@article{mamis_farazmand_2024, title={Modeling correlated uncertainties in stochastic compartmental models}, volume={374}, ISSN={["1879-3134"]}, DOI={10.1016/j.mbs.2024.109226}, abstractNote={We consider compartmental models of communicable disease with uncertain contact rates. Stochastic fluctuations are often added to the contact rate to account for uncertainties. White noise, which is the typical choice for the fluctuations, leads to significant underestimation of the disease severity. Here, starting from reasonable assumptions on the social behavior of individuals, we model the contacts as a Markov process which takes into account the temporal correlations present in human social activities. Consequently, we show that the mean-reverting Ornstein–Uhlenbeck (OU) process is the correct model for the stochastic contact rate. We demonstrate the implication of our model on two examples: a Susceptibles-Infected-Susceptibles (SIS) model and a Susceptibles-Exposed-Infected-Removed (SEIR) model of the COVID-19 pandemic and compare the results to the available US data from the Johns Hopkins University database. In particular, we observe that both compartmental models with white noise uncertainties undergo transitions that lead to the systematic underestimation of the spread of the disease. In contrast, modeling the contact rate with the OU process significantly hinders such unrealistic noise-induced transitions. For the SIS model, we derive its stationary probability density analytically, for both white and correlated noise. This allows us to give a complete description of the model's asymptotic behavior as a function of its bifurcation parameters, i.e., the basic reproduction number, noise intensity, and correlation time. For the SEIR model, where the probability density is not available in closed form, we study the transitions using Monte Carlo simulations. Our modeling approach can be used to quantify uncertain parameters in a broad range of biological systems.}, journal={MATHEMATICAL BIOSCIENCES}, author={Mamis, Konstantinos and Farazmand, Mohammad}, year={2024}, month={Aug} }
 @article{mamis_farazmand_2023, title={Stochastic compartmental models of the COVID-19 pandemic must have temporally correlated uncertainties}, volume={479}, ISSN={["1471-2946"]}, DOI={10.1098/rspa.2022.0568}, abstractNote={Compartmental models are an important quantitative tool in epidemiology, enabling us to forecast the course of a communicable disease. However, the model parameters, such as the infectivity rate of the disease, are riddled with uncertainties, which has motivated the development and use of stochastic compartmental models. Here, we first show that a common stochastic model, which treats the uncertainties as white noise, is fundamentally flawed since it erroneously implies that greater parameter uncertainties will lead to the eradication of the disease. Then, we present a principled modelling of the uncertainties based on reasonable assumptions on the contacts of each individual. Using the central limit theorem and Doob’s theorem on Gaussian Markov processes, we prove that the correlated Ornstein–Uhlenbeck (OU) process is the appropriate tool for modelling uncertainties in the infectivity rate. We demonstrate our results using a compartmental model of the COVID-19 pandemic and the available US data from the Johns Hopkins University COVID-19 database. In particular, we show that the white noise stochastic model systematically underestimates the severity of the Omicron variant of COVID-19, whereas the OU model correctly forecasts the course of this variant. Moreover, using an SIS model of sexually transmitted disease, we derive an exact closed-form solution for the final distribution of infected individuals. This analytical result shows that the white noise model underestimates the severity of the pandemic because of unrealistic noise-induced transitions. Our results strongly support the need for temporal correlations in modelling of uncertainties in compartmental models of infectious disease.}, number={2269}, journal={PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES}, author={Mamis, Konstantinos and Farazmand, Mohammad}, year={2023}, month={Jan} }
 @article{mamis_farazmand_2021, title={Mitigation of rare events in multistable systems driven by correlated noise}, volume={104}, ISSN={["2470-0053"]}, url={https://doi.org/10.1103/PhysRevE.104.034201}, DOI={10.1103/PhysRevE.104.034201}, abstractNote={We consider rare transitions induced by colored noise excitation in multistable systems. We show that undesirable transitions can be mitigated by a simple time-delay feedback control if the control parameters are judiciously chosen. We devise a parsimonious method for selecting the optimal control parameters, without requiring any Monte Carlo simulations of the system. This method relies on a new nonlinear Fokker-Planck equation whose stationary response distribution is approximated by a rapidly convergent iterative algorithm. In addition, our framework allows us to accurately predict, and subsequently suppress, the modal drift and tail inflation in the controlled stationary distribution. We demonstrate the efficacy of our method on two examples, including an optical laser model perturbed by multiplicative colored noise.}, number={3}, journal={PHYSICAL REVIEW E}, author={Mamis, Konstantinos and Farazmand, Mohammad}, year={2021}, month={Sep} }