An Embedded Multiscale Modelling to Guide Control and Elimination of Paratuberculosis in Ruminants.

In recent years, multiscale modelling approach has begun to receive an overwhelming appreciation as an appropriate technique to characterize the complexity of infectious disease systems. In this study, we develop an embedded multiscale model of paratuberculosis in ruminants at host level that integrates the within-host scale and the between-host. A key feature of embedded multiscale models developed at host level of organization of an infectious disease system is that the within-host scale and the between-host scale influence each other in a reciprocal (i.e., both) way through superinfection, that is, through repeated infection before the host recovers from the initial infectious episode. This key feature is demonstrated in this study through a multiscale model of paratuberculosis in ruminants. The results of this study, through numerical analysis of the multiscale model, show that superinfection influences the dynamics of paratuberculosis only at the start of the infection, while the MAP bacteria replication continuously influences paratuberculosis dynamics throughout the infection until the host recovers from the initial infectious episode. This is largely because the replication of MAP bacteria at the within-host scale sustains the dynamics of paratuberculosis at this scale domain. We further use the embedded multiscale model developed in this study to evaluate the comparative effectiveness of paratuberculosis health interventions that influence the disease dynamics at different scales from efficacy data.

Effect of non-pharmacological interventions on the COVID-19 epidemic in Saudi Arabia.

We quantified the potential impact of different social distancing and self-isolation scenarios on the coronavirus disease 2019 (COVID-19) pandemic trajectory in Saudi Arabia and compared the modelling results to the confirmed epidemic trajectory. Using the susceptible, exposed, infected, quarantined and self-isolated, requiring hospitalisation, recovered/immune individuals, fatalities model, we assessed the impact of a non-pharmacological interventions' subset. An unmitigated scenario (baseline), mitigation scenarios (25% reduction in social contact/twofold increase in self-isolation) and enhanced mitigation scenarios (50% reduction in social contact/twofold increase in self-isolation) were assessed and compared to the actual epidemic trajectory. For the unmitigated scenario, mitigation scenarios, enhanced mitigation scenarios and actual observed epidemic, the peak daily incidence rates (per 10 000 population) were 77.00, 16.00, 9.00 and 1.14 on days 71, 54, 35 and 136, respectively. The peak fatality rates were 35.00, 13.00, 5.00 and 0.016 on days 150, 125, 60 and 155, respectively. The R0 was 1.15, 1.14, 1.22 and 2.50, respectively. Aggressive implementation of social distancing and self-isolation contributed to the downward trend of the disease. We recommend using extensive models that comprehensively consider the natural history of COVID-19, social and behavioural patterns, age-specific data, actual network topology and population to elucidate the epidemic's magnitude and trajectory.

Improved estimation of time-varying reproduction numbers at low case incidence and between epidemic waves.

We construct a recursive Bayesian smoother, termed EpiFilter, for estimating the effective reproduction number, R, from the incidence of an infectious disease in real time and retrospectively. Our approach borrows from Kalman filtering theory, is quick and easy to compute, generalisable, deterministic and unlike many current methods, requires no change-point or window size assumptions. We model R as a flexible, hidden Markov state process and exactly solve forward-backward algorithms, to derive R estimates that incorporate all available incidence information. This unifies and extends two popular methods, EpiEstim, which considers past incidence, and the Wallinga-Teunis method, which looks forward in time. We find that this combination of maximising information and minimising assumptions significantly reduces the bias and variance of R estimates. Moreover, these properties make EpiFilter more statistically robust in periods of low incidence, where several existing methods can become destabilised. As a result, EpiFilter offers improved inference of time-varying transmission patterns that are advantageous for assessing the risk of upcoming waves of infection or the influence of interventions, in real time and at various spatial scales.

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.

Mitigation strategies and compliance in the COVID-19 fight; how much compliance is enough?

The U.S. with only 4% of the world's population, bears a disproportionate share of infections in the COVID-19 pandemic. To understand this puzzle, we investigate how mitigation strategies and compliance can work together (or in opposition) to reduce (or increase) the spread of COVID-19 infection. Building on the Oxford index, we create state-specific stringency indices tailored to U.S. conditions, to measure the degree of strictness of public mitigation measures. A modified time-varying SEIRD model, incorporating this Stringency Index as well as a Compliance Indicator is then estimated with daily data for a sample of 6 U.S. states: New York, New Hampshire, New Mexico, Colorado, Texas, and Arizona. We provide a simple visual policy tool to evaluate the various combinations of mitigation policies and compliance that can reduce the basic reproduction number to less than one, the acknowledged threshold in the epidemiological literature to control the pandemic. Understanding of this relationship by both the public and policy makers is key to controlling the pandemic. This tool has the potential to be used in a real-time, dynamic fashion for flexible policy options. Our methodology can be applied to other countries and has the potential to be extended to other epidemiological models as well. With this first step in attempting to quantify the factors that go into the "black box" of the transmission factor ß, we hope that our work will stimulate further research in the dual role of mitigation policies and compliance.

