Population dynamics of fox rabies in Europe

Oral rabies vaccination of foxes in Türkiye, 2019-2022

Background

Rabies in Turkey is maintained by dogs, but following a sustained spill-over, red fox mediated rabies had spread from the Aegean region to the central part of Türkiye. During the past four years from 2019 to 2023 large scale efforts used oral rabies vaccination (ORV) to control rabies in red foxes. Here, we present the results of the largest ORV campaign on the Asian continent.

Methods

ORV campaigns were carried out twice a year in spring and autumn with a targeted bait density of 20-23 baits/km2. Monitoring of ORV campaigns included the GIS-based analyses of bait distribution, the assessment of bait uptake through biomarker detection and the determination of seroconversion (sero-positivity in ELISA) in the target species collected within the vaccination area. For determination of fox rabies incidence in vaccination areas as the main indicator of the performance of the ORV campaigns, epidemiological data was obtained from the national passive surveillance program.

Results

Aerial bait distribution was highly accurate, with >99 % of baits being recorded from targeted zones, thus meeting the desired bait densities. Although the overall bait uptake (28.1 %; 95 %CI: 23.2-32.8) and seroprevalance (36.3 %; 95 %CI: 30.0-43.2) were low, rabies incidence drastically decreased in ORV areas and rabies was eliminated from western and central parts of Turkey, with no reported cases in foxes from ORV areas in 2022 and 2023.

Conclusions

A large-scale ORV campaign against fox rabies using high quality vaccine baits and the GIS-aided and monitored bait distribution was able to control fox mediated rabies in the western and central parts of Türkiye. Rabies control both in dogs and foxes should be expanded to cover also the eastern parts of Türkiye, to become eventually rabies free.

Rabies and the Arctic Fox (Vulpes lagopus): A Review

The Arctic fox (Vulpes lagopus) is the primary infection reservoir of Arctic rabies, the dynamics of which are poorly understood and subject to significant spatiotemporal variation. Although rabies presence has been documented in the region since the mid-19th century, there is currently no evidence of rabies impacting Arctic fox population size. Under the influence of climate change in a rapidly evolving Arctic ecosystem, alterations in transmission dynamics are predicted, with implications for this species. Concurrently, the World Health Organization leads the United Against Rabies collective in the aim of elimination of dog-mediated rabies by 2030, and although efforts have justifiably been directed to tropical regions, elimination will require a good understanding of rabies in the Arctic. Therefore, this review aimed to provide an overview of current Arctic rabies understanding, while identifying the key knowledge gaps. The review covered spatiotemporal trends in rabies populations, population dynamics of the host species, and current theories about Arctic rabies persistence. It is still unclear how Arctic rabies can persist under low host densities, which has led to several hypotheses in recent years. Creation of high animal density "hotspots" caused by heterogenic fox distribution and multispecies congregations in response to food availability, extensive Arctic fox migration patterns, and the potential evolution to a less lethal variant of rabies may all be part of the explanation. Evidence for these theories by using recent genetic and modeling studies was evaluated within the review. There is currently insufficient evidence about the efficacy and feasibility of vaccines against Arctic rabies. Key knowledge gaps need addressing to enable future control campaigns.

Mathematical model of rabies vaccination in the United States

Rabies is one of the oldest viral diseases and it has been present on every continent except Antarctica. Within the U.S. human rabies cases are quite rare. In the eastern USA, raccoons are the main reservoir hosts and pet vaccination serves as an important barrier against human rabies exposure. In this paper, we develop a compartmental model for rabies transmission amongst raccoons and domestic pets. We find the disease-free equilibria, reproduction numbers for the raccoons and domestic pets. We also determine the vaccination coverage/rates, both for raccoons and pets, needed to achieve the elimination of rabies.

Spiking at the edge: Excitability at interfaces in reaction-diffusion systems

Excitable media, ranging from bioelectric tissues and chemical oscillators to forest fires and competing populations, are nonlinear, spatially extended systems capable of spiking. Most investigations of excitable media consider situations where the amplifying and suppressing forces necessary for spiking coexist at every point in space. In this case, spikes arise due to local bistabilities, which require a fine-tuned ratio between local amplification and suppression strengths. But, in nature and engineered systems, these forces can be segregated in space, forming structures like interfaces and boundaries. Here, we show how boundaries can generate and protect spiking when the reacting components can spread out: Even arbitrarily weak diffusion can cause spiking at the edge between two non-excitable media. This edge spiking arises due to a global bistability, which can occur even if amplification and suppression strengths do not allow spiking when mixed. We analytically derive a spiking phase diagram that depends on two parameters: i) the ratio between the system size and the characteristic diffusive length-scale and ii) the ratio between the amplification and suppression strengths. Our analysis explains recent experimental observations of action potentials at the interface between two non-excitable bioelectric tissues. Beyond electrophysiology, we highlight how edge spiking emerges in predator-prey dynamics and in oscillating chemical reactions. Our findings provide a theoretical blueprint for a class of interfacial excitations in reaction-diffusion systems, with potential implications for spatially controlled chemical reactions, nonlinear waveguides and neuromorphic computation, as well as spiking instabilities, such as cardiac arrhythmias, that naturally occur in heterogeneous biological media.

Retrospective analysis of sero-prevalence and bait uptake estimations in foxes after oral rabies vaccination programmes at European level: Lessons learned and paths forward

Rabies caused by the Classical Rabies Virus (Lyssavirus rabies abbreviated RABV) in the European Union has been close to elimination mainly thanks to Oral Rabies Vaccination (ORV) campaigns targeting wildlife (primarily red foxes). ORV programmes co-financed by the European Commission include a monitoring-component to assess the effectiveness of the ORV campaigns at national level. This assessment is performed by a random collection of red foxes in the vaccinated areas with control of antibodies presence by serological analysis and control of bait uptake by detection of biomarkers (tetracycline incorporated into the baits) in the bones and teeth. ORV programmes aim to a vaccine coverage high enough to immunize (ideally) 70 % of the reservoir population to control the spread of the disease. European Union (EU) programmes that led to almost elimination of rabies on the territory have been traditionally found to have a bait uptake average of 70 % (EU countries; 2010-2020 period) while the seroconversion data showed an average level of 40 % (EU countries; 2010-2020 period). To better understand variations of these indicators, a study was been set up to evaluate the impact of several variables (linked to the vaccination programme itself and linked to environmental conditions) on the bait uptake and the seroconversion rate. Thus, pooling data from several countries provides more powerful statistics and the highest probability of detecting trends. Results of this study advocate the use of a single serological test across the EU since data variation due to the type of test used was higher than variations due to field factors, making the interpretation of monitoring results at EU level challenging. In addition, the results indicates a negative correlation between bait uptake and maximum temperatures reached during ORV campaigns questioning the potential impact of climatic change and associated increase of temperatures on the ORV programmes efficiency. Several hypotheses requesting additional investigation are drawn and discussed in this paper.

