Modeling the transmission dynamics and control of rabies in China

Mathematical model to assess the impact of contact rate and environment factor on transmission dynamics of rabies in humans and dogs

This paper presents a mathematical model to understand how rabies spreads among humans, free-range, and domestic dogs. By analyzing the model, we discovered that there are equilibrium points representing both disease-free and endemic states. We calculated the basic reproduction number,R 0 using the next generation matrix method. WhenR 0 < 1 , the disease-free equilibrium is globally stable, whereas whenR 0 ≥ 1 , the endemic equilibrium is globally stable. To identify the most influential parameters in disease transmission, we used the normalized forward sensitivity index. The simulations revealed that the contact rates between the infectious agent and humans, free-range dogs, and domestic dogs, have the most significant impact on rabies transmission. The study also examines how periodic changes in transmission rates affect the disease dynamics, emphasizing the importance of transmission frequency and amplitude on the patterns observed in rabies spread. To reduce disease sensitivity, one should prioritize effective disease control measures that focus on keeping both free-range and domestic dogs indoors. This is a crucial factor in preventing the spread of disease and should be implemented as a primary disease control measure.

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.

Association between ambient temperature and mammalian-related injuries in Guangzhou, China, 2014-2019

BACKGROUND

Meteorological factors are associated with various health outcomes. However, it remains uncertain whether ambient temperature affects animal aggressive behaviors and causes mammalian-related injuries (MRI) in humans. The study aimed to examine the effect of daily mean temperature on MRI in Guangzhou, China.

METHODS

Individual cases of MRI were obtained from Guangzhou Injury Surveillance System during 2014-2019. A combination of a distributed lag nonlinear model and conditional quasi-Poisson regression, implemented within a time-stratified case-crossover design, was employed to evaluate the association between temperature and MRI. Subgroup analyses were conducted by sex, age group, education level, and types of mammals.

RESULT

This study included 24,206 MRI cases among which 89.7 % were caused by cats or dogs. We observed a nonlinear relationship between daily mean temperature and MRI. The impact of high temperatures was most pronounced on the current day and remained statistically significant on the next day. Compared with the reference temperature with a minimum risk of injuries (9.3 °C, approximately 2nd percentile of temperature), 75th percentile of temperature (27.4 °C) exerted the greatest relative risk (RR) of injuries (RR = 1.45, 95 % CI: 1.25-1.68) over lag 0-1 days. In subgroup analyses, the effects of high temperatures among males and females were similar. Individuals aged 15-34 years and 35-59 years were more susceptible to MRI at high temperatures compared to other age groups. The risk of injuries caused by cats or dogs consistently increased with high temperatures. We did not find significant impacts of low temperatures.

CONCLUSION

Short-term heat exposure plays an important role in the occurrence of MRI. The findings highlight the importance of enhancing public awareness regarding the high temperature-associated hazards posed by mammals. There is a need for enhanced regulations and measures on the management for cats and dogs to mitigate the harm caused in hot seasons.

Dynamic analysis of rabies transmission and elimination in mainland China

Rabies is an acute zoonotic infectious disease caused by rabies virus. In 2015, the World Health Organization proposed the goal of eliminating dog-induced human rabies by 2030. In response to this goal positively, China has been dedicated to the control and elimination of rabies mainly caused by dogs, for nearly 10 years. By applying infectious disease dynamics, in this paper, we establish a dog-human rabies transmission model to forecast future epidemic trends of rabies, assess whether the goal of eliminating dog-induced human rabies cases in China can be achieved in 2030, and further evaluate and suggest the follow-up sustained preventive measures after the elimination of human rabies. By analyzing and simulating above dynamic model, it is concluded that rabies has been well controlled in China in recent years, but dog-induced human rabies cannot be eliminated by 2030 according to current situation. In addition, we propose to improve rabies control efforts by increasing the immunization coverage rate of rural domestic dogs, controlling the number of stray dogs and preventing the import of rabies virus in wild animals. Immunization coverage rate of rural domestic dogs which is currently less than 10% is far from requirement, and it needs to reach 50%-60% to meet the goal of 2030. Since it is difficult to immunize stray dogs, we suggest to control the number of stray dogs below 15.27 million to achieve the goal. If the goal of eliminating human rabies is reached in 2030, the essential immunization coverage needs to be maintained for 18 years to reduce the number of canine rabies cases to zero. Lastly, to prevent transmission of rabies virus from wild animals to dogs, the thresholds of the number of dogs and the immunization coverage rate of dogs after eliminating canine rabies cases are also discussed.

