Modeling the impact of SARS-CoV-2 variants and vaccines on the spread of COVID-19.

The continuous mutation of SARS-CoV-2 opens the possibility of the appearance of new variants of the virus with important differences in its spreading characteristics, mortality rates, etc. On 14 December 2020, the United Kingdom reported a potentially more contagious coronavirus variant, present in that country, which is referred to as VOC 202012/01. On 18 December 2020, the South African government also announced the emergence of a new variant in a scenario similar to that of the UK, which is referred to as variant 501.V2. Another important milestone regarding this pandemic was the beginning, in December 2020, of vaccination campaigns in several countries. There are several vaccines, with different characteristics, developed by various laboratories and research centers. A natural question arises: what could be the impact of these variants and vaccines on the spread of COVID-19? Many models have been proposed to simulate the spread of COVID-19 but, to the best of our knowledge, none of them incorporates the effects of potential SARS-CoV-2 variants together with the vaccines in the spread of COVID-19. We develop here a θ - i j -SVEIHQRD mathematical model able to simulate the possible impact of this type of variants and of the vaccines, together with the main mechanisms influencing the disease spread. The model may be of interest for policy makers, as a tool to evaluate different possible future scenarios. We apply the model to the particular case of Italy (as an example of study case), showing different outcomes. We observe that the vaccines may reduce the infections, but they might not be enough for avoiding a new wave, with the current expected vaccination rates in that country, if the control measures are relaxed. Furthermore, a more contagious variant could increase significantly the cases, becoming the most common way of infection. We show how, even with the pandemic cases slowing down (with an effective reproduction number less than 1) and the disease seeming to be under control, the effective reproduction number of just the new variant may be greater than 1 and, eventually, the number of infections would increase towards a new disease wave. Therefore, a rigorous follow-up of the evolution of the number of infections with any potentially more dangerous new variant is of paramount importance at any stage of the pandemic.

A simple but complex enough θ -SIR type model to be used with COVID-19 real data. Application to the case of Italy.

Since the start of the COVID-19 pandemic in China many models have appeared in the literature, trying to simulate its dynamics. Focusing on modeling the biological and sociological mechanisms which influence the disease spread, the basic reference example is the SIR model. However, it is too simple to be able to model those mechanisms (including the three main types of control measures: social distancing, contact tracing and health system measures) to fit real data and to simulate possible future scenarios. A question, then, arises: how much and how do we need to complexify a SIR model? We develop a θ -SEIHQRD model, which may be the simplest one satisfying the mentioned requirements for arbitrary territories and can be simplified in particular cases. We show its very good performance in the Italian case and study different future scenarios.

Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China.

In this paper we develop a mathematical model for the spread of the coronavirus disease 2019 (COVID-19). It is a new θ-SEIHRD model (not a SIR, SEIR or other general purpose model), which takes into account the known special characteristics of this disease, as the existence of infectious undetected cases and the different sanitary and infectiousness conditions of hospitalized people. In particular, it includes a novel approach that considers the fraction θ of detected cases over the real total infected cases, which allows to study the importance of this ratio on the impact of COVID-19. The model is also able to estimate the needs of beds in hospitals. It is complex enough to capture the most important effects, but also simple enough to allow an affordable identification of its parameters, using the data that authorities report on this pandemic. We study the particular case of China (including Chinese Mainland, Macao, Hong-Kong and Taiwan, as done by the World Health Organization in its reports on COVID-19), the country spreading the disease, and use its reported data to identify the model parameters, which can be of interest for estimating the spread of COVID-19 in other countries. We show a good agreement between the reported data and the estimations given by our model. We also study the behavior of the outputs returned by our model when considering incomplete reported data (by truncating them at some dates before and after the peak of daily reported cases). By comparing those results, we can estimate the error produced by the model when identifying the parameters at early stages of the pandemic. Finally, taking into account the advantages of the novelties introduced by our model, we study different scenarios to show how different values of the percentage of detected cases would have changed the global magnitude of COVID-19 in China, which can be of interest for policy makers.

Implementation and validation of an economic module in the Be-FAST model to predict costs generated by livestock disease epidemics: Application to classical swine fever epidemics in Spain.

Be-FAST is a computer program based on a time-spatial stochastic spread mathematical model for studying the transmission of infectious livestock diseases within and between farms. The present work describes a new module integrated into Be-FAST to model the economic consequences of the spreading of classical swine fever (CSF) and other infectious livestock diseases within and between farms. CSF is financially one of the most damaging diseases in the swine industry worldwide. Specifically in Spain, the economic costs in the two last CSF epidemics (1997 and 2001) reached jointly more than 108 million euros. The present analysis suggests that severe CSF epidemics are associated with significant economic costs, approximately 80% of which are related to animal culling. Direct costs associated with control measures are strongly associated with the number of infected farms, while indirect costs are more strongly associated with epidemic duration. The economic model has been validated with economic information around the last outbreaks in Spain. These results suggest that our economic module may be useful for analysing and predicting economic consequences of livestock disease epidemics.

