We have developed mathematical tools to understand how disease propagate through networks. We have tested this feature with aviation networks. Recently, we have developed Kolkata transportation networks and checked how influenza-like diseases can be controlled by exploiting the specific wards of Kolkata Municipality.

How seizure propagates from one part of the brain to another: We target to construct the functional networks from the epileptic data and would like to investigate how the structure of the network changes if the route of epileptic focus changes from one subject to another.

How an optimal network and the dynamical ecological model can enhance the stability of an ecological patch or patches. We introduce here the dynamic Jacobian ensemble, which allows us to systematically investigate the fixed-point dynamics of a range of relevant network-based models. Within this ensemble, we find, complex systems exhibit discrete stability classes, from asymptotically unstable, where stability is unattainable, to sensitive, in which stability abides within a bounded range of the system's parameters.

Symmetry and Stability analysis, observation of first- and second-order synchronization transitions. Theoretical analysis based on Ott-Antonsen ansatz or master stability functions.

We study the role of networks, electrical coupling, and mixed populations on collective neuronal firing. The approach further motivates us to design a "model-free model" to predict the synchronous firing pattern in coupled neurons.