Measurements of individual-level infectivity, susceptibility and baseline infection risk to biological or social contagion are made for large number of entities from their contact relation, sequential infection occurrences and environmental data, using computer implemented MCMC for a Bayesian estimation of an integrative latent trait response model. The method is useful for precise and efficient contagion control and prevention.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A computer implemented method of measuring a plurality of individual entities' infectivity, susceptibility and baseline infection risk (or baseline adoption likelihood) to biological or social contagions, which may involve single or multiple diseases, products or behaviors, and those entities' sensitivity to environmental factors, comprising: obtaining the contact relation matrix data of a plurality of potentially interacted individual entities wherein the matrix element represents the physical contact in disease contagion or any form of communication in social contagion between any two individual entities; obtaining the sequence of infection or adoption occurrences data for single or multiple diseases, products or behaviors of each individual entity during the observation period; pairing the infection or adoption occurrences of single or multiple diseases, products or behaviors of any two individual entities, wherein one is the prior infection or adoption status of another one's infection or adoption status at an occasion during the observation period; obtaining data of the conditions of environmental and other observable factors confronted by any of two individual entities during the observation period, and inferring each individual entity's infectivity and susceptibility to contagion, their baseline infection risk (or adoption likelihood) to single or multiple diseases, products or behaviors, and sensitivity to environmental factors, based at least in part on maximizing the conditional infection probability of each susceptible individual entity that is determined by a baseline infection risk (or Baseline adoption likelihood) plus a product of (i) potential infectious entity's infectivity and infection status, (ii) potential susceptible entity's susceptibility, (iii) contact relation between any two potentially interacted entities, and (iv) environmental conditions. 2. The method of claim 1, wherein the inferring involves the use of a Bayesian learning technique for an integrative latent trait response module that enables joint inferences of each individual entity's infectivity and susceptibility to contagion, their baseline infection risk (or adoption likelihood) to single or multiple diseases, products or behaviours, and sensitivity to environmental factors for a plurality of individual entities. 3. The method of claim 2, wherein the integrative latent trait response model: relates the conditional infection probability of individual entities with their sequential contagion occurrences data using a normal, Logistic or other distribution link. 4. The method of claim 1, wherein the inferring involves the use of a likelihood maximization technique for an integrative latent trait response module that enables the joint inferences of each individual entity's susceptibility to contagion and sensitivity to evironmental factors for a plurality of individual entities. 5. The method of claim 2, wherein the Bayesian learning technique comprises: initializing values for individual entities' (i) infectivity ζ and susceptibility αc to contagion, (ii) baseline infection risk (or baseline adoption likelihood) β to single or multiple diseases, products or behaviors, (iii) sensitivity α−c to environmental factors X, and (iv) latent variables Z and W for Gibbs sampling; assigning prior distributions of individual entities' infectivity, susceptibility, sensitivity and baseline infection risk (or baseline adoption likelihood), in accordance with: ζ˜N (v, σ2), α˜Nk (μ, Σ), β˜Bata(c, d). computing and sampling iteratively each individual entity's infectivity, susceptibility, sensitivity and baseline infection risk (or adoption likelihood), and