ArticlePloS one2017
Dynamic behaviors of a modified SIR model in epidemic diseases using nonlinear incidence and recovery rates.
Article in PloS one, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 19 papers.
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Who cites it
19 citing papers in PubMed.
- SEIRV epidemiological model for COVID 19 with Holling type II functional response.Scientific reports · 2026Article
- A nonlinear relapse model with disaggregated contact rates: Analysis of a forward-backward bifurcation.Infectious Disease Modelling · 2023Article
- Infectious Disease Modeling with Socio-Viral Behavioral Aspects-Lessons Learned from the Spread of SARS-CoV-2 in a University.Tropical medicine and infectious disease · 2022Article
- SEIR-FMi: A coronavirus disease epidemiological model based on intra-city movement, inter-city movement and medical resource investment.Computers in biology and medicine · 2022Article
- Mobility was a significant determinant of reported COVID-19 incidence during the Omicron Surge in the most populous U.S. Counties.BMC infectious diseases · 2022Article
- An extended epidemic model with vaccination: Weak-immune SIRVI.Physica A · 2022Article
- Prediction of COVID-19 Pandemic in Bangladesh: Dual Application of Susceptible-Infective-Recovered (SIR) and Machine Learning Approach.Interdisciplinary perspectives on infectious diseases · 2022Article
- Effects of Nonmonotonic Functional Responses on a Disease Transmission Model: Modeling and Simulation.Communications in mathematics and statistics · 2022Article
- Hospital preparedness during epidemics using simulation: the case of COVID-19.Central European journal of operations research · 2022Article
- Complex dynamics of an epidemic model with saturated media coverage and recovery.Nonlinear dynamics · 2022Article
- Optimal control analysis of COVID-19 vaccine epidemic model: a case study.European physical journal plus · 2022Article
- Nonlinear dynamics of a SIRI model incorporating the impact of information and saturated treatment with optimal control.European physical journal plus · 2022Article
- A simplified math approach to predict ICU beds and mortality rate for hospital emergency planning under Covid-19 pandemic.Computers & chemical engineering · 2020Article
- SBDiEM: A new mathematical model of infectious disease dynamics.Chaos, solitons, and fractals · 2020Article
- A study on the stability behavior of an epidemic model with ratio-dependent incidence and saturated treatment.Theory in biosciences = Theorie in den Biowissenschaften · 2020Article
- A deterministic time-delayed SIR epidemic model: mathematical modeling and analysis.Theory in biosciences = Theorie in den Biowissenschaften · 2020Article
- A novel deterministic forecast model for COVID-19 epidemic based on a single ordinary integro-differential equation.European physical journal plus · 2020Article
- Modelling and analysing the coexistence of dual dilemmas in the proactive vaccination game and retroactive treatment game in epidemic viral dynamics.Proceedings. Mathematical, physical, and engineering sciences · 2019Article
- A theoretical model for Zika virus transmission.PloS one · 2017Article
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2 authors.
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Abstract
The transmission of infectious diseases has been studied by mathematical methods since 1760s, among which SIR model shows its advantage in its epidemiological description of spread mechanisms. Here we established a modified SIR model with nonlinear incidence and recovery rates, to understand the influence by any government intervention and hospitalization condition variation in the spread of diseases. By analyzing the existence and stability of the equilibria, we found that the basic reproduction number [Formula: see text] is not a threshold parameter, and our model undergoes backward bifurcation when there is limited number of hospital beds. When the saturated coefficient a is set to zero, it is discovered that the model undergoes the Saddle-Node bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation of codimension 2. The bifurcation diagram can further be drawn near the cusp type of the Bogdanov-Takens bifurcation of codimension 3 by numerical simulation. We also found a critical value of the hospital beds bc at [Formula: see text] and sufficiently small a, which suggests that the disease can be eliminated at the hospitals where the number of beds is larger than bc. The same dynamic behaviors exist even when a ≠ 0. Therefore, it can be concluded that a sufficient number of the beds is critical to control the epidemic.
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