and a MedAE of 0.852. This performance was comparable to that of the best individual model, XGBoost (R² = 0.855), but with a substantially smaller train-test gap (0.005 versus 0.077–0.082 for the individual gradient boosting models), indicating superior generalisation rather than higher predictive accuracy alone. An exhaustive ablation study across all 26 possible base-model combinations demonstrated that performance remained stable when at least three base learners were retained. A reduced ensemble consisting of LightGBM, XGBoost, and CatBoost matched the performance of the full five-model ensemble while reducing training time by 56%. Feature-importance-based selection further reduced the input space from 1,093 drug features to 175 without compromising predictive performance. A temporal holdout evaluation, in which the model was trained on visits before a fixed cut-off date and evaluated on subsequent admissions, confirmed stable performance with an R² of 0.85. SHAP analysis indicated that no single feature dominated the predictions; instead, patient age, principal diagnosis, and the doses of several medications jointly contributed to LOS estimates. Model performance was assessed using RMSE, MedAE, and R², complemented by bootstrap confidence intervals and residual diagnostics. These findings suggest that the proposed stacked ensemble provides a practical and interpretable approach for LOS prediction in resource-constrained hospital settings. Its primary advantage lies in improved robustness and generalisation to unseen patients rather than substantial gains in predictive accuracy over a well-tuned single model.

Ensemble Learning to Predict Hospital Stay Duration from Diagnostic and Drug Consumption Information

Syarif Hidayatullah