Measuring the impact of an integrated bite case management program on the detection of canine rabies cases in Vietnam

Introduction

Dog-mediated rabies is enzootic in Vietnam, resulting in at least 70 reported human deaths and 500,000 human rabies exposures annually. In 2016, an integrated bite cases management (IBCM) based surveillance program was developed to improve knowledge of the dog-mediated rabies burden in Phu Tho Province of Vietnam.

Methods

The Vietnam Animal Rabies Surveillance Program (VARSP) was established in four stages: (1) Laboratory development, (2) Training of community One Health workers, (3) Paper-based-reporting (VARSP 1.0), and (4) Electronic case reporting (VARSP 2.0). Investigation and diagnostic data collected from March 2016 to December 2019 were compared with historical records of animal rabies cases dating back to January 2012. A risk analysis was conducted to evaluate the probability of a rabies exposure resulting in death after a dog bite, based on data collected over the course of an IBCM investigation.

Results

Prior to the implementation of VARSP, between 2012 and 2015, there was an average of one rabies investigation per year, resulting in two confirmed and two probable animal rabies cases. During the 46 months that VARSP was operational (2016 - 2019), 1048 animal investigations were conducted, which identified 79 (8%) laboratory-confirmed rabies cases and 233 (22%) clinically-confirmed(probable) cases. VARSP produced a 78-fold increase in annual animal rabies case detection (one cases detected per year pre-VARSP vs 78 cases per year under VARSP). The risk of succumbing to rabies for bite victims of apparently healthy dogs available for home quarantine, was three deaths for every 10,000 untreated exposures.

Discussion

A pilot IBCM model used in Phu Tho Province showed promising results for improving rabies surveillance, with a 26-fold increase in annual case detection after implementation of a One Health model. The risk for a person bitten by an apparently healthy dog to develop rabies in the absence of rabies PEP was very low, which supports the WHO recommendations to delay PEP for this category of bite victims, when trained animal assessors are available and routinely communicate with the medical sector. Recent adoption of an electronic IBCM system is likely to expedite adoption of VARSP 2.0 to other Provinces and improve accuracy of field decisions and data collection.

The evolution of parasite virulence under targeted culling and harvesting in wildlife and livestock

There is a clear need to understand the effect of human intervention on the evolution of infectious disease. In particular, culling and harvesting of both wildlife and managed livestock populations are carried out in a wide range of management practices, and they have the potential to impact the evolution of a broad range of disease characteristics. Applying eco-evolutionary theory we show that once culling/harvesting becomes targeted on specific disease classes, the established result that culling selects for higher virulence is only found when sufficient infected individuals are culled. If susceptible or recovered individuals are targeted, selection for lower virulence can occur. An important implication of this result is that when culling to eradicate an infectious disease from a population, while it is optimal to target infected individuals, the consequent evolution can increase the basic reproductive ratio of the infection, R 0 , and make parasite eradication more difficult. We show that increases in evolved virulence due to the culling of infected individuals can lead to excess population decline when sustainably harvesting a population. In contrast, culling susceptible or recovered individuals can select for decreased virulence and a reduction in population decline through culling. The implications to the evolution of virulence are typically the same in wildlife populations, that are regulated by the parasite, and livestock populations, that have a constant population size where restocking balances the losses due to mortality. However, the well-known result that vertical transmission selects for lower virulence and transmission in wildlife populations is less marked in livestock populations for parasites that convey long-term immunity since restocking can enhance the density of the immune class. Our work emphasizes the importance of understanding the evolutionary consequences of intervention strategies and the different ecological feedbacks that can occur in wildlife and livestock populations.

Fifty years of spring censuses in black grouse (Lyrurus tetrix) in the High Fens (Belgium): did the rabies vaccination has a negative impact on a fox prey population?

Since 2017, a reinforcement programme was developed to save the last, endangered, Belgian population of black grouse (Lyrurus tetrix), in the High Fens Natural Park. To improve the success of this programme, an analysis of past data of this population was undertaken to understand the causes of its past decline. A time series analysis was applied, using annual spring male census data recorded between 1967 and 2016. In the period 1967-1993, there was a fluctuation around an equilibrium of a population of ca. 40-45 males. The peak of 85 males observed in 1971 was probably due to a succession of several favourable years in terms of environmental conditions, albeit without an exceptional annual growth rate. It seems that fox density, by using the occurrence of rabies as a proxy, has an impact on the black grouse population. After 1993, the population dynamic changed drastically, decreasing continuously until finally reaching quasi-extinction. On average, the population lost 15.4% of its size each year. Climate models, applied in previous studies to explain these population trends in the High Fens, failed to describe this major modification in this population's dynamic and its recent decline. We suggest that this negative effect was mainly induced by a significant increase in predation by red fox (Vulpes vulpes), whose abundance has increased considerably since the 1990s, in particular, as a consequence of the eradication of fox rabies. We also discuss alternative hypotheses, such as the impact of other predator species, modification of the natural environment and climatic modifications.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10344-023-01642-w.

Analysis of the evolution, infectivity and antigenicity of circulating rabies virus strains

Rabies virus has existed for thousands of years and is circulating in many species. In the present study, a total of 2896 rabies viruses isolated worldwide were phylogenetically classified into ten clusters based on the G gene sequence, and these clusters showed a close relationship with the hosts and regions that they were isolated from. Eighty-three representative G sequences were selected from ten clusters and were used to construct pseudoviruses using the VSV vector. The phylogenetic relationships, infectivity and antigenicity of the representative 83 pseudotyped rabies viruses were comprehensively analyzed. Eighty three pseudoviruses were divided into four antigentic clusters (GAgV), of which GAgV4 showed poor neutralization to all immunized sera. Further analysis showed that almost all strains in the GAgV4 were isolated from wild animals in the America, especially bats and skunks. No significant relationship in terms of phylogeny, infectivity and antigenicity was proved. Amino acid mutations at residues 231and 436 can affect the infectivity, while mutations at residues 113, 164 and 254 may affect the sensitivity to immunized animal sera, especially residue 254. We recommend close monitoring of infectivity and antigenicity, which should be more precise than simple genetic analysis.

