THE COMPUTATION OF REPRODUCTION NUMBERS FOR THE ENVIRONMENT-HOST-ENVIRONMENT CHOLERA TRANSMISSION DYNAMICS

2020 ◽  
Vol 28 (02) ◽  
pp. 183-231
Author(s):  
ANTONELLA LUPICA ◽  
ABBA B. GUMEL ◽  
ANNUNZIATA PALUMBO
Keyword(s):  
Reproduction Number ◽  
Population Level ◽  
Host Population ◽  
Transmission Dynamics ◽  
Host Environment ◽  
Oral Rehydration ◽  
Human Host ◽  
Disease Elimination ◽  
Reproduction Numbers ◽  
Type Reproduction Number

This study presents a new model for the environment-host-environment transmission dynamics of V. cholerae in a community with an interconnected aquatic pond–river water network. For the case when the human host is the sole target of anti-cholera control and the volume of water in the pond is maximum, the disease-free equilibrium of the model is shown to be globally asymptotically stable whenever a certain epidemiological threshold, known as the basic reproduction number [Formula: see text], is less than unity. The epidemiological implication of this result is that cholera can be eliminated from the community if the control strategies implemented can bring (and maintain) [Formula: see text] to a value less than unity. Four scenarios, that represent different interpretations of the role of the V. cholerea pathogen within the environment, were studied. The corresponding basic reproduction numbers were shown to exhibit the same threshold property with respect to the value unity (i.e., if one is less (equal, greater) than unity, then the three others are also less (equal, greater) than unity. Further, it was shown that for the case where anti-cholera control is focused on the human host population, the associated type reproduction number of the model (corresponding to each of the four transmission scenarios considered) is unique. The implication of this result is that the estimate of the effort needed for disease elimination (i.e., the required herd immunity threshold) is unique, regardless of which of the four transmission scenarios is considered. However, when any of the other two bacterial population types in the aquatic environment (i.e., bacterial in the pond or river) is the focus of the control efforts, this study shows that the associated type reproduction number is not unique. Extensive numerical simulations of the model, using a realistic set of parameters from the published literature, show that the community-wide implementation of a strategy that focus on improved water quality, sanitation, and hygiene (known as WASH-only strategy), using the current estimated coverage of 50% and efficacy of 60%, is unable to lead to the elimination of the disease. Such elimination is attainable if the coverage and efficacy are increased (e.g., to 80% and 90%, respectively). Further, elimination can be achieved using a strategy that focuses on oral rehydration therapy and the use of antibiotics to treat the infected humans (i.e., treatment-only strategy) for moderate effectiveness and coverage levels. The combined hybrid WASH-treatment strategy provides far better population-level impact vis a vis disease elimination. This study ranks the three interventions in the following order of population-level effectiveness: combined WASH-treatment, followed by treatment-only and then WASH-only strategy.

scholarly journals Co-circulation of SARS-CoV-2 and Influenza under vaccination scenarios

2021 ◽  
Author(s):  
Manuel A. Acuña-Zegarra ◽  
Mayra Núñez-López ◽  
Andreu Comas-García ◽  
Mario Santana-Cibrian ◽  
Jorge X. Velasco-Hernández
Keyword(s):  
Reproduction Number ◽  
Population Level ◽  
Host Population ◽  
Effective Coverage ◽  
Factors Affecting ◽  
Contact Rates ◽  
Effective Contact ◽  
The One ◽  
Transmission Factors

