Executive Summary Background and objectivesDiabetes mellitus (DM) and hypertension (HTN) are leading causes of cardiovascular disease, death, and disability, with a growing burden in developing countries. Early detection is essential, and machine learning (ML) offers powerful tools for predicting diseases risk by uncovering complex patterns in health data. At the same time, the Health Belief Model (HBM) explains preventive behaviors through constructs such as perceived susceptibility, severity, benefits, barriers, self-efficacy, and cues to action. This study integrates ML-based predictive modeling with the HBM to identify individuals at risk of HTN and DM and to better understand the behavioral factors influencing prevention, employing a dataset collected in 2025. Materials and methodsData on DM and hypertension HTN were collected from 1,771 employees of Debre Markos, Injibara, and Bahir Dar universities in Northwest Ethiopia. The cross-sectional survey included demographic, health-related, and behavioral factors, with constructs from the Health Belief Model (HBM) such as perceived susceptibility, severity, benefits, barriers, self-efficacy, and cues to action. RFE was applied to identify the most relevant predictors of DM and HTN. Four machine learning algorithms—Logistic Regression (LR), Random Forest (RF), Gradient Boosting Decision Tree (GBDT), and k-Nearest Neighbor (kNN) were developed using theselected features. Model performance was evaluated based on accuracy, precision, recall, the F1-score, and the area under the ROC curve. ResultsThis study found that the ensemble ML models, RF and GBDT, outperformed in predicting HTN and DM, achieving higher accuracy, precision, recall, F1-score, and area under the ROC curve. Analysis of Health Belief Model (HBM) constructs further showed that preventive behaviors were positively associated with perceived susceptibility, severity, benefits, self-efficacy, and cues to action, while perceived barriers were negatively associated. Perceived susceptibility emerged as a significant predictor of HTN and DM, and cues to action contributed to the identification of undiagnosed DM cases.

Leptospirosis and melioidosis are emerging tropical diseases that are seriously affecting both human and animal populationsworldwide. The actual incidence and fatal cases of the diseases are underreported due to a lack of awareness of the diseases,underuse of clinical microbiology laboratories test, and limitations of the model. In this paper, a new deterministicmathematical model for the coinfection of leptospirosis and melioidosis with optimal controls is presented. Based on the next-generation matrix approach, the basic reproduction numbers for the coinfection model as well as for submodels are computedto analyze their dynamics behavior. The disease-free equilibrium point of the melioidosis-only submodel is proven to beglobally asymptotically stable when the basic reproduction number (R0m) is less than unity, whereas the existence of its uniquepositive endemic equilibrium is shown if R0m > 1. Based on the center manifold theory, the endemic equilibrium point of theleptospirosis-only submodel is proven to be locally asymptotically stable when the basic reproduction number (R0l ) is greaterthan unity. The disease-free equilibrium point of the full model is locally asymptotically stable whenever the basicreproduction number (R0ml) less than unity. Sensitivity analysis for the basic reproduction number of the model is performedto determine the most influencing parameters on the transmission dynamics of the model. Furthermore, the model wasextended into an optimal control problem by incorporating four time-dependent control functions. Pontryagin’s maximumprinciple was used to derive the optimality system for the optimal control problem. The optimality system was simulated usingthe forward–backward sweep method to show the effectiveness and cost-effectiveness of different optimal control strategies incombating the burden of leptospirosis–melioidosis coinfection. The incremental cost-effectiveness ratio was applied todetermine the most cost-effective strategy. The numerical results revealed that Strategy 6 which implements a combination ofall optimal control measures is the most effective strategy for minimizing the spread of the coinfection of the epidemics,whereas Strategy 1 which implements rodenticide control measure is the most effective when available resources are limited.Keywords: coinfection; cost-effectiveness; leptospirosis; melioidosis; numerical simulation; optimal control; sensitivity analysis

Malaria and leptospirosis are emerging vector-borne diseases that pose significant global healthproblems in tropical and subtropical regions. This study aimed to develop and analyze amathematical model for the transmission dynamics of malaria-leptospirosis co-infection withoptimal control measures. The model’s dynamics are examined through its two sub-models:one for malaria alone and the other for leptospirosis alone. We apply a next-generationmatrix approach to derive the basic reproduction numbers for the sub-models. By using thereproduction number, we demonstrate the local and global asymptotic stability of both disease-free and endemic equilibria in these sub-models. We perform numerical experiments to validatethe theoretical outcomes of the full co-infection model. The graphical results show that malaria-leptospirosis co-infection will be eradicated from the population through time if 𝑅0𝑚𝑙 < 1.Conversely, if 𝑅0𝑚𝑙 > 1, the co-infection will persist in the population. Furthermore, weinvestigate an optimal control model to demonstrate the impact of various time-dependentcontrols in reducing the spread of both diseases and their co-infection. We use the forward–backward sweep iterative method to perform numerical simulations of the optimal controlproblem. Our findings of the optimal control problem imply that strategy 𝐷, which incorporatesall optimal controls, namely malaria prevention 𝜔1(𝑡), leptospirosis prevention 𝜔2(𝑡), insecticidecontrol measure for malaria 𝜔3(𝑡), control sanitation rate of the environment 𝜔4(𝑡) is the mosteffective in minimizing our objective function. We also conduct a cost-effectiveness analysis toidentify the predominant strategy in terms of cost among the optimal strategies.
Keywords: Malaria, Leptospirosis, Co-infection, Global stability, Optimal control, Numerical simulations, Cost-effective strategy

Melioidosis is a significant health problem in tropical and subtropical regions, especially inSoutheast Asia and Northern Australia. Recurrent melioidosis is a major obstacle to eliminatingthe disease from the community in these nations. This work aims to propose and analyzea human melioidosis model with recurrent phenomena and an optimal control model byincorporating time-dependent control functions. The basic reproduction number (𝑅0) of theuncontrolled model is derived using the method of the next-generation matrix. Using theconstruction of a Lyapunov functional, we present the global asymptotic dynamics of theautonomous model in the presence of recurrent for both disease-free and endemic equilibria. Theglobal asymptotic stability of the model’s equilibria shows the absence of a backward bifurcationfor the model in both cases, whether in the absence or presence of relapse. The sensitivityanalysis aims to identify the parameters that have the most significant impact on the model’sdynamics. Furthermore, qualitative analysis of the model’s global dynamics and the changingeffect of the most influential parameters on 𝑅0 are supported by numerical experiments, with theresults being illustrated graphically. The model with time-dependent controls is analyzed usingoptimal control theory to assess the impact of various intervention strategies on the spread ofthe epidemic. The numerical results of the optimality system are carried out using the Forward–Backward Sweep method in Matlab. We also conducted a cost-effectiveness analysis using twoapproaches: the average cost-effectiveness ratio and the incremental cost-effectiveness ratio.
Keywords: Melioidosis model; B.pseudomallei; Recurrent; Global stability; Optimal control; Cost-effective strategy