Quantifying intra- and inter-species contact rates at supplemental feeding sites in Ethiopia to inform rabies maintenance potential of multiple host species

Rabies, a multi-host pathogen responsible for the loss of roughly 59,000 human lives each year worldwide, continues to impose a significant burden of disease despite control efforts, especially in Ethiopia. However, how species other than dogs contribute to rabies transmission throughout Ethiopia remains largely unknown. In this study, we quantified interactions among wildlife species in Ethiopia with the greatest potential for contributing to rabies maintenance. We observed wildlife at supplemental scavenging sites across multiple landscape types and quantified transmission potential. More specifically, we used camera trap data to quantify species abundance, species distribution, and intra- and inter-species contacts per trapping night over time and by location. We derived a mathematical expression for the basic reproductive number (R₀ ) based on within- and between-species contract rates by applying the next generation method to the susceptible, exposed, infectious, removed model. We calculated R₀ for transmission within each species and between each pair of species using camera trap data in order to identify pairwise interactions that contributed the most to transmission in an ecological community. We estimated which species, or species pairs, could maintain transmission ( R 0 > 1 ${R_0} &gt; 1$ ) and which species, or species pairs, had contact rates too low for maintenance ( R 0 < 1 ${R_0} &lt; 1$ ). Our results identified multiple urban carnivores as candidate species for rabies maintenance throughout Ethiopia, with hyenas exhibiting the greatest risk for rabies maintenance through intra-species transmission. Hyenas and cats had the greatest risk for rabies maintenance through inter-species transmission. Urban and peri-urban sites posed the greatest risk for rabies transmission. The night-time hours presented the greatest risk for a contact event that could result in rabies transmission. Overall, both intra- and inter-species contacts posed risk for rabies maintenance. Our results can be used to target future studies and inform population management decisions.

Predicting the evolution of the Lassa virus endemic area and population at risk over the next decades

Lassa fever is a severe viral hemorrhagic fever caused by a zoonotic virus that repeatedly spills over to humans from its rodent reservoirs. It is currently not known how climate and land use changes could affect the endemic area of this virus, currently limited to parts of West Africa. By exploring the environmental data associated with virus occurrence using ecological niche modelling, we show how temperature, precipitation and the presence of pastures determine ecological suitability for virus circulation. Based on projections of climate, land use, and population changes, we find that regions in Central and East Africa will likely become suitable for Lassa virus over the next decades and estimate that the total population living in ecological conditions that are suitable for Lassa virus circulation may drastically increase by 2070. By analysing geotagged viral genomes using spatially-explicit phylogeography and simulating virus dispersal, we find that in the event of Lassa virus being introduced into a new suitable region, its spread might remain spatially limited over the first decades.

Asymmetric host movement reshapes local disease dynamics in metapopulations

Understanding how the movement of individuals affects disease dynamics is critical to accurately predicting and responding to the spread of disease in an increasingly interconnected world. In particular, it is not yet known how movement between patches affects local disease dynamics (e.g., whether pathogen prevalence remains steady or oscillates through time). Considering a set of small, archetypal metapopulations, we find three surprisingly simple patterns emerge in local disease dynamics following the introduction of movement between patches: (1) movement between identical patches with cyclical pathogen prevalence dampens oscillations in the destination while increasing synchrony between patches; (2) when patches differ from one another in the absence of movement, adding movement allows dynamics to propagate between patches, alternatively stabilizing or destabilizing dynamics in the destination based on the dynamics at the origin; and (3) it is easier for movement to induce cyclical dynamics than to induce a steady-state. Considering these archetypal networks (and the patterns they exemplify) as building blocks of larger, more realistically complex metapopulations provides an avenue for novel insights into the role of host movement on disease dynamics. Moreover, this work demonstrates a framework for future predictive modelling of disease spread in real populations.

Guidance on good practice in conducting scientific assessments in animal health using modelling

The EFSA asked the Panel on Animal Health and Welfare to develop a guidance document on good practice in conducting scientific assessments in animal health using modelling. In previous opinions, the AHAW Panel has responded to two‐thirds of animal health‐related mandates using some kind of modelling. These models range from simple to complex, employing a combination of scientific, economic, socio‐economic or other types of data. Hence, there is strong interest in the development of a guidance document to integrate modelling efforts into the routine process of EFSA working groups. In this document, an ‘operating procedure' (OP) for the use of modelling within an AH working group is presented. The OP provides a detailed flowchart enabling modelling to be transparently and consistently integrated in the assessment. The OP is structured into phases. These phases combine the relevant standard operating procedures and working instructions of EFSA with the modelling process. Each phase includes roles and actions to be taken, expected output and the sequence of agreements that need to be made between all partners in the scientific assessment. In conclusion, it is expected that adherence to the OP will improve transparency of models in EFSA outputs, and it is recommended to adopt it as a standard procedure when responding to AHAW mandates.

Transmission models indicate Ebola virus persistence in non-human primate populations is unlikely

Infectious diseases that kill their hosts may persist locally only if transmission is appropriately balanced by susceptible recruitment. Great apes die of Ebola virus disease (EVD) and have transmitted ebolaviruses to people. However, understanding the role that apes and other non-human primates play in maintaining ebolaviruses in Nature is hampered by a lack of data. Recent serological findings suggest that few non-human primates have antibodies to EVD-causing viruses throughout tropical Africa, suggesting low transmission rates and/or high EVD mortality (Ayouba A et al. 2019 J. Infect. Dis. 220, 1599-1608 (doi:10.1093/infdis/jiz006); Mombo IM et al. 2020 Viruses 12, 1347 (doi:10.3390/v12121347)). Here, stochastic transmission models of EVD in non-human primates assuming high case-fatality probabilities and experimentally observed or field-observed parameters did not allow viral persistence, suggesting that non-human primate populations are highly unlikely to sustain EVD-causing infection for prolonged periods. Repeated introductions led to declining population sizes, similar to field observations of apes, but not viral persistence.

Evaluating the Impact of Anthropogenic Factors on the Dissemination of Contemporary Cosmopolitan, Arctic, and Arctic-like Rabies Viruses

Rabies is a globally prevalent viral zoonosis that causes 59,000 deaths per year and has important economic consequences. Most virus spread is associated with the migration of its primary hosts. Anthropogenic dissemination, mainly via the transportation of rabid dogs, shaped virus ecology a few hundred years ago and is responsible for several current outbreaks. A systematic analysis of aberrant long-distance events in the steppe and Arctic-like groups of rabies virus was performed using statistical (Bayesian) phylogeography and plots of genetic vs. geographic distances. The two approaches produced similar results but had some significant differences and complemented each other. No phylogeographic analysis could be performed for the Arctic group because polar foxes transfer the virus across the whole circumpolar region at high velocity, and there was no correlation between genetic and geographic distances in this virus group. In the Arctic-like group and the steppe subgroup of the cosmopolitan group, a significant number of known sequences (15-20%) was associated with rapid long-distance transfers, which mainly occurred within Eurasia. Some of these events have been described previously, while others have not been documented. Most of the recent long-distance transfers apparently did not result in establishing the introduced virus, but a few had important implications for the phylogeographic history of rabies. Thus, human-mediated long-distance transmission of the rabies virus remains a significant threat that needs to be addressed.

