Can India develop herd immunity against COVID-19?

A fractional-order SIRD model with time-dependent memory indexes for encompassing the multi-fractional characteristics of the COVID-19

“…We observe that the nonlinearity is more evident for certain countries than others, e.g., India, US, Saudi Arabia, and Turkey, contrary to Iran, Italy, UK and Germany. It is worthy to remark that we are not trying to predict the persistent or antipersistent evolution of COVID-19, but instead, we are arguing the hypothetical power-law behaviors, which have been reported in previous works [28] , [29] , [30] , [31] , [32] , [33] . In this manner, our results suggest that the time-series exhibit a spectrum of power-law exponents (no just a single one), which agrees with Refs.…”

“…In this manner, our results suggest that the time-series exhibit a spectrum of power-law exponents (no just a single one), which agrees with Refs. [29] , [32] , [33] where was discussed that the COVID-19 infection rate evolve in three stages. Each one with different power-law exponent indicating that the power-law exponents changes with the time, presumably by the containment efforts.…”

“…Additionally, previous works showed that COVID-19 evolution follows scaling features similar to power-law [28] , [29] , [30] , [31] , [32] , [33] . The fractalness, also know as scale-invariant and self-similar, is a universal property of nature that permits the interpretation of the growth of trees, snowflakes, etc.…”

“…studied top 15 affected countries and detect the infection rates behave as a power-law growth. Also, they presented the generalized fractal dimensions of confirmed case and confirmed death of COVID-19, resulting with a different value for each country [33] . Ziff et al.…”

“…Besides, our results suggest that the time-series exhibit a spectrum of power-law exponents (no just a single one), which agrees with Refs. [29] , [32] , [33] where was discussed that the COVID-19 infection rate may cluster in three stages. In the former (growth-stage), the infections obey a power-law behavior characterized by a scaling exponent at a certain speed.…”