A lattice model for influenza spreading

A deterministic compartmental model for the transition between variants in the spread of Covid-19 in Italy

We propose a deterministic epidemic model to describe the transition between two variants of the same virus, through the combination of a series of realistic mechanisms such as partial cross immunity, waning immunity for vaccinated individuals and a novel data-based algorithm to describe the average immunological status of the population. The model is validated on the evolution of Covid-19 in Italy, during the period in which the transition between Delta and Omicron variant occurred, with very satisfactory agreement with the experimental data. According to our model, if the vaccine efficacy had been equal against Delta and Omicron variant infections, the transition would have been smoothed and the epidemic would have gone extinct. This circumstance confirms the fundamental role of vaccines in combating the epidemic, and the importance of identifying vaccines capable of intercepting new variants.

COVID-19 modeling based on real geographic and population data

BACKGROUND

: Intercity travel is one of the most important parameters for combating a pandemic. The ongoing COVID-19 pandemic has resulted in different computational studies involving intercity connections. In this study, the effects of intercity connections during an epidemic such as COVID-19 are evaluated using a new network model.

METHODS

This model considers the actual geographic neighborhood and population density data. This new model is applied to actual Turkish data by means of provincial connections and populations. A Monte Carlo algorithm with a hybrid lattice model is applied to a lattice with 8802 data points.

RESULTS

Around Monte Carlo step 70, the number of active cases in Türkiye reaches up to 8.0% of the total population, which is followed by a second wave at around Monte Carlo step 100. The number of active cases vanishes around Monte Carlo step 160. Starting with İstanbul, the epidemic quickly expands between steps 60 and 100. Simulation results fit the actual mortality data in Türkiye.

DISCUSSION

This model is quantitatively very efficient in modeling real-world COVID-19 epidemic data based on populations and geographical intercity connections, by means of estimating the number of deaths, disease spread, and epidemic termination.

Effects of lattice dilution on the nonequilibrium phase transition in the stochastic susceptible-infectious-recovered model

We investigate how site dilution, as would be introduced by immunization, affects the properties of the active-to-absorbing nonequilibrium phase transition in the paradigmatic susceptible-infectious-recovered (SIR) model on regular cubic lattices. According to the Harris criterion, the critical behavior of the SIR model, which is governed by the universal scaling exponents of the dynamic isotropic percolation (DyIP) universality class, should remain unaltered after introducing impurities. However, when the SIR reactions are simulated for immobile agents on two- and three-dimensional lattices subject to quenched disorder, we observe a wide crossover region characterized by varying effective exponents. Only after a sufficient increase of the lattice sizes does it become clear that the SIR system must transition from that crossover regime before the effective critical exponents asymptotically assume the expected DyIP values. We attribute the appearance of this exceedingly long crossover to a time lag in a complete recovery of small disconnected clusters of susceptible sites, which are apt to be generated when the system is prepared with Poisson-distributed quenched disorder. Finally, we demonstrate that this transient region becomes drastically diminished when we significantly increase the value of the recovery rate or enable diffusive agent mobility through short-range hopping.

Vaccination and variants: Retrospective model for the evolution of Covid-19 in Italy

The last year of Covid-19 pandemic has been characterized by the continuous chase between the vaccination campaign and the appearance of new variants that puts further obstacles to the possibility of eradicating the virus and returning to normality in a short period. In the present paper we develop a deterministic compartmental model to describe the evolution of the Covid-19 in Italy as a combined effect of vaccination campaign, new variant spreading and mobility restrictions. Particular attention is given to the mechanism of waning immunity, appropriately timed with respect to the effective progress of the vaccination campaign in Italy. We perform a retrospective analysis in order to explore the role that different mechanisms, such as behavioral changes, variation of the population mobility, seasonal variability of the virus infectivity, and spreading of new variants have had in shaping the epidemiological curve. We find that, in the large time window considered, the most relevant mechanism is the seasonal variation in the stability of the virus, followed by the awareness mechanism, that induces individuals to increase/relax self-protective measures when the number of active cases increases/decreases. The appearance of the Delta variant and the mobility variations have had instead only marginal effects. In absence of vaccines the emerging scenario would have been dramatic with a percentage difference in the number of total infections and total deaths, in both cases, larger than fifty per cent. The model also predicts the appearance of a more contagious variant (the Omicron variant) and its becoming dominant in January 2022.

