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This paper introduces an innovative model for infectious diseases in predator-prey populations. We not only prove the existence of global non-negative solutions but also establish essential criteria for the system's decline and…

Populations and Evolution · Quantitative Biology 2023-06-16 Yujie Gao , Malay Banerjee , Ton Viet Ta

Multiple Sclerosis is a chronic autoimmune disorder characterized by the degradation of the myelin sheath in the central nervous system, leading to neurological impairments. In this work, we analyze a reaction-diffusion model derived from…

Tissues and Organs · Quantitative Biology 2026-03-10 Romina Travaglini , Rossella Della Marca

This paper approaches the question of existence and uniqueness of stationary solutions to a semilinear hyperbolic-parabolic system and the study of the asymptotic behaviour of global solutions. The system is a model for some biological…

Analysis of PDEs · Mathematics 2017-07-11 Francesca Romana Guarguaglini

We study bacterial diffusion in disordered porous media. Interactions with obstacles, at unknown locations, make this problem challenging. We approach it by abstracting the environment to cell states with memoryless transitions. With this,…

Soft Condensed Matter · Physics 2023-12-29 Henry H. Mattingly

In the present paper, we are concerned with an SIS epidemic reaction-diffusion model governed by mass action infection mechanism and linear birth-death growth with no flux boundary condition. By performing qualitative analysis, we study the…

Analysis of PDEs · Mathematics 2018-07-11 Huicong Li , Rui Peng , Zhi-An Wang

Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…

Statistical Mechanics · Physics 2026-01-16 Gabriel Barreiro , Vladimir Pérez-Veloz

An interesting inference drawn by some Covid-19 epidemiological models is that there exists a proportion of the population who are not susceptible to infection -- even at the start of the current pandemic. This paper introduces a model of…

Quantitative Methods · Quantitative Biology 2020-09-18 Thomas Parr , Anjali Bhat , Peter Zeidman , Aimee Goel , Alexander J. Billig , Rosalyn Moran , Karl J. Friston

Early, reliable detection of disease outbreaks is a critical problem today. This paper reports an investigation of the use of causal Bayesian networks to model spatio-temporal patterns of a non-contagious disease (respiratory anthrax…

Applications · Statistics 2012-07-19 Gregory F. Cooper , Denver Dash , John Levander , Weng-Keen Wong , William Hogan , Michael Wagner

The aim of this paper is to study two models for a bacterial population subject to antibiotic treatments. It is known that some bacteria are sensitive to antibiotics. These bacteria are in a state called persistence and each bacterium can…

Probability · Mathematics 2013-04-15 Fabio Zucca

Cholera remains a significant public health challenge globally, particularly affecting regions with inadequate water, sanitation, and hygiene infrastructures. This study presents a comprehensive mathematical model extending the classical…

Dynamical Systems · Mathematics 2025-05-15 Abdallah Alsammani , Gassan A. M. O. Farah , Mohammed A. Y. Mohammed , Mehmet Yavuz

In this paper, we consider an optimal distributed control problem for a reaction-diffusion-based SIR epidemic model with human behavioral effects. We develop a model wherein non-pharmaceutical intervention methods are implemented, but a…

Analysis of PDEs · Mathematics 2025-02-11 Marcelo Bongarti , Christian Parkinson , Weinan Wang

Models of spread processes over non-trivial networks are commonly motivated by modeling and analysis of biological networks, computer networks, and human contact networks. However, identification of such models has not yet been explored in…

Optimization and Control · Mathematics 2020-01-27 Philip E. Pare , Ji Liu , Carolyn L. Beck , Barret E. Kirwan , Tamer Basar

Human mobility is a key factor in spatial disease dynamics and related phenomena. In computational models host mobility is typically modelled by diffusion in space or on metapolulation networks. Alternatively, an effective force of…

Physics and Society · Physics 2012-03-07 Vitaly Belik , Theo Geisel , Dirk Brockmann

A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…

Dynamical Systems · Mathematics 2025-09-12 Wael El Khateeb , Chanaka Kottegoda , Chunhua Shan

Epidemiological models are an important tool in coping with epidemics, as they offer a forecast, even if often simplistic, of the behavior of the disease in the population. This allows responsible health agencies to organize themselves and…

Populations and Evolution · Quantitative Biology 2023-08-03 Eliza Maria Ferreira , Ricardo Edem Ferreira , Chiara Mocenni

We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the…

Populations and Evolution · Quantitative Biology 2024-03-13 Hidetsugu Sakaguchi , Keito Yamasaki

The aim of this paper is to study the dynamics of a reaction--diffusion SIS (susceptible-infectious-susceptible) epidemic model with a nonlinear incidence rate describing the transmission of a communicable disease between individuals. We…

Analysis of PDEs · Mathematics 2020-11-12 Lamia Djebara , Redouane Douaifia , Salem Abdelmalek , Samir Bendoukha

The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…

Analysis of PDEs · Mathematics 2017-10-11 E. S. Daus , L. Desvillettes , A. Jüngel

We consider a nonlinear model for electrical conduction in biological tissues. The nonlinearity appears in the interface condition prescribed on the cell membrane. The purpose of this paper is proving asymptotic convergence for large times…

Analysis of PDEs · Mathematics 2015-07-24 Micol Amar , Daniele Andreucci , Roberto Gianni

We consider a model of dynamics of the immune system. The model is based on three factors: occasional boosting and continuous waning of immunity and a general description of the period between subsequent boosting events. The antibody…

Probability · Mathematics 2022-12-27 Katarzyna Pichór , Ryszard Rudnicki