arXiv subjects

Urmee Maitra

Publications and source records attributed to Urmee Maitra.

4 recordsLinked to original sources

arXiv2025

Bi-Virus SIS Epidemic Propagation under Mutation and Game-theoretic Protection Adoption

We study a bi-virus susceptible-infected-susceptible (SIS) epidemic model in which individuals are either susceptible or infected with one of two virus strains, and consider mutation-driven transitions between strains. The general case of bi-directional mutation is first analyzed, where we characterize the disease-free equilibrium and establish its global asymptotic stability, as well as the existence, uniqueness, and stability of an endemic equilibrium. We then present a game-theoretic framework where susceptible individuals strategically choose whether to adopt protection or remain unprotected, to maximize their instantaneous payoffs. We derive Nash strategies under bi-directional mutation, and subsequently consider the special case of unidirectional mutation. In the latter case, we show that coexistence of both strains is impossible when mutation occurs from the strain with lower reproduction number and transmission rate to the other strain. Furthermore, we fully characterize the stationary Nash equilibrium (SNE) in the setting permitting coexistence, and examine how mutation rates influence protection adoption and infection prevalence at the SNE. Numerical simulations corroborate the analytical results, demonstrating that infection levels decrease monotonically with higher protection adoption, and highlight the impact of mutation rates and protection cost on infection state trajectories.

q-bio.PE↗

arXiv2025

Optimal protection and vaccination against epidemics with reinfection risk

We consider the problem of the optimal allocation of vaccination and protection measures for the Susceptible-Infected-Recovered-Infected (SIRI) epidemiological model, which generalizes the classical Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Susceptible (SIS) epidemiological models by allowing for reinfection. First, we introduce the controlled SIRI dynamical model, and discuss the existence and stability of the equilibrium points. Then, we formulate a finite-horizon optimal control problem where the cost of vaccination and protection is proportional to the mass of the population that adopts it. Our main contribution in this work arises from a detailed investigation into the existence/non-existence of singular control inputs, and establishing optimality of bang-bang controls. The optimality of bang-bang control is established by solving an optimal control problem with a running cost that is linear with respect to the input variables. The input variables are associated with actions including the vaccination and imposition of protective measures (e.g., masking or isolation). In contrast to most prior works, we rigorously establish the non-existence of singular controls (i.e., the optimality of bang-bang control for our SIRI model). Under the assumption that the reinfection rate exceeds the first-time infection rate, we characterize the structure of both the optimal control inputs, and establish that the vaccination control input admits a bang-bang structure. The numerical results provide valuable insights into the evolution of the disease spread under optimal control.

math.OC↗

arXiv2024

Optimal Bayesian Persuasion for Containing SIS Epidemics

We consider a susceptible-infected-susceptible (SIS) epidemic model in which a large group of individuals decide whether to adopt partially effective protection without being aware of their individual infection status. Each individual receives a signal which conveys noisy information about its infection state, and then decides its action to maximize its expected utility computed using its posterior probability of being infected conditioned on the received signal. We first derive the static signal which minimizes the infection level at the stationary Nash equilibrium under suitable assumptions. We then formulate an optimal control problem to determine the optimal dynamic signal that minimizes the aggregate infection level along the solution trajectory. We compare the performance of the dynamic signaling scheme with the optimal static signaling scheme, and illustrate the advantage of the former through numerical simulations.

eess.SY↗

arXiv2024

Bayesian Persuasion for Containing SIS Epidemics with Asymptomatic Infection

We investigate the strategic behavior of a large population of agents who decide whether to adopt a costly partially effective protection or remain unprotected against the susceptible-infected-susceptible epidemic. In contrast with most prior works on epidemic games, we assume that the agents are not aware of their true infection status while making decisions. We adopt the Bayesian persuasion framework where the agents receive a noisy signal regarding their true infection status, and maximize their expected utility computed using the posterior probability of being infected conditioned on the received signal. We characterize the stationary Nash equilibrium of this setting under suitable assumptions, and identify conditions under which partial information disclosure leads to a smaller proportion of infected individuals at the equilibrium compared to full information disclosure, and vice versa.

eess.SY↗