Perceptive movement of susceptible individuals with memory.

The perception of susceptible individuals naturally lowers the transmission probability of an infectious disease but has been often ignored. In this paper, we formulate and analyze a diffusive SIS epidemic model with memory-based perceptive movement, where the perceptive movement describes a strategy for susceptible individuals to escape from infections. We prove the global existence and boundedness of a classical solution in an n-dimensional bounded smooth domain. We show the threshold-type dynamics in terms of the basic reproduction number [Formula: see text]: when [Formula: see text], the unique disease-free equilibrium is globally asymptotically stable; when [Formula: see text], there is a unique constant endemic equilibrium, and the model is uniformly persistent. Numerical analysis exhibits that when [Formula: see text], solutions converge to the endemic equilibrium for slow memory-based movement and they converge to a stable periodic solution when memory-based movement is fast. Our results imply that the memory-based movement cannot determine the extinction or persistence of infectious disease, but it can change the persistence manner.

Mobility-Guided Estimation of COVID-19 Transmission Rates.

It is of critical importance to estimate changing disease-transmission rates and their dependence on population mobility. A common approach to this problem involves fitting daily transmission rates using a susceptible-exposed-infected-recovered-(SEIR) model (regularizing to avoid overfitting) and then computing the relationship between the estimated transmission rate and mobility. Unfortunately, there are often several very different transmission-rate trajectories that can fit the reported cases well, meaning that the choice of regularization determines the final solution (and thus the mobility-transmission rate relationship) selected by the SEIR model. Moreover, the classical approaches to regularization-penalizing the derivative of the transmission rate trajectory-do not correspond to realistic properties of pandemic spread. Consequently, models fitted using derivative-based regularization are often biased toward underestimating the current transmission rate and future deaths. In this work, we propose mobility-driven regularization of the SEIR transmission rate trajectory. This method rectifies the artificial regularization problem, produces more accurate and unbiased forecasts of future deaths, and estimates a highly interpretable relationship between mobility and the transmission rate. For this analysis, mobility data related to the coronavirus disease 2019 pandemic was collected by Safegraph (San Francisco, California) from major US cities between March and August 2020.

Epidemic modeling with heterogeneity and social diffusion.

We propose and analyze a family of epidemiological models that extend the classic Susceptible-Infectious-Recovered/Removed (SIR)-like framework to account for dynamic heterogeneity in infection risk. The family of models takes the form of a system of reaction-diffusion equations given populations structured by heterogeneous susceptibility to infection. These models describe the evolution of population-level macroscopic quantities S, I, R as in the classical case coupled with a microscopic variable f, giving the distribution of individual behavior in terms of exposure to contagion in the population of susceptibles. The reaction terms represent the impact of sculpting the distribution of susceptibles by the infection process. The diffusion and drift terms that appear in a Fokker-Planck type equation represent the impact of behavior change both during and in the absence of an epidemic. We first study the mathematical foundations of this system of reaction-diffusion equations and prove a number of its properties. In particular, we show that the system will converge back to the unique equilibrium distribution after an epidemic outbreak. We then derive a simpler system by seeking self-similar solutions to the reaction-diffusion equations in the case of Gaussian profiles. Notably, these self-similar solutions lead to a system of ordinary differential equations including classic SIR-like compartments and a new feature: the average risk level in the remaining susceptible population. We show that the simplified system exhibits a rich dynamical structure during epidemics, including plateaus, shoulders, rebounds and oscillations. Finally, we offer perspectives and caveats on ways that this family of models can help interpret the non-canonical dynamics of emerging infectious diseases, including COVID-19.

Correlated stochastic epidemic model for the dynamics of SARS-CoV-2 with vaccination.

In this paper, we propose a mathematical model to describe the influence of the SARS-CoV-2 virus with correlated sources of randomness and with vaccination. The total human population is divided into three groups susceptible, infected, and recovered. Each population group of the model is assumed to be subject to various types of randomness. We develop the correlated stochastic model by considering correlated Brownian motions for the population groups. As the environmental reservoir plays a weighty role in the transmission of the SARS-CoV-2 virus, our model encompasses a fourth stochastic differential equation representing the reservoir. Moreover, the vaccination of susceptible is also considered. Once the correlated stochastic model, the existence and uniqueness of a positive solution are discussed to show the problem's feasibility. The SARS-CoV-2 extinction, as well as persistency, are also examined, and sufficient conditions resulted from our investigation. The theoretical results are supported through numerical/graphical findings.

