How Infections Spread on Networks
In the present work, an attempt to investigate the spread of disease on networks has been made using the algorithm specified in the assignment. The algorithm described in Section 3 was used to simulate the Susceptible Infected Recovery (SIR) Dynamics on three different networks which were provided as part of the assignment and certain properties were measured of both the simulated infection as well as the network topology. The results of SIR dynamics are compared with those obtained on the same network using the Ordinary Differential Equations (ODE) method for different values of infection probability ‘b’ in Section 3. The ODE model treats the whole population as a whole in which individuals interact with each other with equal likelihood. In Section 4, the affect of different values of ‘b’ was investigated on the spread of infections in the network. The network topology was studied to determine which nodes in the network are the most important for spreading the infection. A number of network measures (5 different measures – Degree, Average Shortest Path Length, Betweenness Centrality, Average nearest neighbor degree and Average nearest neighbor Betweenness Centrality) were calculated for each of the nodes for b = 0.2 in the given networks and these were plotted against the size of infection in the simulation starting from that node in Section 5. In Section 6, the network measures discussed in section 5 are explored for three different values of ‘b’ and an attempt has been made to identify which measure is best at identifying influential spreaders for each of these values of ‘b’.