The emergence and re-emergence of infectious diseases has been a global cause of concern in the past few decades. Previous research in the field has revealed that human connectivity and mobility behaviour play a major role in the spreading of an infectious disease. In this work, we propose multi-patch models that take into account the effects of human mobility on the evolution of disease dynamics in a multi-population environment. In particular, we develop SEIRS multi-patch and multi-group epidemic models, extending the work of [1] and [2] to practically account for distinct epidemiological-status-dependent mobilities in each patch. We rigorously show that the disease free equilibria (DFE) for both models are stable when R0 ≤ 1. We also prove that the models have a unique endemic asymptotically stable equilibrium when R0 > 1. We also introduce new local reproduction numbers from the point of view of the sub populations, and establish some important relation between them and the global reproduction number. Various numerical simulations are conducted to study the effects of mobility and the residence time matrix on the evolution of the disease in individual patches and the overall environment.

It is often necessary to introduce the main characteristics of population mobility dynamics to model critical social phenomena such as the economy, violence, transmission of information, or infectious diseases. In this work, we focus on modeling and inferring urban population mobility using the geospatial data of its inhabitants. The objective is to estimate mobility and times inhabitants spend in the areas of interest, such as zip codes and census geographical areas. The proposed method uses the Brownian bridge model for animal movement in ecology. We illustrate its possible applications using mobile phone GPS data in 2020 from the city of Hermosillo, Sonora, in Mexico. We incorporate the estimated residence-mobility matrix into a multi-patch compartmental SEIR model to assess the effect of mobility changes due to governmental interventions.

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