latent variables from the full conditional distributions in accordance with: f  ( Z ijlt |  *) ∝ B ( Φ  ( α i c  ζ j  x jl  ( t - 1 )  n ijlt + X ilt ′  α i - c ) Φ  ( α i c  ζ j  x jl  ( t - 1 )  n ijlt + X ilt ′  α i - c ) + β il  ( 1 - Φ  ( α i c  ζ j  x jl  ( t - 1 )  n ijlt + X ilt ′  α i - c ) ) ) , for   Y ijlt = 1  Z ijlt = 0 , for   Y ijlt = 0  f ( W ijlt |  *) ∝ T  runcated   N  ( α i c  ζ j  x jl  ( t - 1 )  n ijlt + X ilt ′  α i - c ) ;  f ( ζ j |  *) ∝ N  ( ( D T  D + 1 σ 2 ) - 1  ( D T  C + v σ 2 ) , ( D T  D + 1 σ 2 ) - 1 ) f  ( α i |  *) ∝ N  ( ( F T  F + Σ - 1 ) - 1  ( F T  E + Σ - 1  μ ) , ( F T  F + Σ - 1 ) - 1 )  I  ( α i c > 0 )  C = [ W ijlt - X ilt ′  α i - c ] ,  D = [ α i c  x il  ( t - 1 )  n ijt ] ,  E = [ W ijlt ] ,  F = [ ζ j  x ijl  ( t - 1 )  n ijt  X ilt ′ ] f  ( β il |  *) ∝ Bata ( c il + ∑ ( t | Z ilt = 0 )  Y ilt , d il + ∑ t  I  ( Z ilt = 0 ) - ∑ ( t | Z ilt = 0 )  Y ilt ) storing a number of sequences of sampled estimates for individual entities' infectivity, susceptibility, sensitivity and baseline infection risk (or baseline adoption likelihood); comparing the between and within sequence variants or calculating convergence statistics such as the Gelman-Rubin R to evaluate convergence, and; updating and determining the estimates of each individual entity's infectivity susceptibility, sensitivity and baseline infection risk (or adoption likelihood) until convergence. 6. The method of claim 4, wherein the likelihood maximization technique involves: calculating and maximizing the joint likelihood function for individual entity's infectivity, susceptibility and sensitivity conditional on the obtained data, in accordance with: max   L  ( ζ j , α i c , α i - c ) = ∏ j   f  ( ζ j )  ∏ i  ∏ l  ∏ t  P ijlt Y ijlt  ( 1 - P ijlt ) 1 - Y ijlt imposing restrictions on individual entities' infectivity as Σαc−1 and susceptibility ζ˜N (0,1) and; determining each individual entity's susceptibility and sensitivity by solving equations in accordance with: ∑ j J   ∑ l  ∑ t  Y ijlt  x jl  ( t - 1 )  n ijlt  ∫ ζ j  p  ( ζ j | Y ijlt , α i c , α i - c , x jl  ( t - 1 ) , n ijlt , X ilt )   ζ j = ∑ j J   ∑ l  ∑ t  x jl  ( t - 1 )  n ijlt  ∫ ζ j  exp  ( α i c  ζ j  x jl  ( t - 1 )  n ijlt + X ilt ′  α i - c ) p  ( ζ j | Y ijlt , α i c , α i - c , x jl  ( t - 1 ) , n ijlt , X ilt ) 1 + exp  ( α i c  ζ j  x jl  ( t - 1 )  n ijlt + X ilt ′  α i - c )   ζ j  ∑ j J   ∑ l  ∑ t  Y ijlt  X ijlt  ∫ ζ i  p  ( ζ i | Y ijlt , α i c , α i - c , x jl  ( t - 1 ) , n ijlt , X ilt )   ζ j = ∑ j J   ∑ l  ∑ t  X ilt   1 ∫ exp  ( α i c  ζ j  x ij  ( t - 1 )  n ijlt + X ilt ′  α i - c ) p  ( ζ j | Y ijlt , α i c , α i - c , x jl  ( t - 1 ) , n ijlt , X ilt ) 1 + exp  ( α i c  ζ j  x jl  ( t - 1 )  n ijlt + X ilt ′  α i - c )   ζ j  … ∑ j J   ∑ l  ∑ t  Y ijlt  X iltk  ∫ ζ j  p  ( ζ j | Y ijlt , α i c , α i - c , x jl  ( t - 1 ) , n ijlt , X ilt )   ζ j = ∑ j J   ∑ l  ∑ t  X ilt   k   ∫ exp  ( α i c  ζ j  x ij  ( t - 1 )  n ijlt + X ilt ′  α i - c ) p  ( ζ j | Y ijlt , α i c , α i - c , x jl  ( t - 1 ) , n ijlt , X ilt ) 1 + exp  ( α i c  ζ j  x jl  ( t - 1 )  n ijlt + X ilt ′  α i - c )   ζ j  where p  ( ζ j | Y ijlt , α i c , a i - c , x jl  ( t - 1 ) , n ijlt , X ilt ) = Φ  ( ζ j )  ∏ i   ∏ l  ∏ t  P ijlt Y ijlt  ( 1 - P ijlt ) 1 - Y ijlt ∫ Φ  ( ζ j )  ∏ i   ∏ l  ∏ t  P ijlt Y ijlt  ( 1 - P ijlt ) 1 - Y ijlt   ζ j . 7. The method of claim 1, wherein the inferring is based on relating the conditional infection probability of susceptible individual entity with some indexes deduced from the sequential contagion occurrences of each individual entity or of a group of selected individual entities. 