Limits of epidemic prediction using SIR models.

The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the model parameters based on noisy observations early in the outbreak, well before the epidemic reaches its peak. This allows prediction of the subsequent course of the epidemic and design of appropriate interventions. However, accurately inferring SIR model parameters in such scenarios is problematic. This article provides novel, theoretical insight on this issue of practical identifiability of the SIR model. Our theory provides new understanding of the inferential limits of routinely used epidemic models and provides a valuable addition to current simulate-and-check methods. We illustrate some practical implications through application to a real-world epidemic data set.

Adaptive SIR model with vaccination: simultaneous identification of rates and functions illustrated with COVID-19.

An Adaptive Susceptible-Infected-Removed-Vaccinated (A-SIRV) epidemic model with time-dependent transmission and removal rates is constructed for investigating the dynamics of an epidemic disease such as the COVID-19 pandemic. Real data of COVID-19 spread is used for the simultaneous identification of the unknown time-dependent rates and functions participating in the A-SIRV system. The inverse problem is formulated and solved numerically using the Method of Variational Imbedding, which reduces the inverse problem to a problem for minimizing a properly constructed functional for obtaining the sought values. To illustrate and validate the proposed solution approach, the present study used available public data for several countries with diverse population and vaccination dynamics-the World, Israel, The United States of America, and Japan.

Estimating the number of US children susceptible to measles resulting from COVID-19-related vaccination coverage declines.

Measles elimination hinges on vaccination coverage remaining above 95% to retain sufficient community protection. Recent declines in routine measles vaccinations due to the COVID-19 pandemic coupled with prior models indicating the country was close to the 92% herd immunity benchmark are a cause for concern. We evaluated population-level measles susceptibility in the US, including sensitivity analyses accounting for pandemic-related impacts on immunization. We estimated the number of children aged 0-18 currently susceptible to measles and modeled susceptibility proportions in decreased vaccination scenarios. Participants were respondents to the NIS-Teen survey between 2008 and 2017 that also had provider-verified vaccination documentation. The exposure of interest was vaccination with a measles-containing vaccine (MCV), and the age at which they were vaccinated for all doses given. Using age at vaccination, we estimated age-based probabilities of vaccination and modeled population levels of MCV immunization and immunity vs. susceptibility. Currently, 9,145,026 children (13.1%) are estimated to be susceptible to measles. With pandemic level vaccination rates, 15,165,221 children (21.7%) will be susceptible to measles if no attempt at catch-up is made, or 9,454,436 children (13.5%) if catch-up vaccinations mitigate the decline by 2-3%. Models based on increased vaccine hesitancy also show increased susceptibility at national levels, with a 10% increase in hesitancy nationally resulting in 14,925,481 children (21.37%) susceptible to measles, irrespective of pandemic vaccination levels. Current levels of measles immunity remain below herd immunity thresholds. If pandemic-era reductions in childhood immunization are not rectified, population-level immunity to measles is likely to decline further.

Mathematical epidemiologic and simulation modelling of first wave COVID-19 in Malaysia.

