Inference in epidemiological agent-based models using ensemble-based data assimilation.

To represent the complex individual interactions in the dynamics of disease spread informed by data, the coupling of an epidemiological agent-based model with the ensemble Kalman filter is proposed. The statistical inference of the propagation of a disease by means of ensemble-based data assimilation systems has been studied in previous works. The models used are mostly compartmental models representing the mean field evolution through ordinary differential equations. These techniques allow to monitor the propagation of the infections from data and to estimate several parameters of epidemiological interest. However, there are many important features which are based on the individual interactions that cannot be represented in the mean field equations, such as social network and bubbles, contact tracing, isolating individuals in risk, and social network-based distancing strategies. Agent-based models can describe contact networks at an individual level, including demographic attributes such as age, neighborhood, household, workplaces, schools, entertainment places, among others. Nevertheless, these models have several unknown parameters which are thus difficult to prescribe. In this work, we propose the use of ensemble-based data assimilation techniques to calibrate an agent-based model using daily epidemiological data. This raises the challenge of having to adapt the agent populations to incorporate the information provided by the coarse-grained data. To do this, two stochastic strategies to correct the model predictions are developed. The ensemble Kalman filter with perturbed observations is used for the joint estimation of the state and some key epidemiological parameters. We conduct experiments with an agent based-model designed for COVID-19 and assess the proposed methodology on synthetic data and on COVID-19 daily reports from Ciudad Autónoma de Buenos Aires, Argentina.

Vector-Borne Disease Models with Active and Inactive Vectors: A Simple Way to Consider Biting Behavior.

Vector-borne diseases are a serious public health problem, mosquitoes being one of the most important vectors. To analyze the dynamics of this type of disease, Ross-Macdonald models are commonly used. In its simplest formulation and the most common in scientific literature, it is assumed that all mosquitoes are biting at a given rate. To improve this general assumption, we developed a vector-borne disease model with active and inactive vectors as a simple way to incorporate the more general characteristics of mosquito feeding behavior into disease dynamics. Our objective is to obtain an estimate of the Ross-Macdonald biting rate from the feeding parameters that reproduce the same dynamics as the model with active and inactive vectors. Two different cases were analyzed: a SIS-SI model and a SIR-SI model with a single epidemic. Different methods to estimate the biting rate in the Ross-Macdonald model were proposed and analyzed. To compare the results of the models, different epidemiological indicators were considered. When the biting rate is estimated considering that both models have the same basic reproduction number, very similar disease dynamics are obtained. This method is a simple way to incorporate the mosquito feeding behavior into the standard Ross-Macdonald model.

Ross-Macdonald models: Which one should we use?

Ross-Macdonald models are the building blocks of most vector-borne disease models. Even for the same disease, different authors use different model formulations, but a study of the dynamical consequences of assuming different hypotheses is missing. In this work we present different formulations of the basic Ross-Macdonald model together with a careful discussion of the assumptions behind each model. The most general model presented is an agent based model for which arbitrary distributions for latency and infectious periods for both, host and vectors, is considered. At population level we also developed a deterministic Volterra integral equations model for which also arbitrary distributions in the waiting times are included. We compare the model solutions using different distributions for the infectious and latency periods using statistics, like the epidemic peak, or epidemic final size, to characterize the epidemic curves. The basic reproduction number (R0) for each formulation is computed and compared with empirical estimations obtained with the agent based models. The importance of considering realistic distributions for the latent and infectious periods is highlighted and discussed. We also show that seasonality is a key driver of vector-borne disease dynamics shaping the epidemic curve and its duration.