Table 1 Description of model parameters and their corresponding values.

From: Monitoring and investigation to control the brain network disease under immunotherapy by using fractional operator

Symbol

Description51

\(R_0<1\)

\(R_0>1\)

\(\sigma\)

Rate of daily neuron production density

\(10^{-4}\)

\(5 \times 10^{-3}\)

\(\beta\)

Rate of neuron infection

0.4

0.8

\(\mu _1\)

Neuron apoptosis rate

\(1.9\times 10^{-4}\)

\(1.9 \times 10^{-4}\)

\(\mu _2\)

Rate of active microglia annihilation

\(6 \times 10^{-3}\)

\(6 \times 10^{-3}\)

\(\mu _3\)

Rate of activated T cell annihilation

0.015

0.015

\(d_1\)

Neuron death rate from \(\alpha\)-syn aggregations

\(3.4\times 10^{-4}\)

0.1

\(a_1\)

Microglia activation from extracellular \(\alpha\)-syn and neurons

\(2\times 10^{-2}\)

\(2\times 10^{-2}\)

\(a_2\)

T cell activation from extracellular \(\alpha\)-syn, neurons

\(2\times 10^{-2}\)

\(2\times 10^{-2}\)

e

\(\alpha\)-syn survival percentage from neuron death

0.5

0.9