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The generation time, representing the interval between infections in primary and secondary cases, is essential for understanding and predicting the transmission dynamics of seasonal influenza, including the real-time effective reproduction number (Rt). However, comprehensive generation time estimates for seasonal influenza, especially post the 2009 influenza pandemic, are lacking. We estimated the generation time utilizing data from a 7-site case-ascertained household study in the United States over two influenza seasons, 2021/2022 and 2022/2023. More than 200 individuals who tested positive for influenza and their household contacts were enrolled within 7 days of the first illness in the household. All participants were prospectively followed for 10 days completing daily symptom diaries and collecting nasal swabs, which were tested for influenza via RT-PCR. We analyzed these data by modifying a previously published Bayesian data augmentation approach that imputes infection times of cases to obtain both intrinsic (assuming no susceptible depletion) and realized (observed within household) generation times. We assessed the robustness of the generation time estimate by varying the incubation period, and generated estimates of the proportion of transmission before symptomatic onset, infectious period, and latent period. We estimated a mean intrinsic generation time of 3.2 (95% credible interval, CrI: 2.9-3.6) days, with a realized household generation time of 2.8 (95% CrI: 2.7-3.0) days. The generation time exhibited limited sensitivity to incubation period variation. Estimates of the proportion of transmission that occurred before symptom onset, the infectious period, and the latent period were sensitive to variation in incubation periods. Our study contributes to the ongoing efforts to refine estimates of the generation time for influenza. Our estimates, derived from recent data following the COVID-19 pandemic, are consistent with previous pre-pandemic estimates, and will be incorporated into real-time Rt estimation efforts., Competing Interests: Declaration of interest • M. S. S. reports a leadership role as Associate Director of the American Academy of Pediatrics’ Pediatric Research in Office Settings (PROS), paid to Trustees of Columbia University. All other authors report no potential conflicts. • N. M.B. reports grant/contracts from NIH to the University of North Carolina School of Medicine, Doris Duke Charitable Foundation, and North Carolina Collaboratory; participation on a DSMB or advisory board for the Snowball Study Technical Interchange; a leadership or fiduciary role on the American Society of Tropical Medicine and Hygiene Scientific Committee; and other financial or nonfinancial interests with the COVID-19 Equity Evidence Academy (RADx-UP CDCC) Steering Committee and North Carolina Occupational Safety and Health Education Research Center. • E. A. reports serving as a former consultant for Hillevax and Moderna, presenting a Merck-supported lecture at the Latin American Vaccine Summit, and receipt of grant/research support from Pfizer for pneumococcal pneumonia studies. • S. R. reports grant support from BioFire. • H. Q. N. reports grant/research support from CSL Seqirus, GSK, and ModernaTX, and honorarium for participating in a consultancy group for ModernaTX outside the submitted work. • S. H. M. reports grants/contracts from NIH, the American Academy of Pediatrics, and the Doris Duke Charitable Foundation. • E. S. reports grants or contracts to institution from Vanderbilt University Medical Center (originating at CDC #75D30121C11656). • H. K. T. has received research funding from the CDC. • C. G. G. reports participation on an advisory board for Merck, and receipt of grant/research support from AHRQ, CDC, US Food and Drug Administration, NIH, and Syneos Health. • All authors have submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest. Conflicts that the editors consider relevant to the content of the manuscript have been disclosed.

Accurate forecasts can enable more effective public health responses during seasonal influenza epidemics. For the 2021-22 and 2022-23 influenza seasons, 26 forecasting teams provided national and jurisdiction-specific probabilistic predictions of weekly confirmed influenza hospital admissions for one-to-four weeks ahead. Forecast skill is evaluated using the Weighted Interval Score (WIS), relative WIS, and coverage. Six out of 23 models outperform the baseline model across forecast weeks and locations in 2021-22 and 12 out of 18 models in 2022-23. Averaging across all forecast targets, the FluSight ensemble is the 2 nd most accurate model measured by WIS in 2021-22 and the 5 th most accurate in the 2022-23 season. Forecast skill and 95% coverage for the FluSight ensemble and most component models degrade over longer forecast horizons. In this work we demonstrate that while the FluSight ensemble was a robust predictor, even ensembles face challenges during periods of rapid change., (© 2024. This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply.)