Optimal allocation of limited vaccine to minimize the effective reproduction number.

We examine the problem of allocating a limited supply of vaccine for controlling an infectious disease with the goal of minimizing the effective reproduction number Re. We consider an SIR model with two interacting populations and develop an analytical expression that the optimal vaccine allocation must satisfy. With limited vaccine supplies, we find that an all-or-nothing approach is optimal. For certain special cases, we determine the conditions under which the optimal Re is below 1. We present an example of vaccine allocation for COVID-19 and show that it is optimal to vaccinate younger individuals before older individuals to minimize Re if less than 59% of the population can be vaccinated. The analytical conditions we develop provide a simple means of determining the optimal allocation of vaccine between two population groups to minimize Re.

Digital proximity tracing on empirical contact networks for pandemic control.

Digital contact tracing is a relevant tool to control infectious disease outbreaks, including the COVID-19 epidemic. Early work evaluating digital contact tracing omitted important features and heterogeneities of real-world contact patterns influencing contagion dynamics. We fill this gap with a modeling framework informed by empirical high-resolution contact data to analyze the impact of digital contact tracing in the COVID-19 pandemic. We investigate how well contact tracing apps, coupled with the quarantine of identified contacts, can mitigate the spread in real environments. We find that restrictive policies are more effective in containing the epidemic but come at the cost of unnecessary large-scale quarantines. Policy evaluation through their efficiency and cost results in optimized solutions which only consider contacts longer than 15-20 minutes and closer than 2-3 meters to be at risk. Our results show that isolation and tracing can help control re-emerging outbreaks when some conditions are met: (i) a reduction of the reproductive number through masks and physical distance; (ii) a low-delay isolation of infected individuals; (iii) a high compliance. Finally, we observe the inefficacy of a less privacy-preserving tracing involving second order contacts. Our results may inform digital contact tracing efforts currently being implemented across several countries worldwide.

Evaluating the impact of curfews and other measures on SARS-CoV-2 transmission in French Guiana.

While general lockdowns have proven effective to control SARS-CoV-2 epidemics, they come with enormous costs for society. It is therefore essential to identify control strategies with lower social and economic impact. Here, we report and evaluate the control strategy implemented during a large SARS-CoV-2 epidemic in June-July 2020 in French Guiana that relied on curfews, targeted lockdowns, and other measures. We find that the combination of these interventions coincided with a reduction in the basic reproduction number of SARS-CoV-2 from 1.7 to 1.1, which was sufficient to avoid hospital saturation. We estimate that thanks to the young demographics, the risk of hospitalisation following infection was 0.3 times that of metropolitan France and that about 20% of the population was infected by July. Our model projections are consistent with a recent seroprevalence study. The study showcases how mathematical modelling can be used to support healthcare planning in a context of high uncertainty.

Model-based evaluation of school- and non-school-related measures to control the COVID-19 pandemic.

The role of school-based contacts in the epidemiology of SARS-CoV-2 is incompletely understood. We use an age-structured transmission model fitted to age-specific seroprevalence and hospital admission data to assess the effects of school-based measures at different time points during the COVID-19 pandemic in the Netherlands. Our analyses suggest that the impact of measures reducing school-based contacts depends on the remaining opportunities to reduce non-school-based contacts. If opportunities to reduce the effective reproduction number (Re) with non-school-based measures are exhausted or undesired and Re is still close to 1, the additional benefit of school-based measures may be considerable, particularly among older school children. As two examples, we demonstrate that keeping schools closed after the summer holidays in 2020, in the absence of other measures, would not have prevented the second pandemic wave in autumn 2020 but closing schools in November 2020 could have reduced Re below 1, with unchanged non-school-based contacts.

Exit strategies: optimising feasible surveillance for detection, elimination, and ongoing prevention of COVID-19 community transmission.