Epidemiological and clinical features of human rabies in Dazu District, Chongqing, China from 2014 to 2021

The epidemiological and clinical data of human rabies cases in the Dazu District of Chongqing from 2014 to 2021 were analyzed retrospectively to determine the epidemiological and clinical features of human rabies cases in Chonqing, China. Nine cases were reported. All cases occurred in farmers from rural areas associated with lower rabies awareness, and eight cases had a definitive history of animal exposure, most commonly in the form of domestic dog bites. All nine patients presented as manic and died within 1–8 days from disease onset (mortality rate of 100%). Increased public awareness of rabies prevention and control is needed, especially among middle-aged and elderly populations in rural areas.

"BACACIX", a spatial index combining proxies of bovine and badger space use associated with extended Mycobacterium bovis circulation in France

To better prevent and control multi-host pathogen circulation over large areas, it is essential to identify patterns of disease persistence within host communities involved in pathogen circulation at a macroscale. The aim of this study was to design and calculate "BACACIX", a spatial index of indirect contacts between cattle and badgers, two species involved in the circulation of Mycobacterium bovis, one of the main causative agents of bovine tuberculosis (bTB), in some areas of France. The index combined spatial models of land use distribution (the probable distribution defining animal use of space) based on pasture location for cattle, and based on land cover for badgers, with proxies for animal density for both species. For badgers, we used two series of census data of badger setts in two regions of France to evaluate our model of badger space use distribution (also known as utilization distribution), and analyzed the relationship between BACACIX and the upsurge of bovine tuberculosis observed in several regions of France during the decade after the country obtained the officially bTB-free status in 2001. We observed high values of BACACIX from the southwest to the northeast of France and from Brittany to the Channel coast. Conversely, in two areas (north-central area and Mediterranean coast), index values were low, suggesting that indirect cattle-badger contacts were unlikely. In the two series of census data of badger setts that we analyzed, 96.5% and 87% of the global positioning system (GPS) locations of badger setts, respectively were located in the calculated badger space use distribution. A logistic regression model showed that after controlling bTB over the previous decade, the value of the index was positively associated with the risk of cattle outbreaks between 2001 and 2010 (OR = 1.57). In addition, the risk of bTB occurrence in cattle decreased when the pasture area outside the badger space use distribution increased. In the future, the spatial index of indirect cattle-badger contacts we propose could help to better target bTB surveillance and control in France.

Ecological and Socioeconomic Factors in the Occurrence of Rabies: A Forgotten Scenario

In many third world countries, where rabies is endemic in dog populations, humans continue to be at risk of contracting the disease. Vaccination is the most effective form of prophylaxis for people, yet it often fails to adequately protect dogs. The most major implications are the costs of post-exposure prophylaxis (PEP) after an exposure occurs and the loss of human life and productivity due to early mortality from rabies (about 60,000 deaths annually). The largest rabies death tolls can be found in the world's poorest regions, where rabies vaccinations for domestic dogs are uncommon and PEP is scarce. Mass vaccination of dogs, neutering programs, patient PEP, strengthening laboratory and human resources, education and awareness, and animal and human rabies surveillance are all common methods used to prevent, control, and ultimately eradicate dog-mediated human rabies. Current rabies control initiatives, however, pay little attention to the role that ecological and socioeconomic variables play in the disease's occurrence and spread. To help better inform rabies control strategies, we address in this work the ways in which ecological and socioeconomic factors affect the occurrence and spread of rabies.

