Analytical Solution of the Susceptible-Infected-Recovered/Removed Model for the Not-Too-Late Temporal Evolution of Epidemics for General Time-Dependent Recovery and Infection Rates
Abstract
:1. Introduction
2. SIR Model
3. Approximate Analytical Solutions
3.1. Solution in the Limit of Small
3.2. Properties of the Approximate Solution (12)
4. Special Cases
4.1. Constant Ratio
4.2. Linearly Increasing Ratio
5. Illustrative Examples
5.1. Monotonically Rising Ratio
5.2. Oscillating Ratio
6. Summary and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Cumulative Fraction for General Reduced Time Dependencies k(τ)
Appendix B. Solution at Late Times
Appendix B.1. Limit J≃J ∞ =0.7
Appendix B.2. Continuity Conditions
Appendix C. Expansion of H(τ) at Small Times
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Schlickeiser, R.; Kröger, M. Analytical Solution of the Susceptible-Infected-Recovered/Removed Model for the Not-Too-Late Temporal Evolution of Epidemics for General Time-Dependent Recovery and Infection Rates. COVID 2023, 3, 1781-1796. https://doi.org/10.3390/covid3120123
Schlickeiser R, Kröger M. Analytical Solution of the Susceptible-Infected-Recovered/Removed Model for the Not-Too-Late Temporal Evolution of Epidemics for General Time-Dependent Recovery and Infection Rates. COVID. 2023; 3(12):1781-1796. https://doi.org/10.3390/covid3120123
Chicago/Turabian StyleSchlickeiser, Reinhard, and Martin Kröger. 2023. "Analytical Solution of the Susceptible-Infected-Recovered/Removed Model for the Not-Too-Late Temporal Evolution of Epidemics for General Time-Dependent Recovery and Infection Rates" COVID 3, no. 12: 1781-1796. https://doi.org/10.3390/covid3120123