Data-driven dynamical modelling of the transmission of African swine fever in a few places in China

Since the outbreak of African swine fever (ASF) in Shengyang, it has continued spreading in China. In the early stage of the epidemic, multi-point and concentrated outbreaks were mainly in the swill feeding areas. In this paper, we developed compartmental models to investigate the transmission of ASF in several raising units including Guquan, Jinba and Liancheng. Using the data collected from these three infected premises, we calibrated the models to estimate that the average incubation period was between 8 and 11 days, the onset period was about 2-3 days and the basic reproductive number was about 4.83-11.90. We also estimated the infection on the day before culling to be 45.24% (Guquan), 89.20% (Jinba) and 16.35% (Liancheng), respectively. The infection rate of Guquan could reach about 74.8% if culling were postponed by 2 days. We found that the infection was significantly higher than the morbidities (22.11% (Guquan), 49.35% (Jinba) and 12.94% (Liancheng)) calculated by actual statistical data. Besides, we simulated and compared the control effect of stopping transport, disinfecting, stopping swill and culling. Our findings suggest that any single measure was not enough to prevent the spread of ASF on a regional level but the combined measures is the key. Under the current situation, fully culling was recognized as most effective in controlling the epidemic, despite the culling of uninfected pigs.

Atto-Foxes and Other Minutiae

This paper addresses the problem of extinction in continuous models of population dynamics associated with small numbers of individuals. We begin with an extended discussion of extinction in the particular case of a stochastic logistic model, and how it relates to the corresponding continuous model. Two examples of ‘small number dynamics’ are then considered. The first is what Mollison calls the ‘atto-fox’ problem (in a model of fox rabies), referring to the problematic theoretical occurrence of a predicted rabid fox density of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^{-18}$$\end{document}10-18 (atto-) per square kilometre. The second is how the production of large numbers of eggs by an individual can reliably lead to the eventual survival of a handful of adults, as it would seem that extinction then becomes a likely possibility. We describe the occurrence of the atto-fox problem in other contexts, such as the microbial ‘yocto-cell’ problem, and we suggest that the modelling resolution is to allow for the existence of a reservoir for the extinctively challenged individuals. This is functionally similar to the concept of a ‘refuge’ in predator–prey systems and represents a state for the individuals in which they are immune from destruction. For what I call the ‘frogspawn’ problem, where only a few individuals survive to adulthood from a large number of eggs, we provide a simple explanation based on a Holling type 3 response and elaborate it by means of a suitable nonlinear age-structured model.

Epidemiological and numerical simulation of rabies spreading from canines to various human populations in mainland China

BACKGROUND

The mortality of humans due to rabies in China has been declining in recent years, but it is still a significant public health problem. According to the global framework, China strives to achieve the goal of eliminating human rabies before 2030.

METHODS

We reviewed the epidemiology of human deaths from rabies in mainland China from 2004 to 2018. We identified high risk regions, age and occupational groups, and used a continuous deterministic susceptibility-exposure-infection-recovery (SEIR) model with periodic transmission rate to explore seasonal rabies prevalence in different human populations. The SEIR model was used to simulate the data of human deaths from rabies reported by the Chinese Center for Disease Control and Prevention (China CDC). We calculated the relative transmission intensity of rabies from canines to different human groups, and they provided a reliable epidemiological basis for further control and prevention of human rabies.

RESULTS

Results showed that human deaths from rabies exhibited regional differences and seasonal characteristics in mainland China. The annual human death from rabies in different regions, age groups and occupational groups decreased steadily across time. Nevertheless, the decreasing rates and the calculated R0s of canines of various human groups were different. The transmission intensity of rabies from canines to human populations was the highest in the central regions of China, in people over 45 years old, and in farmers.

CONCLUSIONS

Although the annual cases of human deaths from rabies have decreased steadily since 2007, the proportion of human deaths from rabies varies with region, age, gender, and occupation. Further enhancement of public awareness and immunization status in high-risk population groups and blocking the transmission routes of rabies from canines to humans are necessary. The concept of One Health should be abided and human, animal, and environmental health should be considered simultaneously to achieve the goal of eradicating human rabies before 2030.

Current Status of Rabies and Its Eradication in Eastern and Southeastern Europe

The objective of this paper is to provide an overview of the current status of rabies in Europe, with special emphasis on Croatia and Southeast and East Europe. Due to the systematic implementation of a rabies eradication program by oral vaccination of wild animals, by the end of the 20th century, most West and Central European countries were rabies-free. The EU goal was to eradicate rabies in wildlife and domestic animals by 2020. No matter how achievable the goal seemed to be, the disease is still present in the eastern part of the EU, as was notified in 2020 by two member states—Poland and Romania. Croatia has been rabies-free for the last seven years but given that it borders a non-EU country in which a case of rabies was confirmed in 2020, it will continue to contribute to the maintenance of the rabies-free region. A rabies-free EU can only be achieved by continuous oral vaccination, coordination and a regional approach. The prevention of reintroductions from bordering countries in which rabies has not been eradicated yet, and the support for the eradication efforts made by these countries, are goals still pending.

Parasite evolution in an age-structured population

Although mortality increases with age in most organisms, senescence is missing from models of parasite evolution. Since virulence evolves according to the host's mortality, and since virulence influences the intensity of transmission, which determines the average age at infection and thus the mortality rate of a senescing host, we expected that epi-evolutionary feedbacks would underlie the evolution of virulence in a population of senescing hosts. We tested this idea by extending an age-structured model of epidemiological dynamics with the parasite's evolution. A straightforward prediction of our model is that stronger senescence forces the evolution of higher virulence. However, the model also reveals that the evolved virulence depends on the average age at infection, giving an evolutionary feedback with the epidemiological situation, a prediction not found when assuming a constant mortality rate with age. Additionally, and in contrast to most models of parasite evolution, we found that the virulence at the evolutionary equilibrium is influenced by whether the force of infection depends on the density or on the frequency of infected hosts, due to changes in the average age at infection. Our findings suggest that ignoring age-specific effects, and in particular senescence, can give misleading predictions about parasite evolution.

Dynamics of a stochastic rabies epidemic model with Markovian switching

In this paper, we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph noise. First, we prove the existence of the unique global positive solution. Second, by constructing an appropriate Lyapunov function, we establish a sufficient condition for the existence of a unique ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for the extinction of diseases. Finally, numerical simulations are introduced to illustrate our theoretical results.

