Page 71 - GHES-2-1

Global Health Econ Sustain Quantum Data Lake for epidemic analysis

(1916–1917) and subsequently modified by Anderson space-like matrices) are used in quantum field theory, and
McKendrick and William Kermack (1927–1933). they are unitary and Hermitian. In addition, the set of four
{a + ib}, {a – ib}, (XVI) gamma matrices, considered Pauli matrices, can be used
to generate a fifth gamma matrix (Equation XIX). Notably,
{virus |causes| in person with circadian blood pressure the fifth gamma matrix is Hermitian (Equation XX).
a
profile disease case }, γ = i γ γ γ γ , (XIX)
1
0
5
2
3
1
{disease case |has outcome| in person with circadian
1
5
5 †
blood pressure profile death}. γ = (γ ) (XX)
|virus ⊗ causes disease case| = 3.4.2. PT-symmetry
Virus 1 Virus 1 Virus 1 Considering the PT-symmetric quantum mechanics for
Casee 1 Case 2 Case n fermionic and bosonic systems, Pauli matrices and Dirac
matrices can be presented as pseudo-Hermitian (non-
Virus 2 Virus 2 Virus 2 Hermitian) PT-symmetric matrices using a P-operator
= Case 1 Case 2 Case n (XVII) or C-operator (Beygi et al., 2019; Das, 2010; Dogra et al.,
     2021; Gao et al., 2021; Konotop et al., 2016; Melkani,
Virus n Virus n Virus n 2023; Naghiloo et al., 2019; Pati, 2009; Rath, 2020; Song
& Murch, 2022; Sutor, 2019; Viedma Palomo, 2018; Wang,
Case 1 Case 2 Case n 2013; Zhang et al., 2021; Zheng et al., 2013).
For fermionic systems, Beygi et al. (2019) proposed
|compartment ⊗ related with virus case | = an effective PT-symmetric Hamiltonian in matrix form as
Is Case 1 Is Casse 2  Is Case n presented in Equation XXI (Table 11), where m is mass and
g is real mass. The PT-symmetry may be either broken or
i
i
i

VCase 1 V Case 2  VCase n unbroken depending on the mass (Bender et al., 2005b).
i
i
i
SCase 1 S Case 2  S i Case n The PT-symmetry is unbroken if g ≤ m , whereas the
2
2
i
i
2
ICase I Case  I Case PT-symmetry is broken if g > m , resulting in a complex
2
i 1 i i 2 i n
= Cs i Case 1 Cs Case 2  Cs i Case n (XVIII) spectrum in the chiral limit m → 0.
i
QCase 1 QCase 2  QCase n For bosonic systems (photons), Rath (2020) proposed a

i
i
i
Co i Case 1 Co Case 2  Co i Case n PT-symmetric Hamiltonian matrix as presented in Equation
i

RCase 1 RCase 2  RCase n XXII (Table 11). Melkani (2023) denoted the PT-symmetric

i
i
i
DCase 1 DCase 2  DCase n gain and loss in a qubit with Equation XXII.I (Table 11),

i
i
i
where g and g refer to the amplification/dissipation at
1
2
two coupled sites, and k is the coupling constant for the
3.4. Data presentation physical system. Several other studies (Konotop et al., 2016;
3.4.1. Matrices Viedma Palomo, 2018) have also presented a PT-symmetric
non-Hermitian matrix, demonstrating gain and loss, i.e.,
As displayed in Figure 1, epidemic data should be collected increasing or decreasing amplitudes with complex potential
from a very wide range of information: Climate/ecological parameters as proposed in Equation XXII.II, where k and
data, virus carriers in nature, global/local mobility, social g are real parameters. PT-symmetry is unbroken if g < k;
data, virus transmission, vaccination, electronic health whereas the energies become complex conjugate pairs in
records, and human and virus omics data. Regarding the a broken regime if g > k. Similarly, the system exhibits an
logic of the epidemic process, all the data can be presented exceptional point with one degenerate eigenvalue if g = k.
by matrices: Matrix A (includes the association of the virus Bender et al. (2002) also displayed the imaginary potentials
with the disease, electronic health records, and human and
virus omics data), matrix B (includes the compartmental in a matrix (Equation XXII.III).
model dynamics, and data about virus transmission and Any arbitrary superposition of two orthogonal states
vaccination), matrix C (includes social factors, and global represents a single qubit (Equation XXIII, Table 11) (Sutor,
and local mobility), and matrix D (includes environmental 2019). In contrast, a single non-Hermitian PT-symmetric
factors, climate and ecological data, and virus carriers in qubit with two distinct eigenstates is called PT-qubit,
nature). These matrices can be conveyed as Dirac matrices which is different from a pure qubit (Equations XXIV.I–III,
or gamma matrices with Weyl and Majorana representation. Table 11) (Bender et al., 2003; Bender, 2007; Bender, 2015;
Gamma matrices γ (time-like matrix), γ , γ , and γ (three Pati, 2009). Das (2010) suggested a matrix for the non-
0
1
3
2
Volume 2 Issue 1 (2024) 20 https://doi.org/10.36922/ghes.2148