arXiv subjects

Petar Jevtić

Publications and source records attributed to Petar Jevtić.

4 recordsLinked to original sources

arXiv2025

The Basic Reproduction Number for Petri Net Models: A Next-Generation Matrix Approach

The basic reproduction number ($R_0$) is an epidemiological metric that represents the average number of new infections caused by a single infectious individual in a completely susceptible population. The methodology for calculating this metric is well-defined for numerous model types, including, most prominently, Ordinary Differential Equations (ODEs). The basic reproduction number is used in disease modeling to predict the potential of an outbreak and the transmissibility of a disease, as well as by governments to inform public health interventions and resource allocation for controlling the spread of diseases. A Petri Net (PN) is a directed bipartite graph where places, transitions, arcs, and the firing of the arcs determine the dynamic behavior of the system. Petri Net models have been an increasingly used tool within the epidemiology community. However, no generalized method for calculating $R_0$ directly from PN models has been established. Thus, in this paper, we establish a generalized computational framework for calculating $R_0$ directly from Petri Net models. We adapt the next-generation matrix method to be compatible with multiple Petri Net formalisms, including both deterministic Variable Arc Weight Petri Nets (VAPNs) and stochastic continuous-time Petri Nets (SPNs). We demonstrate the method's versatility on a range of complex epidemiological models, including those with multiple strains, asymptomatic states, and nonlinear dynamics. Crucially, we numerically validate our framework by demonstrating that the analytically derived $R_0$ values are in strong agreement with those estimated from simulation data, thereby confirming the method's accuracy and practical utility.

math.AT↗

arXiv2025

Forecasting Coccidioidomycosis (Valley Fever) in Arizona: A Graph Neural Network Approach

Coccidioidomycosis, commonly known as Valley Fever, remains a significant public health concern in endemic regions of the southwestern United States. This study develops the first graph neural network (GNN) model for forecasting Valley Fever incidence in Arizona. The model integrates surveillance case data with environmental predictors using graph structures, including soil conditions, atmospheric variables, agricultural indicators, and air quality metrics. Our approach explores correlation-based relationships among variables influencing disease transmission. The model captures critical delays in disease progression through lagged effects, enhancing its capacity to reflect complex temporal dependencies in disease ecology. Results demonstrate that the GNN architecture effectively models Valley Fever trends and provides insights into key environmental drivers of disease incidence. These findings can inform early warning systems and guide resource allocation for disease prevention efforts in high-risk areas.

cs.LG↗

arXiv2025

A Numerical Comparison of Petri Net and Ordinary Differential Equation SIR Component Models

Petri Nets are an increasingly used modeling framework for the spread of disease across populations or within an individual. For example, the Susceptible-Infectious-Recovered (SIR) compartment model is foundational for population epidemiological modeling and has been implemented in several prior Petri Net studies. While the SIR model is typically expressed as Ordinary Differential Equations (ODEs), with continuous time and variables, Petri Nets operate as discrete event simulations with deterministic or stochastic timings. We present the first systematic study of the numerical convergence of two distinct Petri Net implementations of the SIRS compartment model relative to the standard ODE. In particular, we introduce a novel deterministic implementation of the SIRS model using dynamic transition weights in the GPenSIM package and stochastic Petri Net models using SPIKE. We show how rescaling and rounding procedures are critical for the numerical convergence of Petri Net SIR models relative to the ODEs, and we achieve a relative root mean squared error of less than 1% compared to ODE simulations for biologically relevant parameter ranges. Our findings confirm that both stochastic and deterministic discrete time Petri Nets are valid for modeling SIR-type dynamics with appropriate numerical procedures, laying the foundations for larger-scale use of Petri Net models.

q-bio.OT↗

arXiv2022

Optimal annuitization post-retirement with labor income

Evidence shows that the labor participation rate of retirement age cohorts is non-negligible, and it is a widespread phenomenon globally. In the United States, the labor force participation rate for workers age 75 and older is projected to be over 10 percent by 2026 as reported by the Bureau of Labor Statistics. The prevalence of post-retirement work changes existing considerations of optimal annuitization, a research question further complicated by novel factors such as post-retirement labor rates, wage rates, and capacity or willingness to work. To our knowledge, this poses a practical and theoretical problem not previously investigated in actuarial literature. In this paper, we study the problem of post-retirement annuitization with extra labor income in the framework of stochastic control, optimal stopping, and expected utility maximization. The utility functions are of the Cobb-Douglas type. The martingale methodology and duality techniques are employed to obtain closed-form solutions for the dual and primal problems. The effect of labor income is investigated by exploiting the explicit solutions and Monte-Carlo simulation. The latter reveals that the optimal annuitization time is strongly linear with respect to the initial wealth, with or without labor income. When it comes to optimal annuitization, we find that the wage and labor rates may play opposite roles. However, their impact is mediated by the leverage ratio.

q-fin.PM↗