Here is what I need
1. Algorithm (conceptual approach to this solution (P) ), modelling approach, sample data elements to compute the probability. I am currently using R programming environment.
Within the context of Network Analysis the patterns by which epidemics spread through groups of people is determined not just by the properties of the pathogen carrying it — including its contagiousness, the length of its infectious period, and its severity — but also by network structures within the population it is affecting. The social network within a population — recording who knows whom — determines a lot about how the disease is likely to spread from one person to another. But more generally, the opportunities for a disease to spread are given by a contact network: there is a node for each person, and an edge if two people come into contact with each other in a way that makes it possible for the disease to spread from one to the other. This suggests that accurately modeling the underlying network is crucial to understanding the spread of an epidemic. Contact networks are also important in understanding how diseases spread through animal populations
The pathogen and the network are closely intertwined, even within the same population, the contact networks for two different diseases can have very different structures, depending on the diseases’ respective modes of transmission. For a highly contagious disease, involving airborne transmission based on coughs and sneezes, the contact network will include a huge number of links, including any pair of people who sat together on a bus or an airplane. For a disease requiring close contact, or a sexually transmitted disease, the contact network will be much sparser, with many fewer pairs of people connected by links.
Technical Merit - Disease and the Network that transmit them
Connections to the Diffusion of Ideas and Behaviors. There are clear connections between epidemic disease and the diffusion of ideas through social networks. Both diseases and ideas can spread from person to person, across similar kinds of networks that connect people, and in this respect, they exhibit very similar structural mechanisms — to the extent that the spread of ideas is often referred to as “social contagion”
We begin with perhaps the simplest model of contagion, which we refer to as a
Branching process model. It works as follows.
- (First wave.) Suppose that a person carrying a new disease enters a population, and transmits it to each person he meets independently with a probability of p. Further, suppose that he meets k people while he is contagious; let’s call these k people the first wave of the epidemic. Based on the random transmission of the disease from the initial person, some of the people in the first wave may get infected with the disease, while others may not.
- (Second wave.) Now, each person in the first wave goes out into the population and meets k different people, resulting in a second wave of k · k = k 2 people. Each infected person in the first wave passes the disease independently to each of the k second-wave people they meet, again independently with probability p.
- (Subsequent waves.) Further waves are formed in the same way, by having each person in the current wave meet k new people, passing the disease to each independently with probability p.
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