A multi-analysis approach for space-time and economic evaluation of risks related with livestock diseases: the example of FMD in Peru.

This study presents a multi-disciplinary decision-support tool, which integrates geo-statistics, social network analysis (SNA), spatial-stochastic spread model, economic analysis and mapping/visualization capabilities for the evaluation of the sanitary and socio-economic impact of livestock diseases under diverse epidemiologic scenarios. We illustrate the applicability of this tool using foot-and-mouth disease (FMD) in Peru as an example. The approach consisted on a flexible, multistep process that may be easily adapted based on data availability. The first module (mI) uses a geo-statistical approach for the estimation (if needed) of the distribution and abundance of susceptible population (in the example here, cattle, swine, sheep, goats, and camelids) at farm-level in the region or country of interest (Peru). The second module (mII) applies SNA for evaluating the farm-to-farm contact patterns and for exploring the structure and frequency of between-farm animal movements as a proxy for potential disease introduction or spread. The third module (mIII) integrates mI-II outputs into a spatial-stochastic model that simulates within- and between-farm FMD-transmission. The economic module (mIV) connects outputs from mI-III to provide an estimate of associated direct and indirect costs. A visualization module (mV) is also implemented to graph and map the outputs of module I-IV. After 1000 simulated epidemics, the mean (95% probability interval) number of outbreaks, infected animals, epidemic duration, and direct costs were 37 (1, 1164), 2152 (1, 13, 250), 63 days (0, 442), and US$ 1.2 million (1072, 9.5 million), respectively. Spread of disease was primarily local (<4.5km), but geolocation and type of index farm strongly influenced the extent and spatial patterns of an epidemic. The approach is intended to support decisions in the last phase of the FMD eradication program in Peru, in particular to inform and support the implementation of risk-based surveillance and livestock insurance systems that may help to prevent and control potential FMD virus incursions into Peru.

A novel spatial and stochastic model to evaluate the within and between farm transmission of classical swine fever virus: II validation of the model.

A new, recently published, stochastic and spatial model for the evaluation of classical swine fever virus (CSFV) spread into Spain has been validated by using several methods. Internal validity, sensitivity analysis, validation using historical data, comparison with other models and experiments on data validity were used to evaluate the overall reliability and consistency of the model. More than 100 modifications in input data and parameters were evaluated. Outputs were obtained after 1000 iterations for each new scenario of the model. As a result, the model was shown to be consistent, being the probability of infection by local spread, the time from infectious to clinical signs state, the probability of detection based on clinical signs at day t after detection of the index case outside the control and surveillance zones and the maximum number of farms to be depopulated at day t the parameters that have more influence (>10% of change) on the magnitude and duration of the epidemic. The combination of a within- and between-farm spread model was also shown to give significantly different results than using a purely between-farm spread model. Methods and results presented here were intended to be useful to better understand and apply the model, to identify key parameters for which it will be critical to have good estimates and to provide better support for prevention and control of future CSFV outbreaks.

A novel spatial and stochastic model to evaluate the within- and between-farm transmission of classical swine fever virus. I. General concepts and description of the model.

A new stochastic and spatial model was developed to evaluate the potential spread of classical swine fever virus (CSFV) within- and between-farms, and considering the specific farm-to-farm contact network. Within-farm transmission was simulated using a modified SI model. Between-farm transmission was assumed to occur by direct contacts (i.e. animal movement) and indirect contacts (i.e. local spread, vehicle and person contacts) and considering the spatial location of farms. Control measures dictated by the European legislation (i.e. depopulation of infected farms, movement restriction, zoning, surveillance, contact tracing) were also implemented into the model. Model experimentation was performed using real data from Segovia, one of the provinces with highest density of pigs in Spain, and results were presented using the mean, 95% probability intervals [95% PI] and risk maps. The estimated mean [95% PI] number of infected, quarantined and depopulated farms were 3 [1,17], 23 [0,76] and 115 [0,318], respectively. The duration of the epidemic was 63 [26,177] days and the most important way of transmission was associated with local spread (61.4% of the infections). Results were consistent with the spread of previous CSFV introductions into the study region. The model and results presented here may be useful for the decision making process and for the improvement of the prevention and control programmes for CSFV.