ArticlePhysica D. Nonlinear phenomena2021
Explicit formulae for the peak time of an epidemic from the SIR model. Which approximant to use?
Article in Physica D. Nonlinear phenomena, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 9 papers.
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9 citing papers in PubMed.
- Solving age-dependent infectious diseases and tumor growth models using the contraction approach.MethodsX · 2025Article
- An effective drift-diffusion model for pandemic propagation and uncertainty prediction.Biophysical reports · 2024Article
- Analysis of SIRVI model with time dependent coefficients and the effect of vaccination on the transmission rate and COVID-19 epidemic waves.Infectious Disease Modelling · 2023Article
- Dynamics of Feline Coronavirus and FIP: A Compartmental Modeling Approach.Veterinary medicine international · 2023Article
- An extended epidemic model with vaccination: Weak-immune SIRVI.Physica A · 2022Article
- There exists the "smartest" movement rate to control the epidemic rather than "city lockdown".Applied mathematical modelling · 2022Article
- A network SIRX model for the spreading of COVID-19.Physica A · 2022Article
- An agent-based model of the dual causality between individual and collective behaviors in an epidemic.Computers in biology and medicine · 2022Article
- Caputo Fractal Fractional Order Derivative of Soil Pollution Model Due to Industrial and Agrochemical.International journal of applied and computational mathematics · 2022Article
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Abstract
An analytic evaluation of the peak time of a disease allows for the installment of effective epidemic precautions. Recently, an explicit analytic, approximate expression (MT) for the peak time of the fraction of infected persons during an outbreak within the susceptible-infectious-recovered/removed (SIR) model had been presented and discussed (Turkyilmazoglu, 2021). There are three existing approximate solutions (SK-I, SK-II, and CG) of the semi-time SIR model in its reduced formulation that allow one to come up with different explicit expressions for the peak time of the infected compartment (Schlickeiser and Kröger, 2021; Carvalho and Gonçalves, 2021). Here we compare the four expressions for any choice of SIR model parameters and find that SK-I, SK-II and CG are more accurate than MT as long as the amount of population to which the SIR model is applied exceeds hundred by far (countries, ss, cities). For small populations with less than hundreds of individuals (families, small towns), however, the approximant MT outperforms the other approximants. To be able to compare the various approaches, we clarify the equivalence between the four-parametric dimensional SIR equations and their two-dimensional dimensionless analogue. Using Covid-19 data from various countries and sources we identify the relevant regime within the parameter space of the SIR model.
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