An epidemic model with a limited resource for treatment is proposed to understand the effect of the capacity for treatment. It is assumed that treatment rate is proportional to the number of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low.
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http://dx.doi.org/10.1016/j.mbs.2005.12.022 | DOI Listing |
Infect Dis Model
June 2025
College of Mathematics and System Science, Xinjiang University, Urumqi, 830017, PR China.
This paper formulates an SEIRSHM epidemic model with general birth rate, media report and limited medical resources. Firstly, the well-posedness of the solutions and the extinction of the disease are discussed. Then, the existence of the endemic equilibrium is discussed and we find when ∗ > 1 and = 1, there exhibits a backward bifurcation, if ∗ < 1 and = 1, there exhibits a forward bifurcation.
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January 2025
Department of Mathematics, College of Natural and Computational Science, Debre Berhan University, Debre Berhan, Adis Ababa, Ethiopia.
Tuberculosis (TB) is one of the deadly infectious diseases affecting millions of individuals throughout the world. The main objective of this study is to investigate the impact of media coverage on the transmission dynamics of TB with vaccine and treatment strategy using mathematical model analysis. In the qualitative analysis of the proposed model we proved the existence, uniqueness, positivity, and boundedness of the model solutions, investigated both the disease-free and endemic equilibrium points, computed the basic and effective reproduction numbers using next generation matrix approach, analyzed the stability analysis of the equilibrium points, the backward bifurcation using the Castillo-Chavez and Song theorem and we re-formulated the corresponding optimal control problem and analyzed by applying the Pontryagin's Minimum Principle.
View Article and Find Full Text PDFPLoS One
January 2025
School of Mathematics and Statistics, College of Science, Rochester Institute of Technology, Rochester, New York, United States of America.
This study presents a novel non-autonomous mathematical model to explore the intricate relationship between temperature and desert locust population dynamics, considering the influence of both solitarious and gregarious phases across all life stages. The model incorporates temperature-dependent parameters for key biological processes, including egg development, hopper growth, adult maturation, and reproduction. Theoretical analysis reveals the model's capacity for complex dynamical behaviors, such as multiple stable states and backward bifurcations, suggesting the potential for sudden and unpredictable population shifts.
View Article and Find Full Text PDFChaos
January 2025
Department of Mathematics, Indian Institute of Technology Patna, Patna 801103, India.
Human immunodeficiency virus (HIV) manifests multiple infections in CD4+ T cells, by binding its envelope proteins to CD4 receptors. Understanding these biological processes is crucial for effective interventions against HIV/AIDS. Here, we propose a mathematical model that accounts for the multiple infections of CD4+ T cells and an intracellular delay in the dynamics of HIV infection.
View Article and Find Full Text PDFChaos
January 2025
Department of Mathematics, National Institute of Technology Silchar, Silchar, Assam 788010, India.
This study introduces a five-compartment model to account for the impacts of vaccination-induced recovery and nonlinear treatment rates in settings with limited hospital capacity. To reflect real-world scenarios, the model incorporates multiple reinfections in both vaccinated and recovered groups. It reveals a range of dynamics, including a disease-free equilibrium and up to six endemic equilibria.
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