Basically includes model equations & hypothesis in each case.
The exponential viral growh kinetics shows a Ist order kinetics as mentioned – Ct = C0 * EXP ( - K * t )--------------------------------------------------------- ( 1 ) [ Case – I ]
[ Where C0 = Initial bacterial count, bacterial Colony Count ( Ct ) at time t & K = Ist order growth const & t= time of growth ]
General mathematical expression of Gaussiun Probability distribution of biopolymer can be expressed as :
P ( x )= A exp ( - B * x ^ 2 )............................................... ( 2 )
A,B are constants depending on the physic-chemical properties of bio-polymer chain .
considering one dimension Gaussian probability P ( x ) ranging from - infinity to + infinity with mean distribution is zero .For two /three dimension the expression includes dimension factor . To find best fit analysis through Regression method the Gaussian fit is one of the useful one for hydrodynamic modelling of Covid19 considering the flow of viral infection through our blood .
The Gaussiun probality can be represented as randomisation of monomer chain of biopolymers ( including virus like Covid19) ( N=Number of Monomers vs Rrms = An Important Statistical parameters like Root mean square end to end separation as a F(X) of Radius of gyration ( Rg ) . The representative equation is as follows .The Rg of SARS-COV-2 biopolymer with a tremendous SP3 monomer leads to the virus more and more virulent as well as genetically recombinant .
P ( N, x ) = A * exp ( - 0.042 * Rrms ^ 2 )............ ( 3 ) [ Case – II ]
X = distribution chain length of random biopolymer coil
Rrms = Root mean square end to end separation of bio-polymer chain .
Cuver finder V.1.4 run mode gives the best fit logistic regression as bellow :
Y ( IFR) = Sigmoid f [ X( Age ) ] = [ a / ( 1 + b* exp ( -cx ) ]------- ( 4 ) [ Case –III ]
a , b , c are the coefficients obtained from best fit analysis .
The equation ( 4 ) represents the desired model equation and the measure of a sigmoid probability of Covid infection with a significant correlation ( r ) value [ 0 < r < 1 ] .The pearson –coefficiant ( r ) in this case is 0.9995 with SE = 0.1341 , p < 0.00001 , CI > 95 % , with p < 0.05 makes the sigmoid statistics more significant .
Hypothesis regarding Remdesivir antiviral drug-neucleocapsid protein of Covid19 –Quantum Molecular bonding approach of drug-design. ( Case –IV )
The Theorem of Normalisation - Integration of Shi ( Shi * )dV = Unity . Very useful in quantum chemistry. dv = volume element for a probability Shi*Shi .Considering Covid19 as an uniform sphere we can compare with the spherical symmetrical s - Orbital in Atomic structure . Wave particle duality hypothesis assumes a wave nature for quick viral spreading as well as crown like particle . We can apply the probability density theory on s - Orbital where dv = 4/3 * pie * R^3 .
Applying Cylindrical polar symmetry on spike crown ( R, Theta , Phi ) - The cylindrical probability can be calculated as usual.
Now considering Remedesivir as p-orbital , we can assume the [Drug- Protein] Complex as SP hybridisation for linear overlap .
The modelling relationship from LCAO ( Linear combination of Atomic Orbital ) –
Shi ( Covid19 ) + Shi ( Remedesivir ) = Shi ( Drug- Protein Intermediate ) . [Where Shi represents the Corresponding wave functional probability ] correlating the stability of [ R-P] complex intermediate through the approach of molecular bonding .