AbstractThe interaction and possibly interference between viruses infecting a common host population is the problem addressed in this work. We model two viral diseases both of the SIRS type that have similar mechanism of transmission and for which a vaccine exists. The vaccine is characterized by its coverage, induced temporal immunity and efficacy. The population dynamics of both diseases considers infected individuals of each disease and hosts that are susceptible to one but have recovered from the other. We do not incorporate coinfection. We postulate two main transmission factors affecting the effective contact rates: i) that the virus with higher reproduction number can superinfect the one with lower reproduction number and ii) that there is some protection induced by vaccination against the weaker virus that reduces the probability of infection by the stronger virus. Our results indicate that coexistence of the viruses is possible in the long term. The time-dependent effective contact rate may induce either alternating outbreaks of each disease or synchronous outbreaks. We also found the existence of bi-stability triggered by a backward bifurcation, conducive to scenarios where, at the population level, vaccine application may promote persistence of both diseases provided the effective coverage and vaccine efficacy are low.

scholarly journals Forward-looking serial intervals correctly link epidemic growth to reproduction numbers

2020 ◽  
Vol 118 (2) ◽  
pp. e2011548118
Author(s):  
Sang Woo Park ◽  
Kaiyuan Sun ◽  
David Champredon ◽  
Michael Li ◽  
Benjamin M. Bolker ◽  
...  
Keyword(s):  
Symptom Onset ◽  
Reproduction Number ◽  
Heuristic Method ◽  
Population Level ◽  
Contact Tracing ◽  
Epidemic Dynamics ◽  
Transmission Chain ◽  
Reproduction Numbers ◽  
Serial Interval ◽  
Forward Looking

The reproduction number R and the growth rate r are critical epidemiological quantities. They are linked by generation intervals, the time between infection and onward transmission. Because generation intervals are difficult to observe, epidemiologists often substitute serial intervals, the time between symptom onset in successive links in a transmission chain. Recent studies suggest that such substitution biases estimates of R based on r. Here we explore how these intervals vary over the course of an epidemic, and the implications for R estimation. Forward-looking serial intervals, measuring time forward from symptom onset of an infector, correctly describe the renewal process of symptomatic cases and therefore reliably link R with r. In contrast, backward-looking intervals, which measure time backward, and intrinsic intervals, which neglect population-level dynamics, give incorrect R estimates. Forward-looking intervals are affected both by epidemic dynamics and by censoring, changing in complex ways over the course of an epidemic. We present a heuristic method for addressing biases that arise from neglecting changes in serial intervals. We apply the method to early (21 January to February 8, 2020) serial interval-based estimates of R for the COVID-19 outbreak in China outside Hubei province; using improperly defined serial intervals in this context biases estimates of initial R by up to a factor of 2.6. This study demonstrates the importance of early contact tracing efforts and provides a framework for reassessing generation intervals, serial intervals, and R estimates for COVID-19.

scholarly journals Norovirus transmission dynamics: a modelling review

2017 ◽  
Vol 146 (2) ◽  
pp. 147-158 ◽  
Author(s):  
K. A. M. GAYTHORPE ◽  
C. L. TROTTER ◽  
B. LOPMAN ◽  
M. STEELE ◽  
A. J. K. CONLAN
Keyword(s):  
Reproduction Number ◽  
Population Level ◽  
Transmission Dynamics ◽  
Parameter Estimates ◽  
Viral Gastroenteritis ◽  
Recent Interest ◽  
And Control ◽  
Case Notification ◽  
Substantial Morbidity ◽  
Current Modelling

SUMMARYNorovirus is one of the leading causes of viral gastroenteritis worldwide and responsible for substantial morbidity, mortality and healthcare costs. To further understanding of the epidemiology and control of norovirus, there has been much recent interest in describing the transmission dynamics of norovirus through mathematical models. In this study, we review the current modelling approaches for norovirus transmission. We examine the data and methods used to estimate these models that vary structurally and parametrically between different epidemiological contexts. Many of the existing studies at population level have focused on the same case notification dataset, whereas models from outbreak settings are highly specific and difficult to generalise. In this review, we explore the consistency in the description of norovirus transmission dynamics and the robustness of parameter estimates between studies. In particular, we find that there is considerable variability in estimates of key parameters such as the basic reproduction number, which may mean that the effort required to control norovirus at the population level may currently be underestimated.

