Internal phosphorus recycling in lakes is an important nutrient source that promotes algal growth. Its persistence impedes the effort to improve water quality and thus poses a challenge to the management of eutrophication in lakes, especially in shallow lakes where the occurrence of internal phosphorus recycling is reportedly more common. This paper aims to provide crucial insights on the effects of internal phosphorus recycling on eutrophication dynamics for effective management of lake eutrophication. For this purpose, a mathematical model for lake eutrophication, comprising two compartments of algae and phosphorus, is first formulated for application to a eutrophic tropical lake named Tasik Harapan in Universiti Sains Malaysia. Numerical bifurcation analysis of the model is then performed to assess the combined influences of internal phosphorus recycling, algal mortality and external phosphorus loading on Tasik Harapan eutrophication dynamics. Specifically, co-dimension one bifurcation analysis of algal mortality rate is carried out by means of XPPAUT for various external phosphorus loading rates. The emergence of limit cycle for a certain range of algal mortality rate could be related to the hydra effect (i.e., algal concentration increases in response to greater algal mortality) and the paradox of enrichment (i.e., destabilization of algae in nutrient rich environment). To trace the locus of co-dimension one bifurcation, co-dimension two bifurcation analysis is performed by means of MatCont. The analysis demonstrated that the inclusion of the internal phosphorus recycling term induces rich and complex dynamics of the model. These dynamics include saddle-node bifurcation, cusp, Bogdanov-Takens bifurcation, Generalized Hopf bifurcation and limit point bifurcation of cycles. The results suggest that high internal phosphorus recycling rate promotes bistability and catastrophic shift in a shallow and tropical lake like Tasik Harapan. Hence, the key to effective management of eutrophication in shallow and tropical lakes is the control of internal phosphorus recycling.
Despite the implementation of various initiatives, dengue remains a significant public health concern in Malaysia. Given that dengue has no specific treatment, dengue prediction remains a useful early warning mechanism for timely and effective deployment of public health preventative measures. This study aims to develop a comprehensive approach for forecasting dengue cases in Selangor, Malaysia by incorporating climate variables. An ensemble of Multiple Linear Regression (MLR) model, Long Short-Term Memory (LSTM), and Susceptible-Infected mosquito vectors, Susceptible-Infected-Recovered human hosts (SI-SIR) model were used to establish a relation between climate variables (temperature, humidity, precipitation) and mosquito biting rate. Dengue incidence subject to climate variability can then be projected by SI-SIR model using the forecasted mosquito biting rate. The proposed approach outperformed three alternative approaches and expanded the temporal horizon of dengue prediction for Selangor with the ability to forecast approximately 60 weeks ahead with a Mean Absolute Percentage Error (MAPE) of 13.97 for the chosen prediction window before the implementation of the Movement Control Order (MCO) in Malaysia. Extended validation across subsequent periods also indicates relatively satisfactory forecasting performance (with MAPE ranging from 13.12 to 17.09). This research contributed to the field by introducing a novel framework for the prediction of dengue cases over an extended temporal range.