8. A knowledge discovery system for leaning a plurality of individual entities' infectivity and susceptibility and baseline infection risk (or baseline adoption likelihood) to biological or social to contagion, which may involve single or multiple diseases, products or behaviors, and those entities' sensitivity to environmental factors, the system including one or more processors and memories or a computer-readable medium that stores instructions executable by one or more processors and memories, the system comprising: a component for obtaining the contact relation matrix data of a plurality of potentially interacted individual entities, wherein the matrix element represents the physical contact in disease contagion or any form of communication in social contagion between any two individual entities; a component for obtaining the sequence of infection or adoption occurrences data for single or multiple diseases, products or behaviors of each individual entities during the observation period; a component for pairing the infection or adoption occurrences of any two individual entities, wherein one is the prior infection or adoption status of another one's infection or adoption status at an occasion during the observation period; a component for obtaining data of the conditions of environmental and other observable factors confronted by any of two individual entities during the observation period, and; a component for inferring each individual entity's infectivity and susceptibility to contagion, baseline infection risk (or adoption likelihood) to single or multiple diseases, products or behaviors, and sensitivity to environmental factors, based at least in part on maximizing the conditional infection probability of each individual entity that is determined by a baseline infection risk (or baseline adoption likelihood) plus a product of (i) potential infectious entity's infectivity and infection status, (ii) potential susceptible entity's susceptibility, (iii) contact relation between any two potentially interacted entities, and (iv) environmental conditions; and a component for describing, displaying or communicating those resulted measurements. 9. The system of claim 8, wherein the inferring involves the use of a Bayesian learning technique for an integrative latent trait response model that enables joint inferences of each individual entity's infectivity and susceptibility to contagion, their baseline infection risk (or adoption likelihood) to single or multiple diseases, products or behaviors, and sensitivity to environmental factors for a plurality of individual entities. 10. The system of claim 9, wherein the integrative latent trait response model relates the conditional infection probability of individual entities with their sequential contagion occurrences data using a normal, Logistic or other distribution link. 11. The system of claim 8, wherein the inferring involves the use of a likelihood maximization technique for an integrative latent trait response module that enables the joint inferences of each individual entity's susceptibility to contagion and sensitivity to environmental factors for a plurality of individual entities. 12. The system of claim 9, wherein the Bayesian learning technique comprises: initializing values for individual entities' (i) infectivity ζ and susceptibility αc to contagion, (ii) baseline infection risk (or baseline adoption likelihood) β to single or multiple diseases, products or behaviors, (iii) sensitivity α−c to environmental factors X, and (iv) latent variables Z and W for Gibbs sampling; assigning prior distributions of individual entities' infectivity, susceptibility, sensitivity and baseline infection risk ( or baseline adoption likelihood), in accordance with: ζ˜N (v, σ2), α˜Nk(μ, Σ), β˜Bata(c,d). computing and sampling iteratively each individual entity's infectivity, susceptibility, sensitivity and baseline infection risk (or adoption likelihood), and latent variables from the full conditional distributions in accordance with: f  ( Z ijlt |  *) ∝ B ( Φ  ( α i c  ζ j  x jl  ( t - 1 )  n ijlt + X ilt ′  α i - c ) Φ  ( α i c  ζ j  x jl  ( t - 1 )  n ijlt + X ilt ′  α i - c ) + β il  ( 1 - Φ  ( α i c  ζ j  x jl  ( t - 1 )  n ijlt + X ilt ′  α i - c ) ) ) , for   Y ijlt = 1  Z ijlt = 0 , for   Y ijlt = 0  f ( W ijlt |  *) ∝ T  runcated   N  ( α i c  ζ j  x jl  ( t - 1 )  n ijlt + X ilt ′  α i - c ) ;  f ( ζ j |  *) ∝ N  ( ( D T  D + 1 σ 2 ) - 1  ( D T  C + v σ 2 ) , ( D T  D + 1 σ 2 ) - 1 ) f  ( α i |  *) ∝ N  ( ( F T  F + Σ - 1 ) - 1  ( F T  E + Σ - 1  μ ) , ( F T  F + Σ - 1 ) - 1 )  I  ( α i c > 0 )  C = [ W ijlt - X ilt ′  α i - c ] ,  D = [ α i c  x