The Mindanawan Journal of Mathematics

Analysis and Simulation of Organism Survival: A Toxicokinetic-Toxicodynamic Model for Substance Exposure

2025-01-01T08:56:57+08:00

This study develops a mathematical model to analyze the effects of chemical exposure on organism population dynamics. Using a set of TK-TD differential equations, the model examines the interactions between chemical concentration, damage, and population survival. Numerical simulations validate the theoretical results and explore the system’s behavior under different scenarios. The findings provide insights into the long-term impacts of chemical stress on population resilience and demonstrate the utility of mathematical models for environmental risk assessment.

Generalized Estimating Equations in longitudinal data analysis in the presence of missing data

2025-01-02T22:17:10+08:00

Generalized Estimating Equations (GEE) are a statistical approach used to estimate the parameters of Generalized Linear Models (GLMs) in the presence of potential correlations among observations, particularly across different time points. GEE adjusts for within-cluster correlations, enabling more accurate and efficient parameter estimation when fitting regression models. Correctly specifying the correlation structure in a statistical model enhances the efficiency of parameter estimates. However, the challenge of missing data, which is common in many studies, can significantly impact the reliability of inferences drawn from GEE-based models. This paper explores recently developed selection criteria for identifying the underlying correlation structure, focusing on longitudinal studies with varying degrees of missingness ($\Delta m \in {5\%, 10\%, 15\%}$). The criteria under investigation include: (a) Rotnitzky and Jewell Criterion (RJ), (b) Gaussian Pseudolikelihood Criterion (GP), (c) Quasi-likelihood under Independence Model Criterion (QIC), (d) Correlation Information Criterion (CIC), (e) Pardo and Alonso Criterion (PAC), and (f) Gaussian Bayesian Information Criterion (GBIC). The study examines performance across varying cluster sizes, highlighting the importance of accounting for different degrees of correlation in both complete and incomplete datasets. Across all scenarios with positive results, the findings reveal that GBIC demonstrates robust and consistent performance, even in the presence of missing observations.

Bayesian Quantile Regression with Adaptive MCMC

2025-04-21T13:50:17+08:00

Quantile regression offers a powerful means of characterizing how covariate effects vary across the entire outcome distribution, but standard implementations can suffer from curve crossings or computational burdens. This study proposes an approach that builds conditional quantile curves sequentially—starting from the median and expanding outward—with constrained priors to enforce non-crossing by construction. Posterior inference is carried out via an adaptive Metropolis algorithm, eliminating the need for closed-form full conditionals and improving mixing as the posterior concentrates. Here we report a subset of results—single-predictor simulations under normal, right-skewed Gamma, and heteroscedastic errors across varying sample sizes. Results showed that proposed approach consistently attains lower bias and RMSE than both frequentist fits and Gibbs quantile regression, and achieves superior convergence efficiency. An empirical application to the 2023 Philippine FIES—modeling log educational spending on log household income—demonstrates the proposed approach's ability to produce coherent, non-crossing quantile estimates that uncover increasing income elasticities across spending levels. These results highlight its practical utility for distributional analysis where monotonicity and computational efficiency are essential.

Mathematical Model of Dengue and Leptospirosis Coinfection with Dual Transmission Pathways

2025-08-20T06:41:09+08:00

Dengue and leptospirosis are major public health concerns in tropical countries, where environmental conditions favor the spread of both vector-borne and waterborne pathogens. This paper presents a compartmental mathematical model that captures the coinfection dynamics of dengue and leptospirosis, accounting for their indirect transmission routes and potential interactions. The model incorporates both mosquito vectors for dengue and a contaminated water compartment for leptospirosis, allowing for dual transmission pathways through which each disease spreads. The disease-free equilibrium is established, and the basic reproduction number $\mathcal{R}_0$ is derived using the next-generation matrix approach. Model analysis shows that the disease-free equilibrium is locally asymptotically stable when $\mathcal{R}_0 < 1$, and unstable otherwise. Numerical simulations reveal that if the basic reproduction number is greater than one, the infection persists in the population. Sensitivity analysis highlights that transmission rates significantly increase infection risk, while recovery and decay parameters contribute to disease mitigation. These findings emphasize the importance of integrated control strategies targeting both vector and water environments. Future studies may extend this model by incorporating optimal control interventions, seasonal climate effects, or vaccination strategies to better understand and manage coinfection dynamics.

Theta_beta-Open Sets and theta_beta-Continuous Functions in the Product Space

2025-08-20T05:29:57+08:00

In this paper, we introduced and characterized a new class of open set called theta_beta-open set. Notably, the collection of all theta_beta-open sets forms a topology. We then examined the relationship between theta_beta-open sets and other well-known concepts, such as classical open sets, theta-open sets, and beta-open sets. Additionally, we defined and investigated the concepts of theta_beta-interior and theta_beta-closure of a set, as well as theta_beta-open functions, theta_beta-closed functions, theta_beta-continuous functions, and theta_beta-connectedness. Finally, we present characterizations of theta_beta-continuous functions from an arbitrary topological space into the product space, along with some versions of separation axioms.

Bayesian Modeling of Zero-Inflated Count Time Series Using Adaptive MCMC on Dengue Incidence of Iligan and Tandag City, Philippines

2025-04-21T13:56:31+08:00

This study presents a Bayesian approach to modeling dengue incidence in Iligan and Tandag cities in the Philippines using integer-valued time series models. Recognizing the challenges posed by overdispersion, serial dependence, and excess zeros in dengue count data, we compare five probabilistic models: Generalized Poisson (GP), Log-Generalized Poisson (Log-GP), Negative Binomial (NB), Zero-Inflated Generalized Poisson (ZIGP), and Zero-Inflated Negative Binomial (ZINB) INGARCHX models. These models incorporate rainfall and temperature as lagged exogenous covariates. Parameter estimation is carried out using Adaptive Markov Chain Monte Carlo (MCMC) methods, and model performance is assessed via the Deviance Information Criterion (DIC) and residual diagnostics. Results reveal that the ZINB-INGARCHX model is best suited for the zero-inflated Tandag dataset, while the ZIGP-INGARCHX model provides the best fit for the overdispersed Iligan data. Findings highlight the importance of flexible count models and lagged environmental drivers in accurately capturing the dynamics of dengue transmission.