We reviewed the tools that have been developed to characterize and communicate seasonal influenza activity in the United States. Here we focus on systematic surveillance and applied analytics, including seasonal burden and disease severity estimation, short-term forecasting, and longer-term modeling efforts. For each set of activities, we describe the challenges and opportunities that have arisen because of the COVID-19 pandemic. In conclusion, we highlight how collaboration and communication have been and will continue to be key components of reliable and actionable influenza monitoring, forecasting, and modeling activities., (©Rebecca K Borchering, Matthew Biggerstaff, Lynnette Brammer, Alicia Budd, Shikha Garg, Alicia M Fry, A Danielle Iuliano, Carrie Reed. Originally published in JMIR Public Health and Surveillance (https://publichealth.jmir.org), 08.04.2024.)

Between December 2020 and April 2023, the COVID-19 Scenario Modeling Hub (SMH) generated operational multi-month projections of COVID-19 burden in the US to guide pandemic planning and decision-making in the context of high uncertainty. This effort was born out of an attempt to coordinate, synthesize and effectively use the unprecedented amount of predictive modeling that emerged throughout the COVID-19 pandemic. Here we describe the history of this massive collective research effort, the process of convening and maintaining an open modeling hub active over multiple years, and attempt to provide a blueprint for future efforts. We detail the process of generating 17 rounds of scenarios and projections at different stages of the COVID-19 pandemic, and disseminating results to the public health community and lay public. We also highlight how SMH was expanded to generate influenza projections during the 2022-23 season. We identify key impacts of SMH results on public health and draw lessons to improve future collaborative modeling efforts, research on scenario projections, and the interface between models and policy., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024. Published by Elsevier B.V.)

Our ability to forecast epidemics far into the future is constrained by the many complexities of disease systems. Realistic longer-term projections may, however, be possible under well-defined scenarios that specify the future state of critical epidemic drivers. Since December 2020, the U.S. COVID-19 Scenario Modeling Hub (SMH) has convened multiple modeling teams to make months ahead projections of SARS-CoV-2 burden, totaling nearly 1.8 million national and state-level projections. Here, we find SMH performance varied widely as a function of both scenario validity and model calibration. We show scenarios remained close to reality for 22 weeks on average before the arrival of unanticipated SARS-CoV-2 variants invalidated key assumptions. An ensemble of participating models that preserved variation between models (using the linear opinion pool method) was consistently more reliable than any single model in periods of valid scenario assumptions, while projection interval coverage was near target levels. SMH projections were used to guide pandemic response, illustrating the value of collaborative hubs for longer-term scenario projections., (© 2023. The Author(s).)

Beginning in December 2020, the COVID-19 Scenario Modeling Hub has provided quantitative scenario-based projections for cases, hospitalizations, and deaths, aggregated across up to nine modeling groups. Projections spanned multiple months into the future and provided timely information on potential impacts of epidemiological uncertainties and interventions. Projections results were shared with the public, public health partners, and the Centers for Disease Control COVID-19 Response Team. The projections provided insights on situational awareness and informed decision-making to mitigate COVID-19 disease burden (e.g., vaccination strategies). By aggregating projections from multiple modeling teams, the Scenario Modeling Hub provided rapidly synthesized information in times of great uncertainty and conveyed possible trajectories in the presence of emerging variants. Here we detail several use cases of these projections in public health practice and communication, including assessments of whether modeling results directly or indirectly informed public health communication or guidance. These include multiple examples where comparisons of projected COVID-19 disease outcomes under different vaccination scenarios were used to inform Advisory Committee for Immunization Practices recommendations. We also describe challenges and lessons learned during this highly beneficial collaboration., Competing Interests: Declaration of Competing Interest The authors report no financial/personal interests or beliefs that could affect their objectivity., (Published by Elsevier B.V.)

Policymakers must make management decisions despite incomplete knowledge and conflicting model projections. Little guidance exists for the rapid, representative, and unbiased collection of policy-relevant scientific input from independent modeling teams. Integrating approaches from decision analysis, expert judgment, and model aggregation, we convened multiple modeling teams to evaluate COVID-19 reopening strategies for a mid-sized United States county early in the pandemic. Projections from seventeen distinct models were inconsistent in magnitude but highly consistent in ranking interventions. The 6-mo-ahead aggregate projections were well in line with observed outbreaks in mid-sized US counties. The aggregate results showed that up to half the population could be infected with full workplace reopening, while workplace restrictions reduced median cumulative infections by 82%. Rankings of interventions were consistent across public health objectives, but there was a strong trade-off between public health outcomes and duration of workplace closures, and no win-win intermediate reopening strategies were identified. Between-model variation was high; the aggregate results thus provide valuable risk quantification for decision making. This approach can be applied to the evaluation of management interventions in any setting where models are used to inform decision making. This case study demonstrated the utility of our approach and was one of several multimodel efforts that laid the groundwork for the COVID-19 Scenario Modeling Hub, which has provided multiple rounds of real-time scenario projections for situational awareness and decision making to the Centers for Disease Control and Prevention since December 2020.