scholarly journals Basic Reproduction Number and Transmission Dynamics of Common Serogroups of Enterohemorrhagic Escherichia coli

2016 ◽  
Vol 82 (18) ◽  
pp. 5612-5620 ◽  
Author(s):  
Shi Chen ◽  
Michael W. Sanderson ◽  
Chihoon Lee ◽  
Natalia Cernicchiaro ◽  
David G. Renter ◽  
...  
Keyword(s):  
Escherichia Coli ◽  
Basic Reproduction Number ◽  
Shiga Toxin ◽  
Reproduction Number ◽  
Enterohemorrhagic Escherichia Coli ◽  
Transmission Dynamics ◽  
Cross Sectional ◽  
Content Type ◽  
Group Data ◽  
Reproduction Numbers

ABSTRACTUnderstanding the transmission dynamics of pathogens is essential to determine the epidemiology, ecology, and ways of controlling enterohemorrhagicEscherichia coli(EHEC) in animals and their environments. Our objective was to estimate the epidemiological fitness of common EHEC strains in cattle populations. For that purpose, we developed a Markov chain model to characterize the dynamics of 7 serogroups of enterohemorrhagicEscherichia coli(O26, O45, O103, O111, O121, O145, and O157) in cattle production environments based on a set of cross-sectional data on infection prevalence in 2 years in two U.S. states. The basic reproduction number (R0) was estimated using a Bayesian framework for each serogroup based on two criteria (using serogroup alone [the O-group data] and using O serogroup, Shiga toxin gene[s], and intimin [eae] gene together [the EHEC data]). In addition, correlations between external covariates (e.g., location, ambient temperature, dietary, and probiotic usage) and prevalence/R0were quantified.R0estimates varied substantially among different EHEC serogroups, with EHEC O157 having anR0of >1 (∼1.5) and all six other EHEC serogroups having anR0of less than 1. Using the O-group data substantially increasedR0estimates for the O26, O45, and O103 serogroups (R0> 1) but not for the others. Different covariates had distinct influences on different serogroups: the coefficients for each covariate were different among serogroups. Our modeling and analysis of this system can be readily expanded to other pathogen systems in order to estimate the pathogen and external factors that influence spread of infectious agents.IMPORTANCEIn this paper we describe a Bayesian modeling framework to estimate basic reproduction numbers of multiple serotypes of Shiga toxin-producingEscherichia coliaccording to a cross-sectional study. We then coupled a compartmental model to reconstruct the infection dynamics of these serotypes and quantify their risk in the population. We incorporated different sensitivity levels of detecting different serotypes and evaluated their potential influence on the estimation of basic reproduction numbers.

On the existence of invariant domain and local asymptotic behavior of a delayed onchocerciasis model

2020 ◽  
Vol 31 (10) ◽  
pp. 2050142
Author(s):  
O. M. Ogunmiloro ◽  
A. S. Idowu
Keyword(s):  
Mathematical Model ◽  
Reproduction Number ◽  
Host Population ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Number Formula ◽  
Effective Use ◽  
Steady State Solutions ◽  
Delayed Model ◽  
The Basic Reproduction Number

In this paper, a mathematical model describing the transmission dynamics of onchocerciasis with distributed delays in infection incubation and recovery in humans and blackfly host population is formulated. We showed that the delayed model is positively invariant and bounded. Also, we obtain the onchocerciasis-free and endemic steady-state solutions as well as the basic reproduction number [Formula: see text] of the delayed onchocerciasis model. We found that the delayed onchocerciasis model is locally asymptotically stable whenever [Formula: see text]. The findings suggest that, for [Formula: see text] to be less than unity, effective use of ivermectin drug for treatment, distribution of treated nets and cloths, etc., is necessary for the minimization and possible elimination of onchocerciasis infection.

scholarly journals Emergence of drug resistance: implications for antiviral control of pandemic influenza

