  In the present work the spread of epidemic is studied over complex networks
which are characterized by power law degree distribution of links and
heterogeneous rate of disease transmission. The random allocation of epidemic
transmission rates to the nodes results in the heterogeneity, which in turn
causes the segregation of nodes in terms of various sub populations. The aim of
the study is to gain microscopic insight into the effect of interactions among
various sub populations in the spreading processes of disease over such
networks. The discrete time Markov chain method based upon the susceptible
infected susceptible (SIS) model of diseases transmission has been used to
describe the spreading of epidemic over the networks. The study is
parameterized in terms of variable $\lambda$, defined as the number of contacts
a node makes with the fraction of its neighboring nodes. From the simulation
results, it is found that the spread of epidemic on such networks is critical
in terms of number of minimum contacts made by a node below which there is no
outbreak of disease. The degree of infection in these networks is assessed from
the size of epidemic defined in terms of fraction of infected nodes of the
total number and their corresponding level of infection. The results of the
parametric study demonstrates the dependence of the epidemic size upon number
of concurrent contacts made by a node ($\lambda$ ) and the average number of
links per node. In both these cases, the size of the epidemic is found to
increase with the corresponding increase in respective parameters.