Biophysical analysis of SARS-CoV-2 transmission and theranostic development via N protein computational characterization

Recently, SARS-CoV-2 has been identified as the causative factor of viral infection called COVID-19 that belongs to the zoonotic beta coronavirus family known to cause respiratory disorders or viral pneumonia, followed by an extensive attack on organs that express angiotensin-converting enzyme II (ACE2). Human transmission of this virus occurs via respiratory droplets from symptomatic and asymptomatic patients, which are released into the environment after sneezing or coughing. These droplets are capable of staying in the air as aerosols or surfaces and can be transmitted to persons through inhalation or contact with contaminated surfaces. Thus, there is an urgent need for advanced theranostic solutions to control the spread of COVID-19 infection. The development of such fit-for-purpose technologies hinges on a proper understanding of the transmission, incubation, and structural characteristics of the virus in the external environment and within the host. Hence, this article describes the development of an intrinsic model to describe the incubation characteristics of the virus under varying environmental factors. It also discusses on the evaluation of SARS-CoV-2 structural nucleocapsid protein properties via computational approaches to generate high-affinity binding probes for effective diagnosis and targeted treatment applications by specific targeting of viruses. In addition, this article provides useful insights on the transmission behavior of the virus and creates new opportunities for theranostics development.

Serological Responses of Raccoons and Striped Skunks to Ontario Rabies Vaccine Bait in West Virginia during 2012-2016

Since the 1990s, oral rabies vaccination (ORV) has been used successfully to halt the westward spread of the raccoon rabies virus (RV) variant from the eastern continental USA. Elimination of raccoon RV from the eastern USA has proven challenging across targeted raccoon (Procyon lotor) and striped skunk (Mephitis mephitis) populations impacted by raccoon RV. Field trial evaluations of the Ontario Rabies Vaccine Bait (ONRAB) were initiated to expand ORV products available to meet the rabies management goal of raccoon RV elimination. This study describes the continuation of a 2011 trial in West Virginia. Our objective was to evaluate raccoon and skunk response to ORV occurring in West Virginia for an additional two years (2012–2013) at 75 baits/km² followed by three years (2014–2016) of evaluation at 300 baits/km². We measured the change in rabies virus-neutralizing antibody (RVNA) seroprevalence in targeted wildlife populations by comparing levels pre- and post-ORV during each year of study. The increase in bait density from 75/km² to 300/km² corresponded to an increase in average post-ORV seroprevalence for raccoon and skunk populations. Raccoon population RVNA levels increased from 53% (300/565, 95% CI: 50–57%) to 82.0% (596/727, 95% CI: 79–85%) during this study, and skunk population RVNA levels increased from 11% (8/72, 95% CI: 6–20%) to 39% (51/130, 95% CI: 31–48%). The RVNA seroprevalence pre-ORV demonstrated an increasing trend across study years for both bait densities and species, indicating that multiple years of ORV may be necessary to achieve and maintain RVNA seroprevalence in target wildlife populations for the control and elimination of raccoon RV in the eastern USA.

Modeling transmission dynamics of rabies in Nepal

Even though vaccines against rabies are available, rabies still remains a burden killing a significant number of humans as well as domestic and wild animals in many parts of the world, including Nepal. In this study, we develop a mathematical model to describe transmission dynamics of rabies in Nepal. In particular, an indirect interspecies transmission from jackals to humans through dogs, which is relevant to the context of Nepal, is one of the novel features of our model. Our model utilizes annual dog-bite data collected from Nepal for a decade long period, allowing us to reasonably estimate parameters related to rabies transmission in Nepal. Using our model, we calculated the basic reproduction number ( R 0 = 1.16 ) as well as intraspecies basic reproduction numbers of dogs ( R 0 D = 1.14 ) and jackals ( R 0 J = 0.07 ) for Nepal, and identified that the dog-related parameters are primary contributors to R 0 . Our results show that, along with dogs, jackals may also play an important role, albeit lesser extent, in the persistence of rabies in Nepal. Our model also suggests that control strategies may help reduce the prevalence significantly but the jackal vaccination may not be as effective as dog-related preventive strategies. To get deeper insight into the role of intraspecies and interspecies transmission between dog and jackal populations in the persistence of rabies, we also extended our model analysis into a wider parameter range. Interestingly, for some feasible parameters, even though rabies is theoretically controlled in each dog and jackal populations ( R 0 D < 1 , R 0 J < 1 ) if isolated, the rabies epidemic may still occur ( R 0 > 1 ) due to interspecies transmission. These results may be useful to design effective prevention and control strategies for mitigating rabies burden in Nepal and other parts of the world.

Modeling Rabies Transmission in Spatially Heterogeneous Environments via [Formula: see text]-diffusion

Rabies among dogs remains a considerable risk to humans and constitutes a serious public health concern in many parts of the world. Conventional mathematical models for rabies typically assume homogeneous environments, with a standard diffusion term for the population of rabid animals. It has recently been recognized, however, that spatial heterogeneity plays an important role in determining spatial patterns of rabies and the cost-effectiveness of vaccinations. In this paper, we develop a spatially heterogeneous dog rabies model by using the [Formula: see text]-diffusion equation, where [Formula: see text] reflects the way individual dogs make movement decisions in the underlying random walk. We numerically investigate the dynamics of the model in three diffusion cases: homogeneous, city-wild, and Gaussian-type. We find that the initial conditions affect whether traveling waves or epizootic waves can be observed. However, different initial conditions have little impact on steady-state solutions. An "active" interface is observed between city and wild regions, with a "ridge" on the city side and a "valley" on the wild side for the infectious dog population. In addition, the progressing speed of epizootic waves changes in heterogeneous environments. It is impossible to eliminate rabies in the entire spatial domain if vaccination is focused only in the city region or only in the wild region. When a seasonal transmission is incorporated, the dog population size approaches a positive time-periodic spatially heterogeneous state eventually.

Using host traits to predict reservoir host species of rabies virus

Wildlife are important reservoirs for many pathogens, yet the role that different species play in pathogen maintenance frequently remains unknown. This is the case for rabies, a viral disease of mammals. While Carnivora (carnivores) and Chiroptera (bats) are the canonical mammalian orders known to be responsible for the maintenance and onward transmission of rabies Lyssavirus (RABV), the role of most species within these orders remains unknown and is continually changing as a result of contemporary host shifting. We combined a trait-based analytical approach with gradient boosting machine learning models to identify physiological and ecological host features associated with being a reservoir for RABV. We then used a cooperative game theory approach to determine species-specific traits associated with known RABV reservoirs. Being a carnivore reservoir for RABV was associated with phylogenetic similarity to known RABV reservoirs, along with other traits such as having larger litters and earlier sexual maturity. For bats, location in the Americas and geographic range were the most important predictors of RABV reservoir status, along with having a large litter. Our models identified 44 carnivore and 34 bat species that are currently not recognized as RABV reservoirs, but that have trait profiles suggesting their capacity to be or become reservoirs. Further, our findings suggest that potential reservoir species among bats and carnivores occur both within and outside of areas with current RABV circulation. These results show the ability of a trait-based approach to detect potential reservoirs of infection and could inform rabies control programs and surveillance efforts by identifying the types of species and traits that facilitate RABV maintenance and transmission.