2007 ◽  
Vol 274 (1619) ◽  
pp. 1675-1684 ◽  
Author(s):  
Murray E Alexander ◽  
Christopher S Bowman ◽  
Zhilan Feng ◽  
Michael Gardam ◽  
Seyed M Moghadas ◽  
...  
Keyword(s):  
Drug Resistance ◽  
Type Strain ◽  
Wild Type Strain ◽  
Reproduction Number ◽  
Antiviral Treatment ◽  
Population Level ◽  
Wild Type ◽  
Reproduction Numbers ◽  
Relative Transmission ◽  
Single Strategy

Given the danger of an unprecedented spread of the highly pathogenic avian influenza strain H5N1 in humans, and great challenges to the development of an effective influenza vaccine, antiviral drugs will probably play a pivotal role in combating a novel pandemic strain. A critical limitation to the use of these drugs is the evolution of highly transmissible drug-resistant viral mutants. Here, we develop a mathematical model to evaluate the potential impact of an antiviral treatment strategy on the emergence of drug resistance and containment of a pandemic. The results show that elimination of the wild-type strain depends crucially on both the early onset of treatment in indexed cases and population-level treatment. Given the probable delay of 0.5–1 day in seeking healthcare and therefore initiating therapy, the findings indicate that a single strategy of antiviral treatment will be unsuccessful at controlling the spread of disease if the reproduction number of the wild-type strain exceeds 1.4. We demonstrate the possible occurrence of a self-sustaining epidemic of resistant strain, in terms of its transmission fitness relative to the wild-type, and the reproduction number . Considering reproduction numbers estimated for the past three pandemics, the findings suggest that an uncontrollable pandemic is likely to occur if resistant viruses with relative transmission fitness above 0.4 emerge. While an antiviral strategy is crucial for containing a pandemic, its effectiveness depends critically on timely and strategic use of drugs.

COVID-19: Time-Dependent Effective Reproduction Number and Sub-notification Effect Estimation Modeling (Preprint)

2020 ◽  
Author(s):  
Eduardo Atem De Carvalho ◽  
Rogerio Atem De Carvalho
Keyword(s):  
New York ◽  
Reproduction Number ◽  
Moving Average ◽  
Real Data ◽  
Time Dependent ◽  
Initial Value ◽  
Health Authorities ◽  
Reproduction Numbers ◽  
Effect Estimation ◽  
The Impact

BACKGROUND Since the beginning of the COVID-19 pandemic, researchers and health authorities have sought to identify the different parameters that govern their infection and death cycles, in order to be able to make better decisions. In particular, a series of reproduction number estimation models have been presented, with different practical results. OBJECTIVE This article aims to present an effective and efficient model for estimating the Reproduction Number and to discuss the impacts of sub-notification on these calculations. METHODS The concept of Moving Average Method with Initial value (MAMI) is used, as well as a model for Rt, the Reproduction Number, is derived from experimental data. The models are applied to real data and their performance is presented. RESULTS Analyses on Rt and sub-notification effects for Germany, Italy, Sweden, United Kingdom, South Korea, and the State of New York are presented to show the performance of the methods here introduced. CONCLUSIONS We show that, with relatively simple mathematical tools, it is possible to obtain reliable values for time-dependent, incubation period-independent Reproduction Numbers (Rt). We also demonstrate that the impact of sub-notification is relatively low, after the initial phase of the epidemic cycle has passed.

scholarly journals Multivariate Abundance Analysis of Multi-Host/Multi-Parasite Lungworms in a Sympatric Wild Ruminant Population

Diversity ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 227
Author(s):  
Tessa Carrau ◽  
Carlos Martínez-Carrasco ◽  
María Magdalena Garijo ◽  
Francisco Alonso ◽  
Rocío Ruiz de Ybáñez ◽  
...  
Keyword(s):  
Population Level ◽  
Parasite Load ◽  
Fallow Deer ◽  
Host Population ◽  
Marginal Effect ◽  
Wild Ruminant ◽  
Additional Species ◽  
Parasite Abundance ◽  
Associated Risk Factors ◽  
Natural Dynamics

