Assessing the risk of pandemic outbreaks across municipalities with mathematical descriptors based on age and mobility restrictions.

By March 14th 2022, Spain is suffering the sixth wave of the COVID-19 pandemic. All the previous waves have been intimately related to the degree of imposed mobility restrictions and its consequent release. Certain factors explain the incidence of the virus across regions revealing the weak locations that probably require some medical reinforcements. The most relevant ones relate with mobility restrictions by age and administrative competence, i.e., spatial constrains. In this work, we aim to find a mathematical descriptor that could identify the critical communities that are more likely to suffer pandemic outbreaks and, at the same time, to estimate the impact of different mobility restrictions. We analyze the incidence of the virus in combination with mobility flows during the so-called second wave (roughly from August 1st to November 30th, 2020) using a SEIR compartmental model. After that, we derive a mathematical descriptor based on linear stability theory that quantifies the potential impact of becoming a hotspot. Once the model is validated, we consider different confinement scenarios and containment protocols aimed to control the virus spreading. The main findings from our simulations suggest that the confinement of the economically non-active individuals may result in a significant reduction of risk, whose effects are equivalent to the confinement of the total population. This study is conducted across the totality of municipalities in Spain.

Risk evaluation at municipality level of a COVID-19 outbreak incorporating relevant geographic data: the study case of Galicia.

The COVID-19 pandemic was an inevitable outcome of a globalized world in which a highly infective disease is able to reach every country in a matter of weeks. While lockdowns and strong mobility restrictions have proven to be efficient to contain the exponential transmission of the virus, its pervasiveness has made it impossible for economies to maintain this kind of measures in time. Understanding precisely how the spread of the virus occurs from a territorial perspective is crucial not only to prevent further infections but also to help with policy design regarding human mobility. From the large spatial differences in the behavior of the virus spread we can unveil which areas have been more vulnerable to it and why, and with this information try to assess the risk that each community has to suffer a future outbreak of infection. In this work we have analyzed the geographical distribution of the cumulative incidence during the first wave of the pandemic in the region of Galicia (north western part of Spain), and developed a mathematical approach that assigns a risk factor for each of the different municipalities that compose the region. This risk factor is independent of the actual evolution of the pandemic and incorporates geographic and demographic information. The comparison with empirical information from the first pandemic wave demonstrates the validity of the method. Our results can potentially be used to design appropriate preventive policies that help to contain the virus.

Optimal control of the COVID-19 pandemic: controlled sanitary deconfinement in Portugal.

The COVID-19 pandemic has forced policy makers to decree urgent confinements to stop a rapid and massive contagion. However, after that stage, societies are being forced to find an equilibrium between the need to reduce contagion rates and the need to reopen their economies. The experience hitherto lived has provided data on the evolution of the pandemic, in particular the population dynamics as a result of the public health measures enacted. This allows the formulation of forecasting mathematical models to anticipate the consequences of political decisions. Here we propose a model to do so and apply it to the case of Portugal. With a mathematical deterministic model, described by a system of ordinary differential equations, we fit the real evolution of COVID-19 in this country. After identification of the population readiness to follow social restrictions, by analyzing the social media, we incorporate this effect in a version of the model that allow us to check different scenarios. This is realized by considering a Monte Carlo discrete version of the previous model coupled via a complex network. Then, we apply optimal control theory to maximize the number of people returning to "normal life" and minimizing the number of active infected individuals with minimal economical costs while warranting a low level of hospitalizations. This work allows testing various scenarios of pandemic management (closure of sectors of the economy, partial/total compliance with protection measures by citizens, number of beds in intensive care units, etc.), ensuring the responsiveness of the health system, thus being a public health decision support tool.

Incorporating social opinion in the evolution of an epidemic spread.

The evolution of the COVID19 pandemic worldwide has shown that the most common and effective strategy to control it used worldwide involve imposing mobility constrains to the population. A determinant factor in the success of such policies is the cooperation of the population involved but this is something, at least, difficult to measure. In this manuscript, we propose a method to incorporate in epidemic models empirical data accounting for the society predisposition to cooperate with the mobility restriction policies.