Serious role of non-quarantined COVID-19 patients for random walk simulations

The infectious disease (COVID-19) causes serious damages and outbreaks. A large number of infected people have been reported in the world. However, such a number only represents those who have been tested; e.g. PCR test. We focus on the infected individuals who are not checked by inspections. The susceptible-infected-recovered (SIR) model is modified: infected people are divided into quarantined (Q) and non-quarantined (N) agents. Since N-agents behave like uninfected people, they can move around in a stochastic simulation. Both theory of well-mixed population and simulation of random-walk reveal that the total population size of Q-agents decrease in spite of increasing the number of tests. Such a paradox appears, when the ratio of Q exceeds a critical value. Random-walk simulations indicate that the infection hardly spreads, if the movement of all people is prohibited ("lockdown"). In this case the infected people are clustered and locally distributed within narrow spots. The similar result can be obtained, even when only non-infected people move around. However, when both N-agents and uninfected people move around, the infection spreads everywhere. Hence, it may be important to promote the inspections even for asymptomatic people, because most of N-agents are mild or asymptomatic.

The effect of weekend curfews on epidemics: a Monte Carlo simulation

The ongoing COVID-19 pandemic is being responded with various methods, applying vaccines, experimental treatment options, total lockdowns or partial curfews. Weekend curfews are among the methods for reducing the number of infected persons, and this method is practically applied in some countries such as Turkey. In this study, the effect of weekend curfews on reducing the spread of a contagious disease, such as COVID-19, is modeled using a Monte Carlo algorithm with a hybrid lattice model. In the simulation setup, a fictional country with three towns and 26,610 citizens were used as a model. Results indicate that applying a weekend curfew reduces the ratio of ill cases from 0.23 to 0.15. The results also show that applying personal precautions such as social distancing is important for reducing the number of cases and deaths. If the probability of disease spread can be reduced to 0.1, in that case, the death ratio can be minimized down to 0.

Social distancing and epidemic resurgence in agent-based susceptible-infectious-recovered models

Once an epidemic outbreak has been effectively contained through non-pharmaceutical interventions, a safe protocol is required for the subsequent release of social distancing restrictions to prevent a disastrous resurgence of the infection. We report individual-based numerical simulations of stochastic susceptible-infectious-recovered model variants on four distinct spatially organized lattice and network architectures wherein contact and mobility constraints are implemented. We robustly find that the intensity and spatial spread of the epidemic recurrence wave can be limited to a manageable extent provided release of these restrictions is delayed sufficiently (for a duration of at least thrice the time until the peak of the unmitigated outbreak) and long-distance connections are maintained on a low level (limited to less than five percent of the overall connectivity).

A biological control model to manage the vector and the infection of Xylella fastidiosa on olive trees

Xylella fastidiosa pauca ST53 is the bacterium responsible for the Olive Quick Decline Syndrome that has killed millions of olive trees in Southern Italy. A recent work demonstrates that a rational integration of vector and transmission control measures, into a strategy based on chemical and physical control means, can manage Xylella fastidiosa invasion and impact below an acceptable economic threshold. In the present study, we propose a biological alternative to the chemical control action, which involves the predetermined use of an available natural enemy of Philaenus spumarius, i.e., Zelus renardii, for adult vector population and infection biocontrol. The paper combines two different approaches: a laboratory experiment to test the predation dynamics of Zelus renardii on Philaenus spumarius and its attitude as candidate for an inundation strategy; a simulated experiment of inundation, to preliminary test the efficacy of such strategy, before eventually proceeding to an in-field experimentation. With this double-fold approach we show that an inundation strategy with Zelus renardii has the potential to furnish an efficient and "green" solution to Xylella fastidiosa invasion, with a reduction of the pathogen incidence below 10%. The biocontrol model presented here could be promising for containing the impact and spread of Xylella fastidiosa, after an in-field validation of the inundation technique. Saving the fruit orchard, the production and the industry in susceptible areas could thus become an attainable goal, within comfortable parameters for sustainability, environmental safety, and effective plant health protection in organic orchard management.