Three questions to ask before using model outputs for decision support

Decision makers must have sufficient confidence in models if they are to influence their decisions. We propose three screening questions to critically evaluate models with respect to their purpose, organization, and evidence. They enable a more transparent, robust, and secure use of model outputs.

A systemic approach to assess the potential and risks of wildlife culling for infectious disease control

The maintenance of infectious diseases requires a sufficient number of susceptible hosts. Host culling is a potential control strategy for animal diseases. However, the reduction in biodiversity and increasing public concerns regarding the involved ethical issues have progressively challenged the use of wildlife culling. Here, we assess the potential of wildlife culling as an epidemiologically sound management tool, by examining the host ecology, pathogen characteristics, eco-sociological contexts, and field work constraints. We also discuss alternative solutions and make recommendations for the appropriate implementation of culling for disease control.

Local rabies transmission and regional spatial coupling in European foxes

Infectious diseases are often transmitted through local interactions. Yet, both surveillance and control measures are implemented within administrative units. Capturing local transmission processes and spatial coupling between regions from aggregate level data is therefore a technical challenge that can shed light on both theoretical questions and practical decisions. Fox rabies has been eliminated from much of Europe through oral rabies vaccination (ORV) programmes. The European Union (EU) co-finances ORV to maintain rabies freedom in EU member and border states via a cordon sanitaire. Models to capture local transmission dynamics and spatial coupling have immediate application to the planning of these ORV campaigns and to other parts of the world considering oral vaccination. We fitted a hierarchical Bayesian state-space model to data on three decades of fox rabies cases and ORV campaigns from Eastern Germany. Specifically, we find that (i) combining regional spatial coupling and heterogeneous local transmission allows us to capture regional rabies dynamics; (ii) incursions from other regions account for less than 1% of cases, but allow for re-emergence of disease; (iii) herd immunity achieved through bi-annual vaccination campaigns is short-lived due to population turnover. Together, these findings highlight the need for regular and sustained vaccination efforts and our modelling approach can be used to provide strategic guidance for ORV delivery. Moreover, we show that biological understanding can be gained from inference from partially observed data on wildlife disease.

Vaccination and monitoring strategies for epidemic prevention and detection in the Channel Island fox (Urocyon littoralis)

Disease transmission and epidemic prevention are top conservation concerns for wildlife managers, especially for small, isolated populations. Previous studies have shown that the course of an epidemic within a heterogeneous host population is strongly influenced by whether pathogens are introduced to regions of relatively high or low host densities. This raises the question of how disease monitoring and vaccination programs are influenced by spatial heterogeneity in host distributions. We addressed this question by modeling vaccination and monitoring strategies for the Channel Island fox (Urocyon littoralis), which has a history of substantial population decline due to introduced disease. We simulated various strategies to detect and prevent epidemics of rabies and canine distemper using a spatially explicit model, which was parameterized from field studies. Increasing sentinel monitoring frequency, and to a lesser degree, the number of monitored sentinels from 50 to 150 radio collared animals, reduced the time to epidemic detection and percentage of the fox population infected at the time of detection for both pathogens. Fox density at the location of pathogen introduction had little influence on the time to detection, but a large influence on how many foxes had become infected by the detection day, especially when sentinels were monitored relatively infrequently. The efficacy of different vaccination strategies was heavily influenced by local host density at the site of pathogen entry. Generally, creating a vaccine firewall far away from the site of pathogen entry was the least effective strategy. A firewall close to the site of pathogen entry was generally more effective than a random distribution of vaccinated animals when pathogens entered regions of high host density, but not when pathogens entered regions of low host density. These results highlight the importance of considering host densities at likely locations of pathogen invasion when designing disease management plans.

Optimizing spatial and seasonal deployment of vaccination campaigns to eliminate wildlife rabies

Understanding how the spatial deployment of interventions affects elimination time horizons and potential for disease re-emergence has broad application to control programmes targeting human, animal and plant pathogens. We previously developed an epidemiological model that captures the main features of rabies spread and the impacts of vaccination based on detailed records of fox rabies in eastern Germany during the implementation of an oral rabies vaccination (ORV) programme. Here, we use simulations from this fitted model to determine the best vaccination strategy, in terms of spatial placement and timing of ORV efforts, for three epidemiological scenarios representative of current situations in Europe. We found that consecutive and comprehensive twice-yearly vaccinations across all regions rapidly controlled and eliminated rabies and that the autumn campaigns had the greater impact on increasing the probability of elimination. This appears to result from the need to maintain sufficient herd immunity in the face of large birth pulses, as autumn vaccinations reach susceptible juveniles and therefore a larger proportion of the population than spring vaccinations. Incomplete vaccination compromised time to elimination requiring the same or more vaccination effort to meet similar timelines. Our results have important practical implications that could inform policies for rabies containment and elimination in Europe and elsewhere. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. This theme issue is linked with the earlier issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'.

Separate seasons of infection and reproduction can lead to multi-year population cycles

Many host-pathogen systems are characterized by a temporal order of disease transmission and host reproduction. For example, this can be due to pathogens infecting certain life cycle stages of insect hosts; transmission occurring during the aggregation of migratory birds; or plant diseases spreading between planting seasons. We develop a simple discrete-time epidemic model with density-dependent transmission and disease affecting host fecundity and survival. The model shows sustained multi-annual cycles in host population abundance and disease prevalence, both in the presence and absence of density dependence in host reproduction, for large horizontal transmissibility, imperfect vertical transmission, high virulence, and high reproductive capability. The multi-annual cycles emerge as invariant curves in a Neimark-Sacker bifurcation. They are caused by a carry-over effect, because the reproductive fitness of an individual can be reduced by virulent effects due to infection in an earlier season. As the infection process is density-dependent but shows an effect only in a later season, this produces delayed density dependence typical for second-order oscillations. The temporal separation between the infection and reproduction season is crucial in driving the cycles; if these processes occur simultaneously as in differential equation models, there are no sustained oscillations. Our model highlights the destabilizing effects of inter-seasonal feedbacks and is one of the simplest epidemic models that can generate population cycles.

Rabies virus-neutralising antibodies in healthy, unvaccinated individuals: What do they mean for rabies epidemiology?

