Title: –Epidemic spreading models on networks: Analysis and Control
Date: – 07/01/2019
Time: – 10:00 AM
Venue: – ESB 244
Speaker: – M. V. Surya Prakash (EE15S022)
Guide: – Dr. Arun D. Mahindrakar
The study and analysis of epidemic spreading models help in mitigating the propagation of a disease and itseradication. The problem of epidemic spreading on networks belongs to a more general class of problems:spreading processes on networks. The models studied in this article are Susceptible-Infected-Susceptible (SIS)model on a single layer network and Susceptible-Infected-Susceptible-Unaware-Aware-Unaware (SIS-UAU)model on a multiplex network, under the assumption that all the networks involved can be represented byconnected, undirected graphs. Multiplex networks are interacting two-layer networks having same size withdiﬀerent intra-layer connectivity.
The SIS model captures the infection spreading phenomenon where an individual can be in either of the two states: Susceptible(S) and Infected (I). The SIS-UAU model captures the simultaneous spreading of epidemic and awareness, and their interplay in a population. The possible ways to slow down the spread of the disease include providing treatment, vaccination, disease awareness campaigning, reducing interactions among individuals, etc. In this work, the treatment rate in SIS model, and the treatment and campaigning efforts in SIS-UAU model are considered as control inputs to each node in the network. The practical limitations on the control inputs give rise to an admissible control set. We formulate and solve an optimal control problem where the objective is to bring down the prevalence of disease in the population to a certain level in a prescribed time. As a precursor to solving this problem, we compute the reachable sets of the models, which paves the way for guaranteeing the existence of a solution to the optimal control problem. The solutions to the optimal control problem on two example networks are numerically obtained using direct discretization method.
All are cordially invited.