Spatial Distribution and Population Estimation of Dogs in Thailand: Implications for Rabies Prevention and Control

Poor management of dog populations causes many problems in different countries, including rabies. To strategically design a dog population management, certain sets of data are required, such as the population size and spatial distribution of dogs. However, these data are rarely available or incomplete. Hence, this study aimed to describe the characteristics of dog populations in Thailand, explore their spatial distribution and relevant factors, and estimate the number of dogs in the whole country. First, four districts were selected as representatives of each region. Each district was partitioned into grids with a 300-m resolution. The selected grids were then surveyed, and the number of dogs and related data were collected. Random forest models with a two-part approach were used to quantify the association between the surveyed dog population and predictor variables. The spatial distribution of dog populations was then predicted. A total of 1,750 grids were surveyed (945 grids with dog presence and 805 grids with dog absence). Among the surveyed dogs, 86.6% (12,027/13,895) were owned. Of these, 51% were classified as independent, followed by confined (25%), semi-independent (21%), and unidentified dogs (3%). Seventy-two percent (1,348/1,868) of the ownerless dogs were feral, and the rest were community dogs. The spatial pattern of the dog populations was highly distributed in big cities such as Bangkok and its suburbs. In owned dogs, it was linked to household demographics, whereas it was related to community factors in ownerless dogs. The number of estimated dogs in the entire country was 12.8 million heads including 11.2 million owned dogs (21.7 heads/km²) and 1.6 million ownerless dogs (3.2 heads/km²). The methods developed here are extrapolatable to a larger area and use much less budget and manpower compared to the present practices. Our results are helpful for canine rabies prevention and control programs, such as dog population management and control and rabies vaccine allocation.

Awareness Towards Rabies and Exposure Rate and Treatment of Dog-Bite Injuries Among Rural Residents - Guangxi Zhuang Autonomous Region, China, 2021

What is already known about this topic?

Although fatal once clinical signs appear, rabies is preventable through three proven, effective interventions including mass dog vaccination, post-exposure prophylaxis (PEP), and, though sometimes neglected, awareness of rabies.

What is added by this report?

The total awareness rate of rabies-related knowledge among rural residents was only 57.9% in Guangxi Zhuang Autonomous Region, one of the provincial-level administrative divisions (PLADs) with endemic rabies in China, and the exposure rate of dog-bite injuries was as high as 7.2% in the past year. In addition, 14.8% of bite victims failed to seek PEP service.

What are the implications for public health practice?

This study can provide evidence for the targeted prevention and control program of rabies in rural areas and help realize the international goals of eliminating dog-mediated rabies by 2030.

Control of snakebite envenoming: A mathematical modeling study

A mathematical model is designed to assess the impact of some interventional strategies for curtailing the burden of snakebite envenoming in a community. The model is fitted with real data set. Numerical simulations have shown that public health awareness of the susceptible individuals on snakebite preventive measures could reduce the number of envenoming and prevent deaths and disabilities in the population. The simulations further revealed that if at least fifty percent of snakebite envenoming patients receive early treatment with antivenom a substantial number of deaths will be averted. Furthermore, it is shown using optimal control that combining public health awareness and antivenom treatment averts the highest number of snakebite induced deaths and disability adjusted life years in the study area. To choose the best strategy amidst limited resources in the study area, cost effectiveness analysis in terms of incremental cost effectiveness ratio is performed. It has been established that the control efforts of combining public health awareness of the susceptible individuals and antivenom treatment for victims of snakebite envenoming is the most cost effective strategy. Approximately the sum of US$72,548 is needed to avert 117 deaths or 2,739 disability adjusted life years that are recorded within 21 months in the study area. Thus, the combination of these two control strategies is recommended.