BACKGROUND: Following implementation of strong containment measures, several countries and regions have low detectable community transmission of COVID-19. We developed an efficient, rapid, and scalable surveillance strategy to detect remaining COVID-19 community cases through exhaustive identification of every active transmission chain. We identified measures to enable early detection and effective management of any reintroduction of transmission once containment measures are lifted to ensure strong containment measures do not require reinstatement. METHODS: We compared efficiency and sensitivity to detect community transmission chains through testing of the following: hospital cases; fever, cough and/or ARI testing at community/primary care; and asymptomatic testing; using surveillance evaluation methods and mathematical modelling, varying testing capacities, reproductive number (R) and weekly cumulative incidence of COVID-19 and non-COVID-19 respiratory symptoms using data from Australia. We assessed system requirements to identify all transmission chains and follow up all cases and primary contacts within each chain, per million population. RESULTS: Assuming 20% of cases are asymptomatic and 30% of symptomatic COVID-19 cases present for testing, with R = 2.2, a median of 14 unrecognised community cases (8 infectious) occur when a transmission chain is identified through hospital surveillance versus 7 unrecognised cases (4 infectious) through community-based surveillance. The 7 unrecognised community upstream cases are estimated to generate a further 55-77 primary contacts requiring follow-up. The unrecognised community cases rise to 10 if 50% of cases are asymptomatic. Screening asymptomatic community members cannot exhaustively identify all cases under any of the scenarios assessed. The most important determinant of testing requirements for symptomatic screening is levels of non-COVID-19 respiratory illness. If 4% of the community have respiratory symptoms, and 1% of those with symptoms have COVID-19, exhaustive symptomatic screening requires approximately 11,600 tests/million population using 1/4 pooling, with 98% of cases detected (2% missed), given 99.9% sensitivity. Even with a drop in sensitivity to 70%, pooling was more effective at detecting cases than individual testing under all scenarios examined. CONCLUSIONS: Screening all acute respiratory disease in the community, in combination with exhaustive and meticulous case and contact identification and management, enables appropriate early detection and elimination of COVID-19 community transmission. An important component is identification, testing, and management of all contacts, including upstream contacts (i.e. potential sources of infection for identified cases, and their related transmission chains). Pooling allows increased case detection when testing capacity is limited, even given reduced test sensitivity. Critical to the effectiveness of all aspects of surveillance is appropriate community engagement, messaging to optimise testing uptake and compliance with other measures.

Effect of mitigation measures on the spreading of COVID-19 in hard-hit states in the U.S.

State government-mandated social distancing measures have helped to slow the growth of the COVID-19 pandemic in the United States. Many of the current predictive models of the development of COVID-19, especially after mitigation efforts, partially rely on extrapolations from data collected in other countries. Since most states enacted stay-at-home orders towards the end of March, the resulting effects of social distancing should be reflected in the death and infection counts by the end of April. Using the data available through April 25th, we investigate the change in the infection rate due to the mitigation efforts and project death and infection counts through September 2020 for some of the most heavily impacted states: New York, New Jersey, Michigan, Massachusetts, Illinois, and Louisiana. We find that with the current mitigation efforts, five of those six states have reduced their base reproduction number to a value less than one, stopping the exponential growth of the pandemic. We also project different scenarios after the mitigation is relaxed.

Cost analysis of treatment strategies for the control of HSV-2 infection in the U.S.: A mathematical modeling-based case study.

Infection of Herpes Simplex Virus type 2 (HSV-2) is a lifelong sexually transmitted disease. According to the Center for Disease Control and Prevention (CDC), 11.9% of the United States (U.S.) population was infected with HSV-2 in 2015-2016. The HSV-2 pathogen establishes latent infections in neural cells and can reactivate causing lesions later in life, a strategy that increases pathogenicity and allows the virus to evade the immune system. HSV-2 infections are currently treated by Acyclovir only in the non-constitutional stage, marked by genital skin lesions and ulcers. However, patients in the constitutional stage expressing mild and common (with other diseases) symptoms, such as fever, itching and painful urination, remain difficult to detect and are untreated. In this study, we develop and analyze a mathematical model to study the transmission and control of HSV-2 among the U.S. population between the ages of 15-49 when there are options to treat individuals in different stages of their pathogenicity. In particular, the goals of this work are to study the effect on HSV-2 transmission dynamics and to evaluate and compare the cost-effectiveness of treating HSV-2 infections in both constitutional and non-constitutional stages (new strategy) against the current conventional treatment protocol for treating patients in the non-constitutional stage (current strategy). Our results distinguish model parameter regimes where each of the two treatment strategies can optimize the available resources and consequently gives the long-term reduced cost associated with each treatment and incidence. Moreover, we estimated that the public health cost of HSV-2 with the proposed most cost-effective treatment strategy would increase by approximately 1.63% in 4 years of implementation. However, in the same duration, early treatment via the new strategy will reduce HSV-2 incidence by 42.76% yearly and the reproduction number will decrease to 0.84 from its current estimate of 2.5. Thus, the proposed new strategy will be significantly cost-effective in controlling the transmission of HSV-2 if the strategy is properly implemented.