Since the first coronavirus disease 2019 (COVID-19) outbreak appeared in Wuhan, mainland China on December 31, 2019, the geographical spread of the epidemic was swift. Malaysia is one of the countries that were hit substantially by the outbreak, particularly in the second wave. This study aims to simulate the infectious trend and trajectory of COVID-19 to understand the severity of the disease and determine the approximate number of days required for the trend to decline. The number of confirmed positive infectious cases [as reported by Ministry of Health, Malaysia (MOH)] were used from January 25, 2020 to March 31, 2020. This study simulated the infectious count for the same duration to assess the predictive capability of the Susceptible-Infectious-Recovered (SIR) model. The same model was used to project the simulation trajectory of confirmed positive infectious cases for 80 days from the beginning of the outbreak and extended the trajectory for another 30 days to obtain an overall picture of the severity of the disease in Malaysia. The transmission rate, ß also been utilized to predict the cumulative number of infectious individuals. Using the SIR model, the simulated infectious cases count obtained was not far from the actual count. The simulated trend was able to mimic the actual count and capture the actual spikes approximately. The infectious trajectory simulation for 80 days and the extended trajectory for 110 days depicts that the inclining trend has peaked and ended and will decline towards late April 2020. Furthermore, the predicted cumulative number of infectious individuals tallies with the preparations undertaken by the MOH. The simulation indicates the severity of COVID-19 disease in Malaysia, suggesting a peak of infectiousness in mid-March 2020 and a probable decline in late April 2020. Overall, the study findings indicate that outbreak control measures such as the Movement Control Order (MCO), social distancing and increased hygienic awareness is needed to control the transmission of the outbreak in Malaysia.

Fetal programming of COVID-19: may the barker hypothesis explain the susceptibility of a subset of young adults to develop severe disease?

The risk stratification of young adults between subjects who will develop a mild form COVID-19 and subjects who will undergo a severe disease remains inaccurate. In this review, we propose that the Barker hypothesis might explain the increased susceptibility to severe forms of COVID-19 in subjects who underwent intrauterine growth restriction (IUGR). In this paper evidence indicating an association between a low birth weight and an adult phenotype which might favor a severe outcome of SARS-CoV-2 infection are presented: lower lung functional capacity; increased respiratory morbidity; changes in fibrinogen and Factor VII serum levels and dysregulation of the hemostasis and thrombosis system; acquisition of a pro-thrombotic phenotype; low nephron number, with decreased ability to sustain renal function and increased renal morbidity; heart remodeling, with a less efficient cardiac function; endothelial dysfunction, a risk factor for the insurgence of the multiple organ failure; remodeling of arteries, with changes in the elastic properties of the arterial wall, predisposing to the insurgence and progression of atherosclerosis; dysfunction of the innate immune system, a risk factor for immune diseases in adulthood. These data suggest that young and adult subjects born too small (IUGR) or too early (pre-terms) might represent a subgroup of "at risk subjects", more susceptible toward severe forms of COVID-19. Given that LBW may be considered a surrogate of IUGR, this phenotypic marker should be included among the indispensable clinical data collected in every patient presenting with SARS-COV-2 infection, irrespectively of his/her age.

Simulating the impacts of interregional mobility restriction on the spatial spread of COVID-19 in Japan.

A spatial susceptible-exposed-infectious-recovered (SEIR) model is developed to analyze the effects of restricting interregional mobility on the spatial spread of the coronavirus disease 2019 (COVID-19) infection in Japan. National and local governments have requested that residents refrain from traveling between prefectures during the state of emergency. However, the extent to which restricting interregional mobility prevents infection expansion is unclear. The spatial SEIR model describes the spatial spread pattern of COVID-19 infection when people commute or travel to a prefecture in the daytime and return to their residential prefecture at night. It is assumed that people are exposed to an infection risk during their daytime activities. The spatial spread of COVID-19 infection is simulated by integrating interregional mobility data. According to the simulation results, interregional mobility restrictions can prevent the geographical expansion of the infection. On the other hand, in urban prefectures with many infectious individuals, residents are exposed to higher infection risk when their interregional mobility is restricted. The simulation results also show that interregional mobility restrictions play a limited role in reducing the total number of infected individuals in Japan, suggesting that other non-pharmaceutical interventions should be implemented to reduce the epidemic size.

Transition to endemicity: Understanding COVID-19.

The emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and its associated disease, coronavirus disease 2019 (COVID-19), has caused a devastating pandemic worldwide. Here, we explain basic concepts underlying the transition from an epidemic to an endemic state, where a pathogen is stably maintained in a population. We discuss how the number of infections and the severity of disease change in the transition from the epidemic to the endemic phase and consider the implications of this transition in the context of COVID-19.

Effect of high and low risk susceptibles in the transmission dynamics of COVID-19 and control strategies.