Rabies has been a widely feared disease for thousands of years, with records of rabid dogs as early as ancient Egyptian and Mesopotamian texts. The reputation of rabies as being inevitably fatal, together with its ability to affect all mammalian species, contributes to the fear surrounding this disease. However, the widely held view that exposure to the rabies virus is always fatal has been repeatedly challenged. Although survival following clinical infection in humans has only been recorded on a handful of occasions, a number of studies have reported detection of rabies-specific antibodies in the sera of humans, domestic animals, and wildlife that are apparently healthy and unvaccinated. These 'seropositive' individuals provide possible evidence of exposure to the rabies virus that has not led to fatal disease. However, the variability in methods of detecting these antibodies and the difficulties of interpreting serology tests have contributed to an unclear picture of their importance. In this review, we consider the evidence for rabies-specific antibodies in healthy, unvaccinated individuals as indicators of nonlethal rabies exposure and the potential implications of this for rabies epidemiology. Our findings indicate that whilst there is substantial evidence that nonlethal rabies exposure does occur, serology studies that do not use appropriate controls and cutoffs are unlikely to provide an accurate estimate of the true prevalence of nonlethal rabies exposure.

Zero Endemic Cases of Wildlife Rabies (Classical Rabies Virus, RABV) in the European Union by 2020: An Achievable Goal

The elimination of rabies transmitted by Classical Rabies Virus (RABV) in the European Union (EU) is now in sight. Scientific advances have made it possible to develop oral vaccination for wildlife by incorporating rabies vaccines in baits for foxes. At the start of the 1980s, aerial distribution of vaccine baits was tested and found to be a promising tool. The EU identified rabies elimination as a priority, and provided considerable financial and technical resources to the infected EU Member States, allowing regular and large-scale rabies eradication programs based on aerial vaccination. The EU also provides support to non-EU countries in its eastern and south eastern borders. The key elements of the rabies eradication programs are oral rabies vaccination (ORV), quality control of vaccines and control of their distribution, rabies surveillance and monitoring of the vaccination effectiveness. EU Member States and non-EU countries with EU funded eradication programs counted on the technical support of the rabies subgroup of the Task Force for monitoring disease eradication and of the EU Reference Laboratory (EURL) for rabies. In 2018, eight rabies cases induced by classical rabies virus RABV (six in wild animals and two in domestic animals) were detected in three EU Member States, representing a sharp decrease compared to the situation in 2010, where there were more than 1500 cases in nine EU Member States. The goal is to reach zero cases in wildlife and domestic animals in the EU by 2020, a target that now seems achievable.

Land Use Change Increases Wildlife Parasite Diversity in Anamalai Hills, Western Ghats, India

Anthropogenic landscape changes such as land use change and habitat fragmentation are known to alter wildlife diversity. Since host and parasite diversities are strongly connected, landscape changes are also likely to change wildlife parasite diversity with implication for wildlife health. However, research linking anthropogenic landscape change and wildlife parasite diversity is limited, especially comparing effects of land use change and habitat fragmentation, which often cooccur but may affect parasite diversity substantially differently. Here, we assessed how anthropogenic land use change (presence of plantation, livestock foraging and human settlement) and habitat fragmentation may change the gastrointestinal parasite diversity of wild mammalian host species (n = 23) in Anamalai hills, India. We found that presence of plantations, and potentially livestock, significantly increased parasite diversity due possibly to spillover of parasites from livestock to wildlife. However, effect of habitat fragmentation on parasite diversity was not significant. Together, our results showed how human activities may increase wildlife parasite diversity within human-dominated landscape and highlighted the complex pattern of parasite diversity distribution as a result of cooccurrence of multiple anthropogenic landscape changes.

Spatial Structure in Disease Transmission Models

With the advent of substantial intercontinental air travel, it is possible for diseases to move from one location to a completely separate location very rapidly. This was an essential aspect of modeling SARS during the epidemic of 2002–2003, and has become a very important part of the study of the spread of epidemics. Mathematically, it has led to the study of metapopulation models or models with patchy environments and movement between patches.

Modeling the Transmission Dynamics of Rabies for Dog, Chinese Ferret Badger and Human Interactions in Zhejiang Province, China

Human rabies is one of the major public health problems in China with an average of 1977 cases per year. It is estimated that 95% of these human rabies cases are due to dog bites. In recent years, the number of wildlife-associated human rabies cases has increased, particularly in the southeast and northeast regions of mainland China. Chinese ferret badgers (CFBs) are one of the most popular wildlife animals which are distributed mostly in the southeast region of China. Human cases caused by rabid CFB were first recorded in Huzhou, Zhejiang Province, in 1994. From 1996 to 2004, more than 30 human cases were caused by CFB bites in Zhejiang Province. In this paper, based on the reported data of the human rabies caused by both dogs and CFB in Zhejiang Province, we propose a multi-host zoonotic model for the dog-CFB-human transmission of rabies. We first evaluate the basic reproduction number [Formula: see text] discuss the stability of the disease-free equilibrium, and study persistence of the disease. Then we use our model to fit the reported data in Zhejiang Province from 2004 to 2017 and forecast the trend of human or livestock rabies. Finally by carrying out sensitivity analysis of the basic reproduction number in terms of parameters, we find that the transmission between dogs and CFB, the quantity of dogs, and the vaccination rate of dogs play important roles in the transmission of rabies. Our study suggests that rabies control and prevention strategies should include enhancing public education and awareness about rabies, increasing dog vaccination rate, reducing the dog and CFB interactions, and avoiding CFB bites or contact.

Transmission dynamics of re-emerging rabies in domestic dogs of rural China

Despite ongoing efforts to control transmission, rabies prevention remains a challenge in many developing countries, especially in rural areas of China where re-emerging rabies is under-reported due to a lack of sustained animal surveillance. By taking advantage of detailed genomic and epidemiological data for the re-emerging rabies outbreak in Yunnan Province, China, collected between 1999 and 2015, we reconstruct the demographic and dispersal history of domestic dog rabies virus (RABV) as well as the dynamics of dog-to-dog and dog-to-human transmission. Phylogeographic analyses reveal a lower diffusion coefficient than previously estimated for dog RABV dissemination in northern Africa. Furthermore, epidemiological analyses reveal transmission rates between dogs, as well as between dogs and humans, lower than estimates for Africa. Finally, we show that reconstructed epidemic history of RABV among dogs and the dynamics of rabid dogs are consistent with the recorded human rabies cases. This work illustrates the benefits of combining phylogeographic and epidemic modelling approaches for uncovering the spatiotemporal dynamics of zoonotic diseases, with both approaches providing estimates of key epidemiological parameters.

