The Role of Mobility in the Dynamics of the COVID-19 Epidemic in Andalusia.

Metapopulation models have been a popular tool for the study of epidemic spread over a network of highly populated nodes (cities, provinces, countries) and have been extensively used in the context of the ongoing COVID-19 pandemic. In the present work, we revisit such a model, bearing a particular case example in mind, namely that of the region of Andalusia in Spain during the period of the summer-fall of 2020 (i.e., between the first and second pandemic waves). Our aim is to consider the possibility of incorporation of mobility across the province nodes focusing on mobile-phone time-dependent data, but also discussing the comparison for our case example with a gravity model, as well as with the dynamics in the absence of mobility. Our main finding is that mobility is key toward a quantitative understanding of the emergence of the second wave of the pandemic and that the most accurate way to capture it involves dynamic (rather than static) inclusion of time-dependent mobility matrices based on cell-phone data. Alternatives bearing no mobility are unable to capture the trends revealed by the data in the context of the metapopulation model considered herein.

Backcasting COVID-19: a physics-informed estimate for early case incidence.

It is widely accepted that the number of reported cases during the first stages of the COVID-19 pandemic severely underestimates the number of actual cases. We leverage delay embedding theorems of Whitney and Takens and use Gaussian process regression to estimate the number of cases during the first 2020 wave based on the second wave of the epidemic in several European countries, South Korea and Brazil. We assume that the second wave was more accurately monitored, even though we acknowledge that behavioural changes occurred during the pandemic and region- (or country-) specific monitoring protocols evolved. We then construct a manifold diffeomorphic to that of the implied original dynamical system, using fatalities or hospitalizations only. Finally, we restrict the diffeomorphism to the reported cases coordinate of the dynamical system. Our main finding is that in the European countries studied, the actual cases are under-reported by as much as 50%. On the other hand, in South Korea-which had a proactive mitigation approach-a far smaller discrepancy between the actual and reported cases is predicted, with an approximately 18% predicted underestimation. We believe that our backcasting framework is applicable to other epidemic outbreaks where (due to limited or poor quality data) there is uncertainty around the actual cases.

Reaction-diffusion spatial modeling of COVID-19: Greece and Andalusia as case examples.

We examine the spatial modeling of the outbreak of COVID-19 in two regions: the autonomous community of Andalusia in Spain and the mainland of Greece. We start with a zero-dimensional (0D; ordinary-differential-equation-level) compartmental epidemiological model consisting of Susceptible, Exposed, Asymptomatic, (symptomatically) Infected, Hospitalized, Recovered, and deceased populations (SEAIHR model). We emphasize the importance of the viral latent period (reflected in the exposed population) and the key role of an asymptomatic population. We optimize model parameters for both regions by comparing predictions to the cumulative number of infected and total number of deaths, the reported data we found to be most reliable, via minimizing the ℓ^{2} norm of the difference between predictions and observed data. We consider the sensitivity of model predictions on reasonable variations of model parameters and initial conditions, and we address issues of parameter identifiability. We model both the prequarantine and postquarantine evolution of the epidemic by a time-dependent change of the viral transmission rates that arises in response to containment measures. Subsequently, a spatially distributed version of the 0D model in the form of reaction-diffusion equations is developed. We consider that, after an initial localized seeding of the infection, its spread is governed by the diffusion (and 0D model "reactions") of the asymptomatic and symptomatically infected populations, which decrease with the imposed restrictive measures. We inserted the maps of the two regions, and we imported population-density data into the finite-element software package COMSOL Multiphysics®, which was subsequently used to numerically solve the model partial differential equations. Upon discussing how to adapt the 0D model to this spatial setting, we show that these models bear significant potential towards capturing both the well-mixed, zero-dimensional description and the spatial expansion of the pandemic in the two regions. Veins of potential refinement of the model assumptions towards future work are also explored.

Lockdown measures and their impact on single- and two-age-structured epidemic model for the COVID-19 outbreak in Mexico.

The role of lockdown measures in mitigating COVID-19 in Mexico is investigated using a comprehensive nonlinear ODE model. The model includes both asymptomatic and presymptomatic populations with the latter leading to sickness (with recovery, hospitalization and death as possible outcomes). We consider situations involving the application of social-distancing and other intervention measures in the time series of interest. We find optimal parametric fits to the time series of deaths (only), as well as to the time series of deaths and cumulative infections. We discuss the merits and disadvantages of each approach, we interpret the parameters of the model and assess the realistic nature of the parameters resulting from the optimization procedure. Importantly, we explore a model involving two sub-populations (younger and older than a specific age), to more accurately reflect the observed impact as concerns symptoms and behavior in different age groups. For definiteness and to separate people that are (typically) in the active workforce, our partition of population is with respect to members younger vs. older than the age of 65. The basic reproduction number of the model is computed for both the single- and the two-population variant. Finally, we consider what would be the impact of partial lockdown (involving only the older population) and full lockdown (involving the entire population) on the number of deaths and cumulative infections.

