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Quantitative Biology > Populations and Evolution

arXiv:2007.16069 (q-bio)
[Submitted on 31 Jul 2020 (v1), last revised 10 Nov 2020 (this version, v3)]

Title:Exact closed-form solution of a modified SIR model

Authors:Angel Ballesteros, Alfonso Blasco, Ivan Gutierrez-Sagredo
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Abstract:The exact analytical solution in closed form of a modified SIR system where recovered individuals are removed from the population is presented. In this dynamical system the populations $S(t)$ and $R(t)$ of susceptible and recovered individuals are found to be generalized logistic functions, while infective ones $I(t)$ are given by a generalized logistic function times an exponential, all of them with the same characteristic time. The dynamics of this modified SIR system is analyzed and the exact computation of some epidemiologically relevant quantities is performed. The main differences between this modified SIR model and original SIR one are presented and explained in terms of the zeroes of their respective conserved quantities. Moreover, it is shown that the modified SIR model with time-dependent transmission rate can be also solved in closed form for certain realistic transmission rate functions.
Comments: 17 pages. New section added
Subjects: Populations and Evolution (q-bio.PE); Dynamical Systems (math.DS); Physics and Society (physics.soc-ph)
Cite as: arXiv:2007.16069 [q-bio.PE]
  (or arXiv:2007.16069v3 [q-bio.PE] for this version)
  https://doi.org/10.48550/arXiv.2007.16069

Submission history

From: Ivan Gutierrez-Sagredo [view email]
[v1] Fri, 31 Jul 2020 13:38:40 UTC (1,352 KB)
[v2] Sat, 17 Oct 2020 10:28:09 UTC (1,354 KB)
[v3] Tue, 10 Nov 2020 10:57:22 UTC (1,417 KB)
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