@article{doshi_mallick_eun_2023, title={Convergence of Bi-Virus Epidemic Models With Non-Linear Rates on Networks-A Monotone Dynamical Systems Approach}, volume={31}, ISSN={["1558-2566"]}, DOI={10.1109/TNET.2022.3213015}, abstractNote={We study convergence properties of competing epidemic models of the Susceptible-Infected-Susceptible ( $SIS$ ) type. The SIS epidemic model has seen widespread popularity in modelling the spreading dynamics of contagions such as viruses, infectious diseases, or even rumors/opinions over contact networks (graphs). We analyze the case of two such viruses spreading on overlaid graphs, with non-linear rates of infection spread and recovery. We call this the non-linear bi-virus model and, building upon recent results, obtain precise conditions for global convergence of the solutions to a trichotomy of possible outcomes: a virus-free state, a single-virus state, and to a coexistence state. Our techniques are based on the theory of monotone dynamical systems (MDS), in contrast to Lyapunov based techniques that have only seen partial success in determining convergence properties in the setting of competing epidemics. We demonstrate how the existing works have been unsuccessful in characterizing a large subset of the model parameter space for bi-virus epidemics, including all scenarios leading to coexistence of the epidemics. To the best of our knowledge, our results are the first in providing complete convergence analysis for the bi-virus system with non-linear infection and recovery rates on general graphs.}, number={3}, journal={IEEE-ACM TRANSACTIONS ON NETWORKING}, author={Doshi, Vishwaraj and Mallick, Shailaja and Eun, Do Young}, year={2023}, month={Jun}, pages={1187–1201} }
 @article{doshi_mallick_eun_2021, title={Competing Epidemics on Graphs - Global Convergence and Coexistence}, ISSN={["0743-166X"]}, DOI={10.1109/INFOCOM42981.2021.9488828}, abstractNote={The dynamics of the spread of contagions such as viruses, infectious diseases or even rumors/opinions over contact networks (graphs) have effectively been captured by the well known Susceptible-Infected-Susceptible (SIS) epidemic model in recent years. When it comes to competition between two such contagions spreading on overlaid graphs, their propagation is captured by so-called bi-virus epidemic models. Analysis of such dynamical systems involve the identification of equilibrium points and its convergence properties, which determine whether either of the viruses dies out, or both survive together. We demonstrate how the existing works are unsuccessful in characterizing a large subset of the model parameter space, including all parameters for which the competitiveness of the bi-virus system is significant enough to attain coexistence of the epidemics. In this paper, we fill in this void and obtain convergence results for the entirety of the model parameter space; giving precise conditions (necessary and sufficient) under which the system globally converges to a trichotomy of possible outcomes: a virus-free state, a single-virus state, and to a coexistence state – the first such result.}, journal={IEEE CONFERENCE ON COMPUTER COMMUNICATIONS (IEEE INFOCOM 2021)}, author={Doshi, Vishwaraj and Mallick, Shailaja and Eun, Do Young}, year={2021} }