Effects of Intrinsic and Extrinsic Host Mortality on Disease Spread.

The virulent effects of a pathogen on host fecundity and mortality (both intrinsic and extrinsic mortality due to predation) often increase with the age of infection. Age of infection often is also correlated with parasite fitness, in terms of the number of both infective propagules produced and the between-host transmission rate. We introduce a four-population partial differential equations (PDE) model to investigate the invasibility and prevalence of an obligately killing fungal parasite in a zooplankton host as they are embedded in an ecological network of predators and resources. Our results provide key insights into the role of ecological interactions that vary with the age of infection. First, selective predation, which is known both theoretically and empirically to reduce disease prevalence, does not always limit disease spread. This condition dependency relies on the timing and intensity of selective predation and how that interacts with the direct effects of the parasite on host mortality. Second, low host resources and intense predation can prevent disease spread, but once conditions allow the invasion of the parasite, the qualitative dynamics of the system do not depend on the intensity of the selective predation. Third, a comparison of the PDE model with a model based on ordinary differential equations (ODE model) reveals a parametrization for the ODE version that yields an endemic steady state and basic reproductive ratio that are identical to those in the PDE model. Our results highlight the complexity of resource-host-parasite-predator interactions and suggest the need for additional data-theory coupling exploring how community ecology influences the spread of infectious diseases.

Complex Daphnia interactions with parasites and competitors.

Species interactions can strongly influence the size and dynamics of epidemics in populations of focal hosts. The "dilution effect" provides a particularly interesting type of interaction from a biological standpoint. Diluters - other host species which resist infection but remove environmentally-distributed propagules of parasites (spores) - should reduce disease prevalence in focal hosts. However, diluters and focal hosts may compete for shared resources. This combination of positive (dilution) and negative (competition) effects could greatly complicate, even undermine, the benefits of dilution and diluter species from the perspective of the focal host. Motivated by an example from the plankton (i.e., zooplankton hosts, a fungal parasite, and algal resources), we study a model of dilution and competition. Our model reveals a suite of five results: • A diluter that is a superior competitor wipes out the host, regardless of parasitism. Although expected, this outcome is an ever-present danger in strategies that might use diluters to control disease. • If the diluter is an inferior competitor, it can reduce disease prevalence, despite the competition, as parameterized in our model. However, competition may also reduce density of susceptible hosts to levels below that seen in focal host-parasite systems alone. • As they decrease disease prevalence, diluters destabilize dynamics of the focal host and their resources. Thus, diluters undermine the stabilizing effects of disease. • The four species combination can generate very complex dynamics, including period-doubling bifurcations and torus (Neimark-Sacker) bifurcations. • At lower resource carrying capacity, the diluter's dilution of spores is 'helpful' to the focal host, i.e., dilution can elevate host density by reducing disease. But, as the resource carrying capacity increases further, the equilibrium density of the diluter increases while the density of the focal host decreases, despite competition. Namely, the negative effects of competition start to outweigh the positive effects of dilution from the perspective of equilibrium density of the focal host.

Stationary solutions for a modified Peyrard-Bishop DNA model with up to third-neighbor interactions.

We investigate a DNA model that takes into account stacking interactions with neighbors up to three bases away. The model is a generalization of the well-known Peyrard-Bishop (PB) model and is motivated by studies that suggest that nearest-neighbor models for base-pair interaction in a DNA chain might not be enough to capture the mechanism and dynamics of DNA base-pair opening. We study stationary solutions of the modified model and investigate their stability. A comparison with the PB model reveals that under a wide range of parameter values the main characteristics of the original model --such as the hyperbolicity of the equilibrium at the origin-- are preserved, but new types of stationary solutions emerge.

Healing length and bubble formation in DNA.

It has been suggested that thermally induced separations ("bubbles") of the DNA double-strand may play a role in the initiation of gene transcription, and an accurate understanding of the sequence dependence of thermal strand separation is therefore desirable. Based on the Peyrard-Bishop-Dauxois model, we show here that the bubble forming ability of DNA can be quantified in terms of a healing length L(n), defined as the length (number of base-pairs) over which a base-pair defect affects bubbles involving n consecutive base-pairs. The probability for a bubble of size n is demonstrated to be proportional to the number of adenine-thymine base-pairs found within this length. The method for calculating bubble probabilities in a given sequence derived from this notion requires several order of magnitude less numerical effort than direct evaluation.

Variational approach to the modulational instability.

We study the modulational stability of the nonlinear Schrödinger equation using a time-dependent variational approach. Within this framework, we derive ordinary differential equations (ODE's) for the time evolution of the amplitude and phase of modulational perturbations. Analyzing the ensuing ODE's, we rederive the classical modulational instability criterion. The case (relevant to applications in optics and Bose-Einstein condensation) where the coefficients of the equation are time dependent, is also examined.