Why should we apply ABM for decision analysis for infectious diseases?-An example for dengue interventions

For the evaluation of infectious-diseases interventions, the transmissible nature of such diseases plays a central role. Agent-based models (ABM) allow for dynamic transmission modeling but publications are limited. We aim to provide an overview of important characteristics of ABM for decision-analytic modeling of infectious diseases. A case study of dengue epidemics illustrates model characteristics, conceptualization, calibration and model analysis. First, major characteristics of ABM are outlined and discussed based on ISPOR and ISPOR-SMDM Good Practice guidelines. Second, in our case study, we modeled a dengue outbreak in Cebu City (Philippines) to assess the impact interventions to control the relative growth of the mosquito population. Model outcomes include prevalence and incidence of infected persons. The modular ABM simulates persons and mosquitoes over an annual time horizon considering daily time steps. The model was calibrated and validated. ABM is a dynamic, individual-level modeling approach that is capable to reproduce direct and indirect effects of interventions for infectious diseases. The ability to replicate emerging behavior and to include human behavior or the behavior of other agents is a distinguishing modeling characteristic (e.g., compared to Markov models). Modeling behavior may, however, require extensive calibration and validation. The analyzed hypothetical effectiveness of dengue interventions showed that a reduced human-mosquito ratio of 1:2.5 during rainy seasons leads already to a substantial decrease of infected persons. ABM can support decision-analyses for infectious diseases including disease dynamics, emerging behavior, and providing a high level of reusability due to modularity.

A lattice model to manage the vector and the infection of the Xylella fastidiosa on olive trees

Since October 2013 a new devastating plant disease, known as Olive Quick Decline Syndrome, has been killing most of the olive trees distributed in Apulia, South Italy. Xylella fastidiosa pauca ST53 is the plant pathogenic bacterium responsible for the disease, and the adult Meadow Spittlebug, Philaenus spumarius (L.) (Hemiptera Aphrophoridae), is its main vector. This study proposes a lattice model for the pathogen invasion of olive orchard aimed at identifying an appropriate strategy for arresting the infection, built on the management of the vector throughout its entire life cycle. In our model the olive orchard is depicted as a simple square lattice with olive trees and herbaceous vegetation distributed on the lattice sites in order to mimic the typical structure of an olive orchard; adult vectors are represented by particles moving on the lattice according to rules dictated by the interplay between vector and vegetation life cycles or phenology; the transmission process of the bacterium is regulated by a stochastic Susceptible, Infected and Removed model. On this baseline model, we build-up a proper Integrated Pest Management strategy based on tailoring, timing, and tuning of available control actions. We demonstrate that it is possible to reverse the hitherto unstoppable Xylella fastidiosa pauca ST53 invasion, by a rational vector and transmission control strategy.

Real-time predictive seasonal influenza model in Catalonia, Spain

Influenza surveillance is critical to monitoring the situation during epidemic seasons and predictive mathematic models may aid the early detection of epidemic patterns. The objective of this study was to design a real-time spatial predictive model of ILI (Influenza Like Illness) incidence rate in Catalonia using one- and two-week forecasts. The available data sources used to select explanatory variables to include in the model were the statutory reporting disease system and the sentinel surveillance system in Catalonia for influenza incidence rates, the official climate service in Catalonia for meteorological data, laboratory data and Google Flu Trend. Time series for every explanatory variable with data from the last 4 seasons (from 2010–2011 to 2013–2014) was created. A pilot test was conducted during the 2014–2015 season to select the explanatory variables to be included in the model and the type of model to be applied. During the 2015–2016 season a real-time model was applied weekly, obtaining the intensity level and predicted incidence rates with 95% confidence levels one and two weeks away for each health region. At the end of the season, the confidence interval success rate (CISR) and intensity level success rate (ILSR) were analysed. For the 2015–2016 season a CISR of 85.3% at one week and 87.1% at two weeks and an ILSR of 82.9% and 82% were observed, respectively. The model described is a useful tool although it is hard to evaluate due to uncertainty. The accuracy of prediction at one and two weeks was above 80% globally, but was lower during the peak epidemic period. In order to improve the predictive power, new explanatory variables should be included.

Adaptive diversification in heterogeneous environments

The role of environmental heterogeneity in the evolution of biological diversity has been studied only for simple types of heterogeneities and dispersals. This article broadens previous results by considering heterogeneities and dispersals that are structured by several environmental factors. It studies the evolution of a metapopulation, living in a network of patches connected by dispersal, under the effects of mutation, selection and migration. First, it is assumed that patches are equally connected and that they carry habitats characterized by several factors exerting selection pressures on several individual traits. Habitat factors may vary in the environment independently or they may be correlated. It is shown that correlations between habitat factors promote adaptive diversification and that this effect may be modified by trait interactions on survival. Then, it is assumed that patches are structured by two crossed factors, called the row and column factors, such that patches are more connected when they occur in the same row or in the same column. Environmental patterns in which each habitat appears in each row the same number of times and appears in each column the same number of times are found to hinder adaptive diversification.

