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Mathematics, Interdisciplinary Applications
Mengxin Chen et al.
Summary: In this study, the existence of steady states, bifurcations, and spatiotemporal patterns are investigated for a diffusive predator-prey model. The nonexistence and existence of nonconstant steady states are justified using priori estimates, Poincare inequalities, and Leray-Schauder degree, respectively. The weakly nonlinear analysis is employed to establish the amplitude equations and various complex pattern solutions are identified from these equations.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Kanica Goel et al.
Summary: This study proposes and analyzes a time-delayed SIR epidemic model with logistic growth of susceptibles, specific incidence rates, and treatment rates, investigating the stability behavior of the model and the impact of the basic reproduction number on disease spread.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Biology
Marissa Renardy et al.
Summary: This paper introduces a pipeline for structural identifiability analysis of age-structured partial differential equation (PDE) models using a differential algebra framework. The study shows that age-structured models present additional difficulties due to increased number of variables and partial derivatives as well as the presence of boundary conditions. The authors perform identifiability analysis on a Susceptible-Exposed-Infected model and compare the results with both PDE and corresponding ordinary differential equation (ODE) systems, while also exploring the effects of age-dependent parameters on identifiability.
JOURNAL OF MATHEMATICAL BIOLOGY
(2022)
Article
Mathematics
Abhishek Kumar et al.
Summary: In this article, a novel susceptible-infected-recovered epidemic model with nonmonotonic incidence and treatment rates is proposed and analyzed mathematically. The stability of the disease-free equilibrium (DFE) and endemic equilibrium (EE) has been investigated under different conditions, along with the identification of conditions for the existence of EE. Theoretical findings have been supported through numerical simulations.
COMMUNICATIONS IN MATHEMATICS AND STATISTICS
(2022)
Article
Mathematics, Applied
Mengxin Chen et al.
Summary: The paper introduces and investigates a depletion-type reaction-diffusion Gierer-Meinhardt model with Langmuir-Hinshelwood reaction scheme and homogeneous Neumann boundary conditions. It provides theoretical analysis and numerical simulations to explore stability, existence, and bifurcation properties in the model. The results confirm the theoretical findings and provide additional insights through numerical simulations.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2022)
Article
Mathematics, Applied
Lizhong Qiang et al.
Summary: This paper proposes and studies an almost periodic reaction-diffusion epidemic model incorporating disease latency, spatial heterogeneity, and general seasonal fluctuations. By computing the upper Lyapunov exponent lambda*, the global threshold dynamics of the model is established, showing that the disease-free state is globally attractive when lambda* < 0. The effects of diffusion rate, incubation period, and spatial heterogeneity on disease transmission are investigated through numerical simulations.
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
(2021)
Article
Mathematical & Computational Biology
Jayanta Kumar Ghosh et al.
Summary: This paper presents an SIR model with specific characteristics such as logistic growth rate of susceptible population, non-monotonic incidence rate and saturated treatment rate. The existence and stability of equilibria, as well as the stability of different endemic equilibria, are investigated and analyzed. Results show that the disease free equilibrium point is globally asymptotically stable when certain conditions are met, and the system exhibits transcritical bifurcation and other bifurcations. Numerical simulations also show the existence of Bogdanov-Takens bifurcation. Control functions such as vaccination and treatment are used to solve the optimal control problem and determine the best control strategy.
MATHEMATICAL MODELLING OF NATURAL PHENOMENA
(2021)
Article
Mathematics, Applied
M. R. S. Kulenovic et al.
Summary: The study investigates the impact of density dependence on the spread of infectious diseases using a discrete-time SI epidemic model. The basic reproductive number R-0 plays a crucial role, where R-0 less than 1 leads to disease extinction, while R-0 greater than 1 under certain conditions results in persistent infection.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2021)
Article
Mathematics, Applied
Tanuja Das et al.
Summary: When a disease spreads, individual behaviors are influenced by disease prevalence information, while limitations in medical resources impact disease dynamics. A proposed SEIR model with information-induced non-monotonic incidences and saturated treatments reveals potential multi-stability and multiple endemic equilibria. Information and medical resource availability play key roles in determining the complex dynamical behavior of the model.
Article
Mathematics, Interdisciplinary Applications
Sandeep Sharma et al.
Summary: This paper presents a new deterministic cholera model with vaccination and treatment as control measures, analyzing the stability and equilibrium points through numerical simulations and theoretical analysis.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Peng Wu et al.
Summary: This study proposed a new age-space structured model for analyzing the dynamics of HIV/AIDS epidemic among MSM, incorporating infection ages, spatial diffusion, and HAART. Numerical simulations reinforced analytical results that spatial factor plays a crucial role in controlling HIV transmission, suggesting the improvement of treatment adherence during HAART for HIV infected individuals among MSM.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2021)
Article
Engineering, Mechanical
Pritam Saha et al.
Summary: The paper analyzes a deterministic epidemic model with logistic growth rate of susceptible population, non-monotone incidence rate, and nonlinear treatment function with limited hospital bed impact, along with control strategies. It studies the existence, stability, persistence, and extinction of infections, as well as different types of bifurcations at equilibrium points under parametric restrictions. Numerical simulations and optimal control strategies reveal complex dynamics of infectious diseases, leading to effective control strategies for two cases through efficiency analysis.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
Rui Peng et al.
Summary: This paper focuses on an epidemic reaction-diffusion system with a nonlinear incidence mechanism. The coefficients of the system are spatially heterogeneous and time dependent, and the study reveals the delicate effects of various parameters on the infection dynamics. The analysis can be applied to models with different infection incidence mechanisms.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
(2021)
Article
Engineering, Mechanical
Ke Wu et al.
NONLINEAR DYNAMICS
(2020)
Article
Nanoscience & Nanotechnology
Hamdy M. Youssef et al.
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Mathematics
Fei-Ying Yang et al.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2019)
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Eric Avila-Vales et al.
CHAOS SOLITONS & FRACTALS
(2019)
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Mathematics, Applied
H. M. Srivastava et al.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2019)
Article
Mathematics, Applied
Kousuke Kuto et al.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2017)
Article
Mathematics, Interdisciplinary Applications
Hongyong Zhao et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2016)
Article
Mathematics
Renhao Cui et al.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2016)
Article
Mathematics, Interdisciplinary Applications
Yongli Cai et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2015)
Article
Mathematics, Applied
Wendi Wang et al.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
(2012)
Article
Biology
P van den Driessche et al.
MATHEMATICAL BIOSCIENCES
(2002)