Role of Media and Effects of Infodemics and Escapes in the Spatial Spread of Epidemics: A Stochastic Multi-Region Model with Optimal Control Approach

Multi-region infectious disease prediction modeling based on spatio-temporal graph neural network and the dynamic model

Human mobility between different regions is a major factor in large-scale outbreaks of infectious diseases. Deep learning models incorporating infectious disease transmission dynamics for predicting the spread of multi-regional outbreaks due to human mobility have become a hot research topic. In this study, we incorporate the Graph Transformer Neural Network and graph learning mechanisms into a metapopulation SIR model to build a hybrid framework, Metapopulation Graph Transformer Neural Network (M-Graphormer), for high-dimensional parameter estimation and multi-regional epidemic prediction. The framework effectively solves the problem that existing models may lose some hidden spatial dependencies in the data when dealing with the dynamic graph structure of the network due to human mobility. We performed multi-wave infectious disease prediction in multiple regions based on real epidemic data. The results show that the framework is capable of performing high-dimensional parameter estimation and accurately predicting epidemic transmission dynamics in multiple regions even with low data quality. In addition, we retrospectively extrapolate the temporal evolution patterns of contact rate under different interventions implemented in different regions, reflecting the dynamics of intervention intensity and the need for flexibility in adjusting interventions in different regions. To provide early warning of infectious disease transmission, we retrospectively predicted the arrival time of infectious diseases using data from the early stages of outbreaks.

Pandæsim: An Epidemic Spreading Stochastic Simulator

Many methods have been used to model epidemic spreading. They include ordinary differential equation systems for globally homogeneous environments and partial differential equation systems to take into account spatial localisation and inhomogeneity. Stochastic differential equations systems have been used to model the inherent stochasticity of epidemic spreading processes. In our case study, we wanted to model the numbers of individuals in different states of the disease, and their locations in the country. Among the many existing methods we used our own variant of the well known Gillespie stochastic algorithm, along with the sub-volumes method to take into account the spatial localisation. Our algorithm allows us to easily switch from stochastic discrete simulation to continuous deterministic resolution using mean values. We applied our approaches on the study of the Covid-19 epidemic in France. The stochastic discrete version of Pandæsim showed very good correlations between the simulation results and the statistics gathered from hospitals, both on day by day and on global numbers, including the effects of the lockdown. Moreover, we have highlighted interesting differences in behaviour between the continuous and discrete methods that may arise in some particular conditions.

Optimal Propagating Fronts Using Hamilton-Jacobi Equations

The optimal handling of level sets associated to the solution of Hamilton-Jacobi equations such as the normal flow equation is investigated. The goal is to find the normal velocity minimizing a suitable cost functional that accounts for a desired behavior of level sets over time. Sufficient conditions of optimality are derived that require the solution of a system of nonlinear Hamilton-Jacobi equations. Since finding analytic solutions is difficult in general, the use of numerical methods to obtain approximate solutions is addressed by dealing with some case studies in two and three dimensions.

Optimal Impulse Vaccination Approach for an SIR Control Model with Short-Term Immunity

Vaccines are not administered on a continuous basis, but injections are practically introduced at discrete times often separated by an important number of time units, and this differs depending on the nature of the epidemic and its associated vaccine. In addition, especially when it comes to vaccination, most optimization approaches in the literature and those that have been subject to epidemic models have focused on treating problems that led to continuous vaccination schedules but their applicability remains debatable. In search of a more realistic methodology to resolve this issue, a control modeling design, where the control can be characterized analytically and then optimized, can definitely help to find an optimal regimen of pulsed vaccinations. Therefore, we propose a susceptible-infected-removed (SIR) hybrid epidemic model with impulse vaccination control and a compartment that represents the number of vaccinated individuals supposed to not acquire sufficient immunity to become permanently recovered due to the short-term effect of vaccines. A basic reproduction number, when the control is defined as a constant parameter, is calculated. Since we also need to find the optimal values of this impulse control when it is defined as a function of time, we start by stating a general form of an impulse version of Pontryagin’s maximum principle that can be adapted to our case, and then we apply it to our model. Finally, we provide our numerical simulations that are obtained via an impulse progressive-regressive iterative scheme with fixed intervals between impulse times (theoretical example of an impulse at each week), and we conclude with a discussion of our results.