In this study, we formulate and analyze a deterministic model for the transmission of COVID-19 and evaluate control strategies for the epidemic. It has been well documented that the severity of the disease and disease related mortality is strongly correlated with age and the presence of co-morbidities. We incorporate this in our model by considering two susceptible classes, a high risk, and a low risk group. Disease transmission within each group is modelled by an extension of the SEIR model, considering additional compartments for quarantined and treated population groups first and vaccinated and treated population groups next. Cross Infection across the high and low risk groups is also incorporated in the model. We calculate the basic reproduction number [Formula: see text] and show that for [Formula: see text] the disease dies out, and for [Formula: see text] the disease is endemic. We note that varying the relative proportion of high and low risk susceptibles has a strong effect on the disease burden and mortality. We devise optimal medication and vaccination strategies for effective control of the disease. Our analysis shows that vaccinating and medicating both groups is needed for effective disease control and the controls are not very sensitive to the proportion of the high and low risk populations.

[Evaluation of interventions during the COVID-19 pandemic: development of a model based on subpopulations with different contact rates]. / Evaluación de intervenciones durante la pandemia COVID-19: desarrollo de un modelo basado en subpoblaciones con distintas tasas de contacto.

Although multiple attempts have been made to mathematically model the current epidemic of SARS-CoV-2, the causative agent of coronavirus disease 2019 (COVID-19), few models have been conceived as accessible interactive tools for users from various backgrounds. The goal of this study was to develop a model that took into account the heterogeneity in contact rates within the population and to implement it in an accessible application allowing to estimate the impact of possible interventions based on available information. An extended version of the Susceptible-Exposed-Infected-Resistant (SEIR) model, named SEIR-HL, was developed, assuming a population divided into two subpopulations, with different contact rates. Additionally, a formula for the calculation of the basic reproduction number (R0) for a population divided into n subpopulations was proposed, where the contact rates for each subpopulation can be distinguished according to contact type or context. The predictions made by SEIR-HL were compared to those of SEIR, showing that the heterogeneity in contact rates can dramatically affect the dynamics of simulations, even when run from the same initial conditions and with the same parameters. SEIR-HL was used to predict the effect on the epidemic evolution of the displacement of individuals from high-contact positions to low-contact positions. Lastly, by way of example, SEIR-HL was applied to the analysis of the SARS-CoV-2 epidemic in Argentina and an example of the application of the R0 formula was also developed. Both the SEIR-HL model and an R0 calculator were computerized and made available to the community.

Modeling neutral viral mutations in the spread of SARS-CoV-2 epidemics.

Although traditional models of epidemic spreading focus on the number of infected, susceptible and recovered individuals, a lot of attention has been devoted to integrate epidemic models with population genetics. Here we develop an individual-based model for epidemic spreading on networks in which viruses are explicitly represented by finite chains of nucleotides that can mutate inside the host. Under the hypothesis of neutral evolution we compute analytically the average pairwise genetic distance between all infecting viruses over time. We also derive a mean-field version of this equation that can be added directly to compartmental models such as SIR or SEIR to estimate the genetic evolution. We compare our results with the inferred genetic evolution of SARS-CoV-2 at the beginning of the epidemic in China and found good agreement with the analytical solution of our model. Finally, using genetic distance as a proxy for different strains, we use numerical simulations to show that the lower the connectivity between communities, e.g., cities, the higher the probability of reinfection.

Susceptibility of lung cancer patients to COVID-19: A review of the pandemic data from multiple nationalities.

Several studies have highlighted that cancer patients tend to be more susceptible to develop severe infection and to die from COVID-19. Certain medical conditions such as immunosuppression, presence of comorbidities, and underlying pulmonary damage are possible determinants of disease severity, especially in lung cancer patients. While recent studies have shown that lung cancer is one of the most prevalent tumor types among COVID-19 cancer patients, we still have an incomplete view of how data from several countries work as a whole. The aim of this review was to investigate COVID-19 prevalence in lung cancer patient cohorts and their probability to develop severe illness and death when compared to nonlung cancer patients from multiple nationalities, including countries that have been the epicenters of the pandemic. We also focus on some intrinsic lung cancer features that might influence COVID-19 outcomes. An integrative view of the susceptibility of lung cancer patients might be especially relevant to assist physicians in evaluating the risks of COVID-19 in these patients, and to foster better decisions on treatment delay.