In the analysis of a multi-host/multi-parasite system and its associated risk factors, it is particularly interesting to understand the natural dynamics among pathogens, their hosts, and the environment in wildlife populations. This analysis is particularly feasible in a scenario where multiple overlapping host populations are present in high densities, along with a complex community of parasites. We aimed to describe and analyze the naturally occurring lungworm polyparasitism in a wild ruminant community in Southeast Spain. The respiratory tracts of 250 specimens belonging to four different species (red deer, mouflon, Iberian ibex, and fallow deer) were studied. Almost half (48.0%) of the animals were infected with bronchopulmonary nematodes. Seven different nematodes were identified of which two genera (Protostrongylus spp. and Dictyocaulus spp.) and three additional species (Cystocaulus ocreatus, Muellerius capillaris, and Neostrongylus linearis) were recorded in at least two ruminants, with the mouflon as the commonest host. Our study shows a significant effect of host species and sampling area, plus a marginal effect of age, on parasite multivariate abundance at the host population level. Mouflon and adults of all hosts appear to carry the highest parasite load on average. From a spatial perspective, the highest parasite abundance was detected at the central part of the park.

scholarly journals Development of the reproduction number from coronavirus SARS-CoV-2 case data in Germany and implications for political measures

BMC Medicine ◽  
2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Sahamoddin Khailaie ◽  
Tanmay Mitra ◽  
Arnab Bandyopadhyay ◽  
Marta Schips ◽  
Pietro Mascheroni ◽  
...  
Keyword(s):  
Structural Changes ◽  
Reproduction Number ◽  
National Level ◽  
Transmission Dynamics ◽  
Federal State ◽  
Parameter Estimates ◽  
Time Varying ◽  
Short Term ◽  
Robert Koch Institute ◽  
Federal States

Abstract Background SARS-CoV-2 has induced a worldwide pandemic and subsequent non-pharmaceutical interventions (NPIs) to control the spread of the virus. As in many countries, the SARS-CoV-2 pandemic in Germany has led to a consecutive roll-out of different NPIs. As these NPIs have (largely unknown) adverse effects, targeting them precisely and monitoring their effectiveness are essential. We developed a compartmental infection dynamics model with specific features of SARS-CoV-2 that allows daily estimation of a time-varying reproduction number and published this information openly since the beginning of April 2020. Here, we present the transmission dynamics in Germany over time to understand the effect of NPIs and allow adaptive forecasts of the epidemic progression. Methods We used a data-driven estimation of the evolution of the reproduction number for viral spreading in Germany as well as in all its federal states using our model. Using parameter estimates from literature and, alternatively, with parameters derived from a fit to the initial phase of COVID-19 spread in different regions of Italy, the model was optimized to fit data from the Robert Koch Institute. Results The time-varying reproduction number (Rt) in Germany decreased to <1 in early April 2020, 2–3 weeks after the implementation of NPIs. Partial release of NPIs both nationally and on federal state level correlated with moderate increases in Rt until August 2020. Implications of state-specific Rt on other states and on national level are characterized. Retrospective evaluation of the model shows excellent agreement with the data and usage of inpatient facilities well within the healthcare limit. While short-term predictions may work for a few weeks, long-term projections are complicated by unpredictable structural changes. Conclusions The estimated fraction of immunized population by August 2020 warns of a renewed outbreak upon release of measures. A low detection rate prolongs the delay reaching a low case incidence number upon release, showing the importance of an effective testing-quarantine strategy. We show that real-time monitoring of transmission dynamics is important to evaluate the extent of the outbreak, short-term projections for the burden on the healthcare system, and their response to policy changes.

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