il  ( t - 1 )  n ijt ] ,  E = [ W ijlt ] ,  F = [ ζ j  x ijl  ( t - 1 )  n ijt  X ilt ′ ] f  ( β il |  *) ∝ Bata ( c il + ∑ ( t | Z ilt = 0 )  Y ilt , d il + ∑ t  I  ( Z ilt = 0 ) - ∑ ( t | Z ilt = 0 )  Y ilt ) storing a number of sequences of sampled estimates for individual entities' infectivity, susceptibility, sensitivity and baseline infection risk (or baseline adoption likelihood); comparing the between and within sequence variances or calculating convergence statistics such as the Gelman-Rubin R to evaluate convergence, and; updating and determining the estimates of each individual entity's infectivity susceptibility, sensitivity and baseline infection risk (or adoption likelihood) until convergence. 13. The method of claim 11, wherein the likelihood maximization technique involves: calculating and maximizing the joint likelihood function for individual entity's infectivity, susceptibility and sensitivity conditional on the obtained data, in accordance with: max   L  ( ζ j , α i c , α i - c ) = ∏ j   f  ( ζ j )  ∏ i  ∏ l  ∏ t  P ijlt Y ijlt  ( 1 - P ijlt ) 1 - Y ijlt imposing restrictions on individual entities' infectivity as Σαc=1 and susceptibility ζ˜N (0,1); and determining each individual entity's susceptibility and sensitivity by solving equations in accordance with: ∑ j J   ∑ l  ∑ t  Y ijlt  x jl  ( t - 1 )  n ijlt  ∫ ζ j  p  ( ζ j | Y ijlt , α i c , α i - c , x jl  ( t - 1 ) , n ijlt , X ilt )   ζ j = ∑ j J   ∑ l  ∑ t  x jl  ( t - 1 )  n ijlt  ∫ ζ j  exp  ( α i c  ζ j  x jl  ( t - 1 )  n ijlt + X ilt ′  α i - c ) p  ( ζ j | Y ijlt , α i c , α i - c , x jl  ( t - 1 ) , n ijlt , X ilt ) 1 + exp  ( α i c  ζ j  x jl  ( t - 1 )  n ijlt + X ilt ′  α i - c )   ζ j  ∑ j J   ∑ l  ∑ t  Y ijlt  X ijlt  ∫ ζ i  p  ( ζ i | Y ijlt , α i c , α i - c , x jl  ( t - 1 ) , n ijlt , X ilt )   ζ j = ∑ j J   ∑ l  ∑ t  X ilt   1 ∫ exp  ( α i c  ζ j  x ij  ( t - 1 )  n ijlt + X ilt ′  α i - c ) p  ( ζ j | Y ijlt , α i c , α i - c , x jl  ( t - 1 ) , n ijlt , X ilt ) 1 + exp  ( α i c  ζ j  x jl  ( t - 1 )  n ijlt + X ilt ′  α i - c )   ζ j  … ∑ j J   ∑ l  ∑ t  Y ijlt  X iltk  ∫ ζ j  p  ( ζ j | Y ijlt , α i c , α i - c , x jl  ( t - 1 ) , n ijlt , X ilt )   ζ j = ∑ j J   ∑ l  ∑ t  X ilt   k   ∫ exp  ( α i c  ζ j  x ij  ( t - 1 )  n ijlt + X ilt ′  α i - c ) p  ( ζ j | Y ijlt , α i c , α i - c , x jl  ( t - 1 ) , n ijlt , X ilt ) 1 + exp  ( α i c  ζ j  x jl  ( t - 1 )  n ijlt + X ilt ′  α i - c )   ζ j  where p  ( ζ j | Y ijlt , α i c , a i - c , x jl  ( t - 1 ) , n ijlt , X ilt ) = Φ  ( ζ j )  ∏ i   ∏ l  ∏ t  P ijlt Y ijlt  ( 1 - P ijlt ) 1 - Y ijlt ∫ Φ  ( ζ j )  ∏ i   ∏ l  ∏ t  P ijlt Y ijlt  ( 1 - P ijlt ) 1 - Y ijlt   ζ j . 14. A computer implemented method or a knowledge discovery system that involves: analyzing sequential contagion events among multilaterally interacted individuals; using Bayesian learning or likelihood maximization techniques for estimating a latent variable model; and providing individual-level infectivity, susceptibility and baseline infection risk measurements for use in precise contagion control. 15. The method of claim 1, wherein the individual entities include: humans, animals, plants, organizations, particles and machines, etc. 16. The method of claim 1, wherein the biological or social contagions include: infectious diseases, fashions, product adoptions, service adoptions, financial shocks, riots, behaviors, and opinions, etc. 17. The system of claim 8, wherein the inferring is based on relating the conditional infection probability of individual entity with some indexes deduced from the sequential contagion occurrences of each individual entity or a group of selected individual entities. 18. The method of claim 8, wherein the learning is performed (or the instructions are conducted) randomly, at certain frequency or at a real-time basis. 19. The method of claim 1, wherein the environmental and observable factors include: temperature, humidity, wind speed, living conditions, product attributes, price, promotion, channel, entity characteristics, market characteristics, etc. 20. The system of claim 8, wherein the obtaining data is executed through searching or crawling the Web.