The interplay between environmental exposures and COVID-19 risks in the health of children.

BACKGROUND: An unusual feature of SARS-Cov-2 infection and the COVID-19 pandemic is that children are less severely affected than adults. This is especially paradoxical given the epidemiological links between poor air quality and increased COVID-19 severity in adults and that children are generally more vulnerable than adults to the adverse consequences of air pollution. OBJECTIVES: To identify gaps in knowledge about the factors that protect children from severe SARS-Cov-2 infection even in the face of air pollution, and to develop a transdisciplinary research strategy to address these gaps. METHODS: An international group of researchers interested in children's environmental health was invited to identify knowledge gaps and to develop research questions to close these gaps. DISCUSSION: Key research questions identified include: what are the effects of SAR-Cov-2 infection during pregnancy on the developing fetus and child; what is the impact of age at infection and genetic susceptibility on disease severity; why do some children with COVID-19 infection develop toxic shock and Kawasaki-like symptoms; what are the impacts of toxic environmental exposures including poor air quality, chemical and metal exposures on innate immunity, especially in the respiratory epithelium; what is the possible role of a "dirty" environment in conveying protection - an example of the "hygiene hypothesis"; and what are the long term health effects of SARS-Cov-2 infection in early life. CONCLUSION: A concerted research effort by a multidisciplinary team of scientists is needed to understand the links between environmental exposures, especially air pollution and COVID-19. We call for specific research funding to encourage basic and clinical research to understand if/why exposure to environmental factors is associated with more severe disease, why children appear to be protected, and how innate immune responses may be involved. Lessons learned about SARS-Cov-2 infection in our children will help us to understand and reduce disease severity in adults, the opposite of the usual scenario.

Optimal timing of one-shot interventions for epidemic control.

The interventions and outcomes in the ongoing COVID-19 pandemic are highly varied. The disease and the interventions both impose costs and harm on society. Some interventions with particularly high costs may only be implemented briefly. The design of optimal policy requires consideration of many intervention scenarios. In this paper we investigate the optimal timing of interventions that are not sustainable for a long period. Specifically, we look at at the impact of a single short-term non-repeated intervention (a "one-shot intervention") on an epidemic and consider the impact of the intervention's timing. To minimize the total number infected, the intervention should start close to the peak so that there is minimal rebound once the intervention is stopped. To minimise the peak prevalence, it should start earlier, leading to initial reduction and then having a rebound to the same prevalence as the pre-intervention peak rather than one very large peak. To delay infections as much as possible (as might be appropriate if we expect improved interventions or treatments to be developed), earlier interventions have clear benefit. In populations with distinct subgroups, synchronized interventions are less effective than targeting the interventions in each subcommunity separately.

Modelling suggests ABO histo-incompatibility may substantially reduce SARS-CoV-2 transmission.

Several independent datasets suggest blood type A is over-represented and type O under-represented among COVID-19 patients. However, blood group antigens appear not to be conventional susceptibility factors in that they do not affect disease severity, and the relative risk to non-O individuals is attenuated when population prevalence is high. Here, I model a scenario in which ABO transfusion incompatibility reduces the chance of a patient transmitting the virus to an incompatible recipient - thus in Western populations type A and AB individuals are "super-recipients" while type O individuals are "super-spreaders". This results in an offset in the timing of the epidemic among individuals of different blood types, and an increased relative risk to type A/AB patients that is most pronounced during early stages of the epidemic. However, once the majority of any given population is infected, the relative risk to each blood type approaches unity. Published data on COVID-19 prevalence from regions in the early stages of the SARS-CoV-2 epidemic suggests that if this model holds true, ABO incompatibility reduces virus transmissibility by at least 60 %. Exploring the implications of this model for vaccination strategies shows that paradoxically, targeted vaccination of either high-susceptibility type A/AB or "super-spreader" type O individuals is less effective than random vaccination at blocking community spread of the virus. Instead, the key is to maintain blood type diversity among the remaining susceptible individuals. Given the good agreement between this model and observational data on disease prevalence, the underlying biochemistry urgently requires experimental investigation.