arXiv subjects

Mahmudul Bari Hridoy

Publications and source records attributed to Mahmudul Bari Hridoy.

4 recordsLinked to original sources

arXiv2026

A stochastic dose-response framework for environmentally persistent pathogens

Infectious diseases caused by environmentally persistent pathogens can strongly affect host populations as transmission occurs not only through direct host-host contact but also via indirect exposure to contaminated environments. While in some systems environmental reservoirs help sustain exposure even when infected host numbers are low, reliance on environmental transmission pathway may also increase pathogen extinction risk. Infection risk may depend on both pathogen dose and timing of exposure. Thus, understanding how dose-response, stochasticity, and seasonal changes in host susceptibility or contact rates shape pathogen invasion and persistence remains an important challenge for environmentally transmitted disease systems. To address this, we develop a stochastic dose-response framework that integrates host infection dynamics with an explicit environmental pathogen reservoir. Transmission occurs through both direct contact with infectious hosts and indirect environmental exposure, with infection probability governed by dose-response functions. We focus on stochastic continuous-time Markov chain formulation and use branching process approximation to estimate disease extinction probabilities when infected hosts or environmental pathogen loads are low. We extend the framework to include seasonality in host susceptibility, environmental contact, and host-host contact. As a case study, we apply the model to snake fungal disease. Numerical simulations show that dose-response influences epidemic takeoff and infection levels, while seasonality creates windows of high and low extinction risk. These extinction risks depend strongly on the route and timing of introduction within the seasonal cycle. These results, coupled with global sensitivity analysis, illustrate how stochasticity, nonlinear dose-response, and seasonal timing shape outbreak dynamics for environmentally persistent pathogens.

q-bio.PE↗

arXiv2026

Dynamical Survival Analysis for Modeling Hazard Functions with Nonlinear Systems

Hazard functions play a central role in survival analysis, providing insight into the underlying risk dynamics of time-to-event data, with broad applications in medicine, epidemiology, and related fields. First-order ordinary differential equation (ODE) formulations of the hazard function have been explored as extensions beyond classical parametric models. However, such approaches typically produce monotonic hazard patterns, limiting their ability to represent oscillatory behavior, nonlinear damping, or coupled growth-decay dynamics. We propose a general statistical framework for modeling and simulating hazard functions governed by higher-order ODEs, allowing the hazard to depend on both its current level, its rate of change, and time. This formulation accommodates complex temporal risk behaviors arising in a range of applications. Building on this framework, we develop a class of nonlinear and oscillatory hazard models, each associated with an interpretable dynamical mechanism and an induced survival distribution. We also present a simulation procedure for solving a system of non-linear higher-order ODEs, with failure times generated via cumulative hazard inversion. Likelihood-based Bayesian inference under right censoring is also developed, and moment generating function analysis is used to characterize tail behavior. The proposed framework is evaluated through simulation studies and illustrated using real data, demonstrating its ability to capture temporal risk patterns not well represented by standard monotone models. In contrast to existing linear ODE-based hazard models, the proposed approach accommodates nonlinear and non-equilibrium dynamics, enabling the representation of temporal risk patterns that are not well captured by first-order or linear oscillator-based formulations.

stat.AP↗

arXiv2024

An Exploration of Modeling Approaches for Capturing Seasonal Transmission in Stochastic Epidemic Models

Seasonal variations in the incidence of infectious diseases are a well-established phenomenon, driven by factors such as climate changes, social behaviors, and ecological interactions that influence host susceptibility and transmission rates. While seasonality plays a significant role in shaping epidemiological dynamics, it is often overlooked in both empirical and theoretical studies. Incorporating seasonal parameters into mathematical models of infectious diseases is crucial for accurately capturing disease dynamics, enhancing the predictive power of these models, and developing successful control strategies. This paper highlights key modeling approaches for incorporating seasonality into disease transmission, including sinusoidal functions, periodic piecewise linear functions, Fourier series expansions, Gaussian functions, and data-driven methods, accompanied by real-world examples. Additionally, a stochastic Susceptible-Infected-Recovered (SIR) model with seasonal transmission is demonstrated through numerical simulations. Important outcome measures, such as the basic and instantaneous reproduction numbers and the probability of a disease outbreak using branching process approximation of the Markov chain, are also presented to illustrate the impact of seasonality on disease dynamics.

q-bio.PE↗

arXiv2024

Data-Driven Modeling of Seasonal Dengue Dynamics in Bangladesh: A Bayesian-Stochastic Approach

Bangladesh's worsening dengue crisis, fueled by its tropical climate, poor waste management infrastructure, rapid urbanization, and dense population, has led to increasingly deadly outbreaks, posing a significant public health threat. To address this, we propose a nonlinear, time-nonhomogeneous SEIR model incorporating seasonality through a novel transmission rate function. The model parameters are estimated using Bayesian inference with the Metropolis-Hastings algorithm in a Markov Chain Monte Carlo (MCMC) framework, calibrated with real-life dengue data from Bangladesh. To account for stochasticity and better assess outbreak probabilities, we extend the model to a time-nonhomogeneous continuous-time Markov chain (CTMC) framework. Our model provides new insights that can guide policymakers and offer a robust mathematical framework to better combat this crisis.

stat.AP↗