Background: The COVID-19 Scenario Modeling Hub convened nine modeling teams to project the impact of expanding SARS-CoV-2 vaccination to children aged 5-11 years on COVID-19 burden and resilience against variant strains., Methods: Teams contributed state- and national-level weekly projections of cases, hospitalizations, and deaths in the United States from September 12, 2021 to March 12, 2022. Four scenarios covered all combinations of 1) vaccination (or not) of children aged 5-11 years (starting November 1, 2021), and 2) emergence (or not) of a variant more transmissible than the Delta variant (emerging November 15, 2021). Individual team projections were linearly pooled. The effect of childhood vaccination on overall and age-specific outcomes was estimated using meta-analyses., Findings: Assuming that a new variant would not emerge, all-age COVID-19 outcomes were projected to decrease nationally through mid-March 2022. In this setting, vaccination of children 5-11 years old was associated with reductions in projections for all-age cumulative cases (7.2%, mean incidence ratio [IR] 0.928, 95% confidence interval [CI] 0.880-0.977), hospitalizations (8.7%, mean IR 0.913, 95% CI 0.834-0.992), and deaths (9.2%, mean IR 0.908, 95% CI 0.797-1.020) compared with scenarios without childhood vaccination. Vaccine benefits increased for scenarios including a hypothesized more transmissible variant, assuming similar vaccine effectiveness. Projected relative reductions in cumulative outcomes were larger for children than for the entire population. State-level variation was observed., Interpretation: Given the scenario assumptions (defined before the emergence of Omicron), expanding vaccination to children 5-11 years old would provide measurable direct benefits, as well as indirect benefits to the all-age U.S. population, including resilience to more transmissible variants., Funding: Various (see acknowledgments)., Competing Interests: JL has served as an expert witness on cases where the likely length of the pandemic was of issue. MCR reports stock ownership in Becton Dickinson & Co., which manufactures medical equipment used in COVID-19 testing, vaccination, and treatment. JS and Columbia University disclose partial ownership of SK Analytics. JS discloses consulting for BNI. There are no other competing interests to declare.

Probabilistic predictions support public health planning and decision making, especially in infectious disease emergencies. Aggregating outputs from multiple models yields more robust predictions of outcomes and associated uncertainty. While the selection of an aggregation method can be guided by retrospective performance evaluations, this is not always possible. For example, if predictions are conditional on assumptions about how the future will unfold (e.g. possible interventions), these assumptions may never materialize, precluding any direct comparison between predictions and observations. Here, we summarize literature on aggregating probabilistic predictions, illustrate various methods for infectious disease predictions via simulation, and present a strategy for choosing an aggregation method when empirical validation cannot be used. We focus on the linear opinion pool (LOP) and Vincent average, common methods that make different assumptions about between-prediction uncertainty. We contend that assumptions of the aggregation method should align with a hypothesis about how uncertainty is expressed within and between predictions from different sources. The LOP assumes that between-prediction uncertainty is meaningful and should be retained, while the Vincent average assumes that between-prediction uncertainty is akin to sampling error and should not be preserved. We provide an R package for implementation. Given the rising importance of multi-model infectious disease hubs, our work provides useful guidance on aggregation and a deeper understanding of the benefits and risks of different approaches.