Multiple Lattice Model for Influenza Spreading

Behavioral differences among age classes, together with the natural tendency of individuals to prefer contacts with individuals of similar age, naturally point to the existence of a community structure in the population network, in which each community can be identified with a different age class. Data on age-dependent contact patterns also reveal how relevant is the role of the population age structure in shaping the spreading of an infectious disease. In the present paper we propose a simple model for epidemic spreading, in which a contact network with an intrinsic community structure is coupled with a simple stochastic SIR model for the epidemic spreading. The population is divided in 4 different age-communities and hosted on a multiple lattice, each community occupying a specific age-lattice. Individuals are allowed to move freely to nearest neighbor empty sites on the age-lattice. Different communities are connected with each other by means of inter-lattices edges, with a different number of external links connecting different age class populations. The parameters of the contact network model are fixed by requiring the simulated data to fully reproduce the contact patterns matrices of the Polymod survey. The paper shows that adopting a topology which better implements the age-class community structure of the population, one gets a better agreement between experimental contact patterns and simulated data, and this also improves the accordance between simulated and experimental data on the epidemic spreading.

Disease prediction models and operational readiness

The objective of this manuscript is to present a systematic review of biosurveillance models that operate on select agents and can forecast the occurrence of a disease event. We define a disease event to be a biological event with focus on the One Health paradigm. These events are characterized by evidence of infection and or disease condition. We reviewed models that attempted to predict a disease event, not merely its transmission dynamics and we considered models involving pathogens of concern as determined by the US National Select Agent Registry (as of June 2011). We searched commercial and government databases and harvested Google search results for eligible models, using terms and phrases provided by public health analysts relating to biosurveillance, remote sensing, risk assessments, spatial epidemiology, and ecological niche modeling. After removal of duplications and extraneous material, a core collection of 6,524 items was established, and these publications along with their abstracts are presented in a semantic wiki at http://BioCat.pnnl.gov. As a result, we systematically reviewed 44 papers, and the results are presented in this analysis. We identified 44 models, classified as one or more of the following: event prediction (4), spatial (26), ecological niche (28), diagnostic or clinical (6), spread or response (9), and reviews (3). The model parameters (e.g., etiology, climatic, spatial, cultural) and data sources (e.g., remote sensing, non-governmental organizations, expert opinion, epidemiological) were recorded and reviewed. A component of this review is the identification of verification and validation (V&V) methods applied to each model, if any V&V method was reported. All models were classified as either having undergone Some Verification or Validation method, or No Verification or Validation. We close by outlining an initial set of operational readiness level guidelines for disease prediction models based upon established Technology Readiness Level definitions.

Lattice model for influenza spreading with spontaneous behavioral changes

Individual behavioral response to the spreading of an epidemic plays a crucial role in the progression of the epidemic itself. The risk perception induces individuals to adopt a protective behavior, as for instance reducing their social contacts, adopting more restrictive hygienic measures or undergoing prophylaxis procedures. In this paper, starting with a previously developed lattice-gas SIR model, we construct a coupled behavior-disease model for influenza spreading with spontaneous behavioral changes. The focus is on self-initiated behavioral changes that alter the susceptibility to the disease, without altering the contact patterns among individuals. Three different mechanisms of awareness spreading are analyzed: the local spreading due to the presence in the neighborhood of infective individuals; the global spreading due to the news published by the mass media and to educational campaigns implemented at institutional level; the local spreading occurring through the "thought contagion" among aware and unaware individuals. The peculiarity of the present approach is that the awareness spreading model is calibrated on available data on awareness and concern of the population about the risk of contagion. In particular, the model is validated against the A(H1N1) epidemic outbreak in Italy during the 2009/2010 season, by making use of the awareness data gathered by the behavioral risk factor surveillance system (PASSI). We find that, increasing the accordance between the simulated awareness spreading and the PASSI data on risk perception, the agreement between simulated and experimental epidemiological data improves as well. Furthermore, we show that, within our model, the primary mechanism to reproduce a realistic evolution of the awareness during an epidemic, is the one due to globally available information. This result highlights how crucial is the role of mass media and educational campaigns in influencing the epidemic spreading of infectious diseases.