Global dynamics of SIR model with switched transmission rate.

We propose a new epidemiological model, based on the classical SIR model, taking additionally into account a switching prevention strategy. The model has two distinct thresholds that determine the beginning and the end of an intervention and two different transmission rates. We study the global dynamics of the proposed two-dimensional model.

El número reproductivo básico (R0): consideraciones para su aplicación en la salud pública / Unraveling R0: considerations for public health applications

Evaluamos el uso en la salud pública del número reproductivo básico (R0), por el cual se estima la velocidad con que una enfermedad puede propagarse en una población. Estas estimaciones son de gran interés en el campo de la salud pública como quedó de manifiesto en ocasión de la pandemia del 2009 por el virus gripal A (H1N1). Revisamos los métodos usados comúnmente para estimar el R0, examinamos su utilidad práctica y determinamos la forma en que las estimaciones de este parámetro epidemiológico pueden servir de fundamento para tomar decisiones relativas a las estrategias de mitigación. Por sí solo, el R0 es una medida insuficiente de la dinámica de las enfermedades infecciosas en las poblaciones; hay otros parámetros que pueden aportar información más útil. No obstante, la estimación del R0 en una población determinada es útil para entender la transmisión de una enfermedad en ella. Si se considera el R0 en el contexto de otros parámetros epidemiológicos importantes, su utilidad puede consistir en que permite conocer mejor un brote epidémico y preparar la respuesta de salud pública correspondiente.

We assessed public health use of R0, the basic reproduction number, which estimates the speed at which a disease is capable of spreading in a population. These estimates are of great public health interest, as evidenced during the 2009 influenza A (H1N1) vírus pandemic. We reviewed methods commonly used to estimate R0, examined their practical utility, and assessed how estimates of this epidemiological parameter can inform mitigation strategy decisions. In isolation, R0 is a suboptimal gauge of infectious disease dynamics across populations; other disease parameters may provide more useful information. Nonetheless, estimation of R0 for a particular population is useful for understanding transmission in the study population. Considered in the context of other epidemiologically important parameters, the value of R0 may lie in better understanding an outbreak and in preparing a public health response.

A model of bi-mode transmission dynamics of hepatitis C with optimal control.

In this paper, we present a rigorous mathematical analysis of a deterministic model for the transmission dynamics of hepatitis C. The model is suitable for populations where two frequent modes of transmission of hepatitis C virus, namely unsafe blood transfusions and intravenous drug use, are dominant. The susceptible population is divided into two distinct compartments, the intravenous drug users and individuals undergoing unsafe blood transfusions. Individuals belonging to each compartment may develop acute and then possibly chronic infections. Chronically infected individuals may be quarantined. The analysis indicates that the eradication and persistence of the disease is completely determined by the magnitude of basic reproduction number R(c). It is shown that for the basic reproduction number R(c) < 1, the disease-free equilibrium is locally and globally asymptotically stable. For R(c) > 1, an endemic equilibrium exists and the disease is uniformly persistent. In addition, we present the uncertainty and sensitivity analyses to investigate the influence of different important model parameters on the disease prevalence. When the infected population persists, we have designed a time-dependent optimal quarantine strategy to minimize it. The Pontryagin's Maximum Principle is used to characterize the optimal control in terms of an optimality system which is solved numerically. Numerical results for the optimal control are compared against the constant controls and their efficiency is discussed.

The influence of nurse cohorting on hand hygiene effectiveness.

BACKGROUND: Direct contact between health care staff and patients is generally considered to be the primary route by which most exogenously-acquired infections spread within and between wards. Handwashing is therefore perceived to be the single most important infection control measure that can be adopted, with the continuing high infection rates generally attributed to poor hand hygiene compliance. METHODS: Through the use of simple mathematical models, this paper demonstrates that under conditions of high patient occupancy or understaffing, handwashing alone is unlikely to prevent the transmission of infection. CONCLUSIONS: The study demonstrates that applying strict nurse cohorting in combination with good hygiene practice is likely to be a more effective method of reducing transmission of infection in hospitals.