Given a sequence of epidemic events, can a single epidemic model capture its dynamics during the entire period? How should we divide the sequence into segments to better capture the dynamics? Throughout human history, infectious diseases (e.g., the Black Death and COVID-19) have been serious threats. Consequently, understanding and forecasting the evolving patterns of epidemic events are critical for prevention and decision making. To this end, epidemic models based on ordinary differential equations (ODEs), which effectively describe dynamic systems in many fields, have been employed. However, a single epidemic model is not enough to capture long-term dynamics of epidemic events especially when the dynamics heavily depend on external factors (e.g., lockdown and the capability to perform tests). In this work, we demonstrate that properly dividing the event sequence regarding COVID-19 (specifically, the numbers of active cases, recoveries, and deaths) into multiple segments and fitting a simple epidemic model to each segment leads to a better fit with fewer parameters than fitting a complex model to the entire sequence. Moreover, we propose a methodology for balancing the number of segments and the complexity of epidemic models, based on the Minimum Description Length principle. Our methodology is (a) Automatic: not requiring any user-defined parameters, (b) Model-agnostic: applicable to any ODE-based epidemic models, and (c) Effective: effectively describing and forecasting the spread of COVID-19 in 70 countries.
This research presents a new fractional-order discrete-time susceptible-infected-recovered (SIR) epidemic model with vaccination. The dynamical behavior of the suggested model is examined analytically and numerically. Through using phase attractors, bifurcation diagrams, maximum Lyapunov exponent and the 0−1 test, it is verified that the newly introduced fractional discrete SIR epidemic model vaccination with both commensurate and incommensurate fractional orders has chaotic behavior. The discrete fractional model gives more complex dynamics for incommensurate fractional orders compared to commensurate fractional orders. The reasonable range of commensurate fractional orders is between γ = 0.8712 and γ = 1, while the reasonable range of incommensurate fractional orders is between γ2 = 0.77 and γ2 = 1. Furthermore, the complexity analysis is performed using approximate entropy (ApEn) and C0 complexity to confirm the existence of chaos. Finally, simulations were carried out on MATLAB to verify the efficacy of the given findings.