In Spring 2021, the highly transmissible SARS-CoV-2 Delta variant began to cause increases in cases, hospitalizations, and deaths in parts of the United States. At the time, with slowed vaccination uptake, this novel variant was expected to increase the risk of pandemic resurgence in the US in summer and fall 2021. As part of the COVID-19 Scenario Modeling Hub, an ensemble of nine mechanistic models produced 6-month scenario projections for July-December 2021 for the United States. These projections estimated substantial resurgences of COVID-19 across the US resulting from the more transmissible Delta variant, projected to occur across most of the US, coinciding with school and business reopening. The scenarios revealed that reaching higher vaccine coverage in July-December 2021 reduced the size and duration of the projected resurgence substantially, with the expected impacts was largely concentrated in a subset of states with lower vaccination coverage. Despite accurate projection of COVID-19 surges occurring and timing, the magnitude was substantially underestimated 2021 by the models compared with the of the reported cases, hospitalizations, and deaths occurring during July-December, highlighting the continued challenges to predict the evolving COVID-19 pandemic. Vaccination uptake remains critical to limiting transmission and disease, particularly in states with lower vaccination coverage. Higher vaccination goals at the onset of the surge of the new variant were estimated to avert over 1.5 million cases and 21,000 deaths, although may have had even greater impacts, considering the underestimated resurgence magnitude from the model., Competing Interests: ST, CS, MQ, LM, RB, KS, EH, LC, JL, JK, HH, MK, KT, SW, LS, KR, JL, JD, JK, EL, JP, AH, DK, MC, JD, KM, XX, AP, AV, AS, PP, SV, AA, BL, BK, JO, MO, GH, BH, JC, AV, MM, SH, PB, DM, SC, RP, DJ, JT, MG, TY, SP, JH, RS, MB, MJ, CV No competing interests declared, JL has served as an expert witness on cases where the likely length of the pandemic was of issue, JS and Columbia University disclose partial ownership of SK Analytics. Discloses consulting for BNI, MR reports stock ownership in Becton Dickinson & Co, which manufactures medical equipment used in COVID testing, vaccination, and treatment

Stay-at-home orders and shutdowns of non-essential businesses are powerful, but socially costly, tools to control the pandemic spread of SARS-CoV-2. Mass testing strategies, which rely on widely administered frequent and rapid diagnostics to identify and isolate infected individuals, could be a potentially less disruptive management strategy, particularly where vaccine access is limited. In this paper, we assess the extent to which mass testing and isolation strategies can reduce reliance on socially costly non-pharmaceutical interventions, such as distancing and shutdowns. We develop a multi-compartmental model of SARS-CoV-2 transmission incorporating both preventative non-pharmaceutical interventions (NPIs) and testing and isolation to evaluate their combined effect on public health outcomes. Our model is designed to be a policy-guiding tool that captures important realities of the testing system, including constraints on test administration and non-random testing allocation. We show how strategic changes in the characteristics of the testing system, including test administration, test delays, and test sensitivity, can reduce reliance on preventative NPIs without compromising public health outcomes in the future. The lowest NPI levels are possible only when many tests are administered and test delays are short, given limited immunity in the population. Reducing reliance on NPIs is highly dependent on the ability of a testing program to identify and isolate unreported, asymptomatic infections. Changes in NPIs, including the intensity of lockdowns and stay at home orders, should be coordinated with increases in testing to ensure epidemic control; otherwise small additional lifting of these NPIs can lead to dramatic increases in infections, hospitalizations and deaths. Importantly, our results can be used to guide ramp-up of testing capacity in outbreak settings, allow for the flexible design of combined interventions based on social context, and inform future cost-benefit analyses to identify efficient pandemic management strategies., Competing Interests: The authors have declared that no competing interests exist.

More than 1.6 million Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) tests were administered daily in the United States at the peak of the epidemic, with a significant focus on individual treatment. Here, we show that objective-driven, strategic sampling designs and analyses can maximize information gain at the population level, which is necessary to increase situational awareness and predict, prepare for, and respond to a pandemic, while also continuing to inform individual treatment. By focusing on specific objectives such as individual treatment or disease prediction and control (e.g., via the collection of population-level statistics to inform lockdown measures or vaccine rollout) and drawing from the literature on capture-recapture methods to deal with nonrandom sampling and testing errors, we illustrate how public health objectives can be achieved even with limited test availability when testing programs are designed a priori to meet those objectives., Competing Interests: The authors have declared that no competing interests exist.

