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Stochastic modeling of disease dynamics has had a long tradition. Among the first epidemic models including a spatial structure in the form of local interactions is the contact process. In this article we investigate two extensions of the…

Probability · Mathematics 2007-05-23 L. Belhadji , N. Lanchier

The emergence of novel infectious agents presents challenges to statistical models of disease transmission. These challenges arise from limited, poor-quality data and an incomplete understanding of the agent. Moreover, outbreaks manifest…

Methodology · Statistics 2024-03-20 Jiasheng Shi , Jeffrey S. Morris , David M. Rubin , Jing Huang

The importance of spatial networks in the spread of an epidemic is an essential aspect in modeling the dynamics of an infectious disease. Additionally, any realistic data-driven model must take into account the large uncertainty in the…

Populations and Evolution · Quantitative Biology 2022-01-17 Giulia Bertaglia , Lorenzo Pareschi

Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible-infected-susceptible setting, spectral conditions characterise whether the disease vanishes. However, modelling human…

Social and Information Networks · Computer Science 2021-09-15 Desmond John Higham , Henry-Louis de Kergorlay

Many vector-borne disease epidemic models neglect the fact that in modern human civilization, social awareness as well as self-defence system are overwhelming against advanced propagation of the disease. News are becoming more effortlessly…

Populations and Evolution · Quantitative Biology 2020-02-28 Karunia Putra Wijaya , Joseph Páez Chávez , Dipo Aldila

Understanding the dynamics of the spread of diseases within populations is critical for effective public health interventions. We extend the classical SIR model by incorporating additional complexities such as the introduction of a cure and…

Populations and Evolution · Quantitative Biology 2025-10-30 Daniel Perkins , Davis Hunter , Drake Brown , Trevor Garrity , Wyatt Pochman

Phenomenological and deterministic models are often used for the estimation of transmission parameters in an epidemic and for the prediction of its growth trajectory. Such analyses are usually based on single peak outbreak dynamics. In…

Populations and Evolution · Quantitative Biology 2022-01-20 D. P. Mahapatra , S. Triambak

In the present work the spread of epidemic is studied over complex networks which are characterized by power law degree distribution of links and heterogeneous rate of disease transmission. The random allocation of epidemic transmission…

Physics and Society · Physics 2016-07-19 Vikram Sagar , Yi Zhao

We propose a new network-based SIR epidemic model in which transmission is modulated by a curvature-weighted contact matrix that encodes structural and geometric features of the underlying graph. The formulation encompasses both…

Dynamical Systems · Mathematics 2025-12-29 Marcilio Ferreira dos Santos

Given the growth of urbanization and emerging pandemic threats, more sophisticated models are required to understand disease propagation and investigate the impacts of intervention strategies across various city types. We introduce a fully…

Physics and Society · Physics 2020-08-03 Nishant Kumar , Jimi B. Oke , Bat-hen Nahmias-Biran

Recently developed techniques to acquire high-quality human mobility data allow large-scale simulations of the spread of infectious diseases with high spatial and temporal resolution.Analysis of such data has revealed the oversimplification…

Physics and Society · Physics 2015-12-08 Naoya Fujiwara , Abhijeet R. Sonawane , Koji Iwayama , Kazuyuki Aihara

We investigate how the properties of epidemic networks change depending on the availability of different types of data on a disease outbreak. This is achieved by introducing mathematical and computational methods that estimate the…

Computational Physics · Physics 2025-09-03 Oscar Fajardo-Fontiveros , Carl J. E. Suster , Eduardo G. Altmann

Many epidemic models approximate social contact behavior by assuming random mixing within mixing groups (e.g., homes, schools and workplaces). The effect of more realistic social network structure on estimates of epidemic parameters is an…

Methodology · Statistics 2012-08-27 Gail E. Potter , Mark S. Handcock , Ira M. Longini, , M. Elizabeth Halloran

Metapopulation models are commonly used in ecology, evolution, and epidemiology. These models usually entail homogeneity assumptions within patches and study networks of migration between patches to generate insights into conservation of…

Populations and Evolution · Quantitative Biology 2025-06-06 Diepreye Ayabina , Hasan Sevil , Adam Kleczkowski , M. Gabriela M. Gomes

In this paper we analyze the effects of commuting and social inequalities for the epidemic development of the novel coronavirus (COVID-19). With this aim we consider a SEIRD (susceptible, exposed, infected, recovered and dead by disease)…

Populations and Evolution · Quantitative Biology 2020-08-18 João A. M. Gondim , Thiago Yukio Tanaka

For many infectious diseases, a small-world network on an underlying regular lattice is a suitable simplified model for the contact structure of the host population. It is well known that the contact network, described in this setting by a…

Populations and Evolution · Quantitative Biology 2009-11-11 M. M. Telo da Gama , A. Nunes

We present a systematic review of some basic results on the derivation of classical epidemiological models from simple agent-based dynamics. The evolution of large populations is coupled with the dynamics of the contact distribution,…

Populations and Evolution · Quantitative Biology 2024-10-14 Mattia Zanella

We show that precise knowledge of epidemic transmission parameters is not required to build an informative model of the spread of disease. We propose a detailed model of the topology of the contact network under various external control…

Populations and Evolution · Quantitative Biology 2020-06-15 Michael Small , David Cavanagh

We rigorously investigate the convergence of a new numerical method, recently proposed by the authors, to approximate the reproduction numbers of a large class of age-structured population models with finite age span. The method consists in…

Numerical Analysis · Mathematics 2024-09-04 Simone De Reggi , Francesca Scarabel , Rossana Vermiglio

Disease spreading models such as the ubiquitous SIS compartmental model and its numerous variants are widely used to understand and predict the behaviour of a given epidemic or information diffusion process. A common approach to imbue more…

Dynamical Systems · Mathematics 2025-11-18 Eugene Tan , Michael Small , Shannon D. Algar