A metapopulation model of dog rabies transmission in N'Djamena, Chad

Rabies transmission was interrupted for several months in N'Djamena, the capital city of Chad, after two mass vaccination campaigns of dogs. However, there was a resurgence in cases, which was not predicted by previous models of rabies transmission. We developed a deterministic metapopulation model with importation of latent dogs, calibrated to four years of weekly incidence data from passive surveillance, to investigate possible causes for the early resurgence. Our results indicate that importation of latently infective dogs better explains the data than heterogeneity or underreporting. Stochastic implementations of the model suggest that the two vaccination campaigns averted approximately 67 cases of dog rabies (out of an estimated 74 cases without vaccination) and 124 human exposures (out of an estimated 148 human exposures without vaccination) over two years. Dog rabies vaccination is therefore an effective way of preventing rabies in the dog population and to subsequently reduce human exposure. However, vaccination campaigns have to be repeated to maintain the effect or reintroduction through importation has to be prevented.

Cost-effectiveness of dog rabies vaccination programs in East Africa

BACKGROUND

Dog rabies annually causes 24,000-70,000 deaths globally. We built a spreadsheet tool, RabiesEcon, to aid public health officials to estimate the cost-effectiveness of dog rabies vaccination programs in East Africa.

METHODS

RabiesEcon uses a mathematical model of dog-dog and dog-human rabies transmission to estimate dog rabies cases averted, the cost per human rabies death averted and cost per year of life gained (YLG) due to dog vaccination programs (US 2015 dollars). We used an East African human population of 1 million (approximately 2/3 living in urban setting, 1/3 rural). We considered, using data from the literature, three vaccination options; no vaccination, annual vaccination of 50% of dogs and 20% of dogs vaccinated semi-annually. We assessed 2 transmission scenarios: low (1.2 dogs infected per infectious dog) and high (1.7 dogs infected). We also examined the impact of annually vaccinating 70% of all dogs (World Health Organization recommendation for dog rabies elimination).

RESULTS

Without dog vaccination, over 10 years there would a total of be approximately 44,000-65,000 rabid dogs and 2,100-2,900 human deaths. Annually vaccinating 50% of dogs results in 10-year reductions of 97% and 75% in rabid dogs (low and high transmissions scenarios, respectively), approximately 2,000-1,600 human deaths averted, and an undiscounted cost-effectiveness of $451-$385 per life saved. Semi-annual vaccination of 20% of dogs results in in 10-year reductions of 94% and 78% in rabid dogs, and approximately 2,000-1,900 human deaths averted, and cost $404-$305 per life saved. In the low transmission scenario, vaccinating either 50% or 70% of dogs eliminated dog rabies. Results were most sensitive to dog birth rate and the initial rate of dog-to-dog transmission (Ro).

CONCLUSIONS

Dog rabies vaccination programs can control, and potentially eliminate, dog rabies. The frequency and coverage of vaccination programs, along with the level of dog rabies transmission, can affect the cost-effectiveness of such programs. RabiesEcon can aid both the planning and assessment of dog rabies vaccination programs.

The spread and evolution of rabies virus: conquering new frontiers

Rabies is a lethal zoonotic disease that is caused by lyssaviruses, most often rabies virus. Despite control efforts, sporadic outbreaks in wildlife populations are largely unpredictable, underscoring our incomplete knowledge of what governs viral transmission and spread in reservoir hosts. Furthermore, the evolutionary history of rabies virus and related lyssaviruses remains largely unclear. Robust surveillance efforts combined with diagnostics and disease modelling are now providing insights into the epidemiology and evolution of rabies virus. The immune status of the host, the nature of exposure and strain differences all clearly influence infection and transmission dynamics. In this Review, we focus on rabies virus infections in the wildlife and synthesize current knowledge in the rapidly advancing fields of rabies virus epidemiology and evolution, and advocate for multidisciplinary approaches to advance our understanding of this disease.

Infectious Disease in Wild Animal Populations: Examining Transmission and Control with Mathematical Models

The mathematical modeling of ecological interactions is an essential tool in predicting the behavior of complex systems across landscapes. The scientific literature is growing with examples of models used to explore predator-prey interactions, resource selection, population growth, and dynamics of disease transmission. These models provide managers with an efficient alternative means of testing new management and control strategies without resorting to empirical testing that is often costly, time-consuming, and impractical. This chapter presents a review of four types of mathematical models used to understand and predict the spread of infectious diseases in wild animals: compartmental, metapopulation, spatial, and contact network models. Descriptions of each model’s uses and limitations are used to provide a look at the complexities involved in modeling the spread of diseases and the trade-offs that accompany selecting one modeling approach over another. Potential avenues for the improvement and use of these models in future studies are also discussed, as are specific examples of how each type of model has improved our understanding of infectious diseases in populations of wild animals.

Dynamic, spatial models of parasite transmission in wildlife: Their structure, applications and remaining challenges

Individual differences in contact rate can arise from host, group and landscape heterogeneity and can result in different patterns of spatial spread for diseases in wildlife populations with concomitant implications for disease control in wildlife of conservation concern, livestock and humans. While dynamic disease models can provide a better understanding of the drivers of spatial spread, the effects of landscape heterogeneity have only been modelled in a few well-studied wildlife systems such as rabies and bovine tuberculosis. Such spatial models tend to be either purely theoretical with intrinsic limiting assumptions or individual-based models that are often highly species- and system-specific, limiting the breadth of their utility. Our goal was to review studies that have utilized dynamic, spatial models to answer questions about pathogen transmission in wildlife and identify key gaps in the literature. We begin by providing an overview of the main types of dynamic, spatial models (e.g., metapopulation, network, lattice, cellular automata, individual-based and continuous-space) and their relation to each other. We investigate different types of ecological questions that these models have been used to explore: pathogen invasion dynamics and range expansion, spatial heterogeneity and pathogen persistence, the implications of management and intervention strategies and the role of evolution in host-pathogen dynamics. We reviewed 168 studies that consider pathogen transmission in free-ranging wildlife and classify them by the model type employed, the focal host-pathogen system, and their overall research themes and motivation. We observed a significant focus on mammalian hosts, a few well-studied or purely theoretical pathogen systems, and a lack of studies occurring at the wildlife-public health or wildlife-livestock interfaces. Finally, we discuss challenges and future directions in the context of unprecedented human-mediated environmental change. Spatial models may provide new insights into understanding, for example, how global warming and habitat disturbance contribute to disease maintenance and emergence. Moving forward, better integration of dynamic, spatial disease models with approaches from movement ecology, landscape genetics/genomics and ecoimmunology may provide new avenues for investigation and aid in the control of zoonotic and emerging infectious diseases.