After a period of rapidly declining U.S. COVID-19 incidence during January-March 2021, increases occurred in several jurisdictions (1,2) despite the rapid rollout of a large-scale vaccination program. This increase coincided with the spread of more transmissible variants of SARS-CoV-2, the virus that causes COVID-19, including B.1.1.7 (1,3) and relaxation of COVID-19 prevention strategies such as those for businesses, large-scale gatherings, and educational activities. To provide long-term projections of potential trends in COVID-19 cases, hospitalizations, and deaths, COVID-19 Scenario Modeling Hub teams used a multiple-model approach comprising six models to assess the potential course of COVID-19 in the United States across four scenarios with different vaccination coverage rates and effectiveness estimates and strength and implementation of nonpharmaceutical interventions (NPIs) (public health policies, such as physical distancing and masking) over a 6-month period (April-September 2021) using data available through March 27, 2021 (4). Among the four scenarios, an accelerated decline in NPI adherence (which encapsulates NPI mandates and population behavior) was shown to undermine vaccination-related gains over the subsequent 2-3 months and, in combination with increased transmissibility of new variants, could lead to surges in cases, hospitalizations, and deaths. A sharp decline in cases was projected by July 2021, with a faster decline in the high-vaccination scenarios. High vaccination rates and compliance with public health prevention measures are essential to control the COVID-19 pandemic and to prevent surges in hospitalizations and deaths in the coming months., Competing Interests: All authors have completed and submitted the International Committee of Medical Journal Editors form for disclosure of potential conflicts of interest. Katriona Shea reports receipt of two National Science Foundation (NSF) COVID-19 RAPID awards, and a Huck Institutes of the Life Sciences Coronavirus Research Seed Grant. Rebecca Borchering reports funding from an NSF COVID-19 RAPID award. Katharine Tallaksen, Kaitlin Rainwater-Lovett, Laura Asher, Luke C. Mullany, Molly E. Gallagher, Matt Kinsey, Richard F. Obrecht, and Lauren Shin report funding from the U.S. Department of Health and Human Services (HHS), Office of the Assistant Secretary for Preparedness and Response to the Johns Hopkins Applied Physics Laboratory. Matteo Chinazzi reports grants from the National Institutes of Health (NIH), the Council of State and Territorial Epidemiologists (CSTE), and Metabiota to Northeastern University. Ana Pastore y Piontti reports funding from Metabiota, Inc. to Northeastern University and royalties from Springer Publishing. Joseph Lemaitre reports funding from the Swiss National Science Foundation, State of California, HHS, and the Department of Homeland Security (DHS). Kyra H. Grantz reports support from the California Department of Public Health, Johns Hopkins Bloomberg School of Public Health, NIH, and travel support from the World Health Organization (WHO). Elizabeth Lee and Claire Smith report support from the California Department of Public Health, Johns Hopkins Bloomberg School of Public Health, Johns Hopkins Health System, HHS, and DHS, and computing resources from Amazon Web Services, Johns Hopkins University Modeling and Policy Hub, and the Office of the Dean at the Johns Hopkins Bloomberg School of Public Health. Justin Lessler reports support from DHHS, DHS, California Institute of Technology, NIH, honorarium from the American Association for Cancer Research, personal fees for expert testimony from Paul, Weiss, Rifkind, Wharton & Garrison, LLP. Lindsay Keegan reports support from the State of California, and NIH, a University of Utah Immunology, Inflammation, and Infectious Disease Seed Grant, and a scholarship from the University of Washington Summer Institute in Statistics and Modeling of Infectious Diseases. Lucie Contamin, John Levander, Jessica Salerno, and Willem Gijsbert van Panhuis report a National Institute of General Medical Sciences grant. Ajitesh Srivastava reports a grant from the National Science Foundation. Michael C. Runge reports stock ownership in Becton Dickinson & Co., which manufactures medical equipment used in COVID testing, vaccination, and treatment. Alessandro Vespignani reports grants from NIH, NSF, WHO, CSTE, Metabiota Inc., Templeton Foundation, Scientific Interchange Foundation, Bill & Melinda Gates Foundation; royalties from Cambridge University Press, World Scientific, Springer Publishing, and Il Saggiatore; consulting fees from Human Technopole Foundation, Institute for Scientific Interchange Foundation, honorarium for lecture module at University of Washington; Scientific Advisory Board member of the Institute for Scientific Interchange Foundation, Italy, Supervisory Board member of the Human Technopole Foundation, Italy; and gifts to Northeastern University from the McGovern Foundation, the Chleck Foundation, the Sternberg Family, J. Pallotta, and Google Cloud research credits for COVID-19 from Google. Akhil Sai Peddireddy, Pyrros A. Telionis, Anil Vullikanti, Jiangzhuo Chen, Benjamin Hurt, Brian D. Klahn, Bryan Lewis, James Schlitt, Joseph Outten, Lijing Wang, Madhav Marathe, Patrick Corbett, Przemyslaw Porebski, and Srinivasan Venkatramanan report institutional support from the National Science Foundation, Expeditions, NIH, the U.S. Department of Defense, Virginia Department of Health, Virginia Department of Emergency Management, University of Virginia (internal seed grants), and Accuweather. No other potential conflicts of interest were disclosed.