Snakebite envenoming (SBE) is currently one of the life-threatening neglected diseases especially in developing countries. The fight against this menace requires multidisciplinary approach. Owing to significant number of deaths and disabilities recorded per year in West African savanna region, we developed a new mathematical model for SBE in order to gain more insights into the dynamics and control of SBE. It is clear that communities in northeast Nigeria do not have adequate health information on self-protection against SBE and the antivenom is almost scarce and unaffordable. Thus, we evaluated the cost-effectiveness and potential impact of both public health awareness campaign and treatment for SBE as interventional strategies against snakebite. We discovered that public health awareness is crucial in averting SBE, deaths and disabilities. Also, if at least 50% of SBE victims received treatment within 24 hours of bite, a significant number of deaths and disabilities will be prevented. Furthermore, the study revealed that the combination of public health awareness and treatment decreases the burden of the disease in terms of deaths and disability adjusted life years at a lesser cost as compared with implementing one of these interventions separately. These results can be used as a guide for planning SBE control policy in northeast Nigeria and beyond.

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.

Stability and bifurcation for a stochastic differential algebraic Holling-II predator–prey model with nonlinear harvesting and delay

In this paper, a stochastic delayed differential algebraic predator–prey model with Michaelis–Menten-type prey harvesting is proposed. Due to the influence of gestation delay and stochastic fluctuations, the proposed model displays a complex dynamics. Criteria on the local stability of the interior equilibrium are established, and the effect of gestation delay on the model dynamics is discussed. Taking the gestation delay and economic profit as bifurcation parameters, Hopf bifurcation and singularity induced bifurcation can occur as they cross through some critical values, respectively. Moreover, the solution of the model will blow up in a limited time when delay [Formula: see text]. Then, we calculate the fluctuation intensity of the stochastic fluctuations by Fourier transform method, which is the key to illustrate the effect of stochastic fluctuations. Finally, we demonstrate our theoretical results by numerical simulations.

Stochastic models of infectious diseases in a periodic environment with application to cholera epidemics

Seasonal variation affects the dynamics of many infectious diseases including influenza, cholera and malaria. The time when infectious individuals are first introduced into a population is crucial in predicting whether a major disease outbreak occurs. In this investigation, we apply a time-nonhomogeneous stochastic process for a cholera epidemic with seasonal periodicity and a multitype branching process approximation to obtain an analytical estimate for the probability of an outbreak. In particular, an analytic estimate of the probability of disease extinction is shown to satisfy a system of ordinary differential equations which follows from the backward Kolmogorov differential equation. An explicit expression for the mean (resp. variance) of the first extinction time given an extinction occurs is derived based on the analytic estimate for the extinction probability. Our results indicate that the probability of a disease outbreak, and mean and standard derivation of the first time to disease extinction are periodic in time and depend on the time when the infectious individuals or free-living pathogens are introduced. Numerical simulations are then carried out to validate the analytical predictions using two examples of the general cholera model. At the end, the developed theoretical results are extended to more general models of infectious diseases.

Probability of a zoonotic spillover with seasonal variation

Zoonotic infectious diseases are spread from animals to humans. It is estimated that over 60% of human infectious diseases are zoonotic and 75% of them are emerging zoonoses. The majority of emerging zoonotic infectious diseases are caused by viruses including avian influenza, rabies, Ebola, coronaviruses and hantaviruses. Spillover of infection from animals to humans depends on a complex transmission pathway, which is influenced by epidemiological and environmental processes. In this investigation, the focus is on direct transmission between animals and humans and the effects of seasonal variations on the transmission and recovery rates. Fluctuations in transmission and recovery, besides being influenced by physiological processes and behaviors of pathogen and host, are driven by seasonal variations in temperature, humidity or rainfall. A new time-nonhomogeneous stochastic process is formulated for infectious disease spread from animals to humans when transmission and recovery rates are time-periodic. A branching process approximation is applied near the disease-free state to predict the probability of the first spillover event from animals to humans. This probability is a periodic function of the time when infection is introduced into the animal population. It is shown that the highest risk of a spillover depends on a combination of animal to human transmission, animal to animal transmission and animal recovery. The results are applied to a stochastic model for avian influenza with spillover from domestic poultry to humans.

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.

Dog Rabies in Dhaka, Bangladesh, and Implications for Control

Controlling rabies among free-roaming street dogs has been a huge challenge in many parts of the world. Vaccination is a commonly used strategy to control rabies, however, sufficient vaccination coverage is very challenging when it comes to street dogs. Also, dog rabies data is scarce, making it difficult to develop proper strategies. In this study, we use a logistic growth incorporated epidemic model to understand the prevalence of rabies in the dog population of Dhaka, Bangladesh. The study shows that, the basic reproduction number for dog rabies in Dhaka lies between 1.1 to 1.249 and the environmental carrying capacity lies approximately between 58,110 to 194,739. Considering the vaccination and neuter programs administered in the last decade, we attempt to explain rabies transmission among dogs in this population. We found that the high basic reproduction number is associated with high environmental carrying capacity and vice versa. Further, we compare different type of control strategies, viz., constant vaccination, pulse vaccination, and optimal vaccination strategies. In the case of high environmental carrying capacity, vaccination, and neuter strategy is not sufficient for controlling rabies in street dogs, whereas carrying capacity control through waste management coupled with vaccination and neuter is more effective.

Regional and age difference of human rabies prevalence of the past fourteen years in China

OBJECTIVE

The aim of this study is to describe the epidemiological characteristics about regional and age difference of human rabies in the past fourteen years in China, and provide a reliable epidemiology basis for further control and prevention of human rabies.

METHODS

The database of "China Public Health Science Data Center" affiliated Chinese CDC was searched with the key words of "rabies" or "epidemiology" or "morbidity" or "mortality" from 2004 to 2018 and the corresponding data about human rabies cases was collected referred to regional and age difference for describing the epidemiological characteristics of human rabies.

RESULTS

In this study, a total of nearly 26,315 rabies cases (1754 ± 253) and 25,691 rabies-related deaths (1712 ± 255) (Mean ± SE) were reported, and a decreasing trend about the morbidity and mortality of human rabies existed from 0.2039 and 0.2039 (1/100,000) in 2004 to 0.0304 and 0.0295 in 2018. Otherwise, regional difference of human rabies prevalence significantly existed, and juvenile and middle-aged population especially in 50-60 years old were more easily attacked and infected with rabies (all p < 0.05).

CONCLUSION

This study proved that human rabies still is a major public health problem in China though a decreasing trend about the morbidity and mortality of human rabies existed in the past fourteen years.

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.

AVIAN INFLUENZA A H7N9 VIRUS HAS BEEN ESTABLISHED IN CHINA

In March 2013, a novel avian-origin influenza A H7N9 virus was identified among human patients in China and a total of 124 human cases with 24 related deaths were confirmed by May 2013. From November 2013 to July 2017, H7N9 broke out four more times in China. A deterministic model is proposed to study the transmission dynamics of the avian influenza A H7N9 virus between wild and domestic birds and from birds to humans, and is applied to simulate the open data on numbers of the infected human cases and related deaths reported from March to May 2013 and from November 2013 to June 2014 by the Chinese Center for Disease Control and Prevention. The basic reproduction number [Formula: see text] is estimated and sensitivity analysis of [Formula: see text] in terms of model parameters is performed. Taking into account the fact that it broke out again from November 2014 to June 2015, from November 2015 to July 2016, and from October 2016 to July 2017, we believe that H7N9 virus has been well established in birds and will likely cause regular outbreaks in humans again in the future. Control measures for the future spread of H7N9 include (i) reducing the transmission opportunities between wild birds and domestic birds, (ii) closing or monitoring the retail live-poultry markets in the infected areas, and (iii) culling the infected domestic birds in the epidemic regions.

Spatiotemporal epidemic models for rabies among animals

Rabies is a serious concern to public health and wildlife management worldwide. Over the last three decades, various mathematical models have been proposed to study the transmission dynamics of rabies. In this paper we provide a mini-review on some reaction-diffusion models describing the spatial spread of rabies among animals. More specifically, we introduce the susceptible-exposed-infectious models for the spatial transmission of rabies among foxes (Murray et al., 1986), the spatiotemporal epidemic model for rabies among raccoons (Neilan and Lenhart, 2011), the diffusive rabies model for skunk and bat interactions (Bonchering et al., 2012), and the reaction-diffusion model for rabies among dogs (Zhang et al., 2012). Numerical simulations on the spatiotemporal dynamics of these models from these papers are presented.