The 2019/2020 influenza season in the United States began earlier than any season since the 2009 H1N1 pandemic, with an increase in influenza-like illnesses observed as early as August. Also noteworthy was the numerical domination of influenza B cases early in this influenza season, in contrast to their typically later peak in the past. Here, we dissect the 2019/2020 influenza season not only with regard to its unusually early activity, but also with regard to the relative dynamics of type A and type B cases. We propose that the recent expansion of a novel influenza B/Victoria clade may be associated with this shift in the composition and kinetics of the influenza season in the United States. We use epidemiological transmission models to explore whether changes in the effective reproduction number or short-term cross-immunity between these viruses can explain the dynamics of influenza A and B seasonality. We find support for an increase in the effective reproduction number of influenza B, rather than support for cross-type immunity-driven dynamics. Our findings have clear implications for optimal vaccination strategies., Competing Interests: The authors declare no competing interest.

In 2015 and 2016, Zika virus (ZIKV) swept through dengue virus (DENV) endemic areas of Latin America. These viruses are of the same family, share a vector and may interact competitively or synergistically through human immune responses. We examine dengue incidence from Brazil and Colombia before, during, and after the Zika epidemic. We find evidence that dengue incidence was atypically low in 2017 in both countries. We investigate whether subnational Zika incidence is associated with changes in dengue incidence and find mixed results. Using simulations with multiple assumptions of interactions between DENV and ZIKV, we find cross-protection suppresses incidence of dengue following Zika outbreaks and low periods of dengue incidence are followed by resurgence. Our simulations suggest correlations in DENV and ZIKV reproduction numbers could complicate associations between ZIKV incidence and post-ZIKV DENV incidence and that periods of low dengue incidence are followed by large increases in dengue incidence.

Animals share a variety of common resources, which can be a major driver of conspecific encounter rates. In this work, we implement a spatially explicit mathematical model for resource visitation behaviour in order to examine how changes in resource availability can influence the rate of encounters among consumers. Using simulations and asymptotic analysis, we demonstrate that, under a reasonable set of assumptions, the relationship between resource availability and consumer conspecific encounters is not monotonic. We characterize how the maximum encounter rate and associated critical resource density depend on system parameters like consumer density and the maximum distance from which consumers can detect and respond to resources. The assumptions underlying our theoretical model and analysis are motivated by observations of large aggregations of black-backed jackals at carcasses generated by seasonal outbreaks of anthrax among herbivores in Etosha National Park, Namibia. As non-obligate scavengers, black-backed jackals use carcasses as a supplemental food resource when they are available. While jackals do not appear to acquire disease from ingesting anthrax carcasses, changes in their movement patterns in response to changes in carcass abundance do alter jackals' conspecific encounter rate in ways that may affect the transmission dynamics of other diseases, such as rabies. Our theoretical results provide a method to quantify and analyse the hypothesis that the outbreak of a fatal disease among herbivores can potentially facilitate outbreaks of an entirely different disease among jackals. By analysing carcass visitation data, we find support for our model's prediction that the number of conspecific encounters at resource sites decreases with additional increases in resource availability. Whether or not this site-dependent effect translates to an overall decrease in encounters depends, unexpectedly, on the relationship between the maximum distance of detection and the resource density., (© 2017 The Authors.)

We formulate a simple partial differential equation model in an effort to qualitatively reproduce the spread dynamics and spatial pattern of rabies in northeast Texas with overlapping reservoir species (skunks and bats). Most existing models ignore reservoir species or model them with patchy models by ordinary differential equations. In our model, we incorporate interspecies rabies infection in addition to rabid population random movement. We apply this model to the confirmed case data from northeast Texas with most parameter values obtained or computed from the literature. Results of simulations using both our skunk-only model and our skunk and bat model demonstrate that the model with overlapping reservoir species more accurately reproduces the progression of rabies spread in northeast Texas., (Copyright © 2012 Elsevier Ltd. All rights reserved.)