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The migration routes of migrant birds in all the world. There are eight migratory routes for birds in the world. Three routes of them pass by China: purple line, orange line and blue line. Light green region represents China and Red star represents the location of H7N9 outbreak, which is the Yangtze river delta area. World map is drawn by Matlab R2009a. China map is drawn by ArcGIS 10. Lines and red star are added by Microsoft Office Word 2003.
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H7N9, a newly emerging virus in China, travels among poultry and human. Although H7N9 has not aroused massive outbreaks, recurrence in the second half of 2013 makes it essential to control the spread. It is believed that the most effective control measure is to locate the original infection source and cut off the source of infection from human. How...
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... Currently there are eight migratory routes for birds in the world 19 , see Fig. 1. Three of these routes pass through China: the west line (purple), the center line (orange) and the east line (blue). Among these three lines, the east route is closely related to the location of the 2013 outbreak of H7N9 bird flu, the Yangtze river delta area 18 (the red star in Fig. 1). Due to bird migration, the behaviors of migrant ...
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... are eight migratory routes for birds in the world 19 , see Fig. 1. Three of these routes pass through China: the west line (purple), the center line (orange) and the east line (blue). Among these three lines, the east route is closely related to the location of the 2013 outbreak of H7N9 bird flu, the Yangtze river delta area 18 (the red star in Fig. 1). Due to bird migration, the behaviors of migrant birds among breeding, stopover and wintering grounds are different, see Fig. ...
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... information criterion values. In order to check the adequacy of the model, we take a look at the residuals between theoretic and the real data under three cases, see Fig. 12, and autocorrelations of residuals are shown in Fig. 13. In Fig. 13, the areas between the two blue lines on the plots represent the regions within which residuals correlation are non-significant at the 95% level. Therefore, it is reasonable to conclude that the residuals are not correlated, which illustrates that we can apply Akaike's ...
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... information criterion values. In order to check the adequacy of the model, we take a look at the residuals between theoretic and the real data under three cases, see Fig. 12, and autocorrelations of residuals are shown in Fig. 13. In Fig. 13, the areas between the two blue lines on the plots represent the regions within which residuals correlation are non-significant at the 95% level. Therefore, it is reasonable to conclude that the residuals are not correlated, which illustrates that we can apply Akaike's information criterion to compare the validity of the three results. ...
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... this paper, there is an assumption addressed in introduction section that other host species infected by H7N9 virus cannot infect the original host species in turn. If the other host species can transmit virus to the original host species and interspecies transmission rates are very small, the fitting results are given in Fig. 14, which have small difference with the results in Figs. 9(a), 10(a) and 11(a). All corres- ponding AIC c values are AIC cm 5 171.6606, AIC cw 5 170.0092, AIC cp 5 190.7212, and AIC min 5 AIC cw 5 170.0092, which is the case that the residents birds are considered as the original resource. D m 5 1.6514 , 4 and D p 5 20.712 . 4, which ...
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... there is no this assumption, the original host species cannot be precisely located. From Fig. 14(c), if the do- mestic poultry is the original transmission source, the human cases in winter would delay to appear. ...
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... there is no solid evidence to confirm human-to-human transmission, it is happened in at least three families 3,26,27 . If human- to-human transmission, b hh , is added in model (5), the new model (6) is obtained and fitting results are given in Figs. 15, 16 and 17. Applying the real confirmed human cases during the first 14 weeks, we can firstly estimate b 1 , b 2 and b hh and find that adding human-to- human transmission rate can lead to the decrease of b 1 and increase of b 2 , which may enlarge the basic reproduction number. However, if human-to-human transmission rate is relatively small, ...
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... reproduction number. However, if human-to-human transmission rate is relatively small, there is no obvious difference between Figs. 15(a), 16(a), 17(a) and Figs. 9(a), 10(a), 11(a). On the contrary, if b hh is relatively bigger, the prevalence situation of H7N9 may be serious and the number of the individual infected can reach thousands shown in Figs. 15(b), 16(b) and 17(b). So, according to real epidemic situation, even if human-to-human transmission exists, it must be very small. Table ...
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... birds and domestic fowls can shed the virus to environment within the infected period. It is domestic poultry that brings virus to human. Human can be infected by H7N9 virus through the close contact with domestic poultry or by environment transmission and there exists no human-to-human transmission. All these connections are reflected in Fig. ...
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... the people may be killed by the influenza virus, and others can be cured. Thus, N h (t) is divided into four subclasses: the susceptible, the infected, the confirmed and the recovered denoted by S h (t), E h (t), I h (t) and R h (t). The detailed description of dynamical transmission of H7N9 avian influenza is described in the following flowchart (Fig. 19). The corresponding dynamical model can be seen in equations (5), where the interpretation of the variables and parameters are shown in Table 1 ...
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... Chong et al. [25] assumed that the avian populations are subject to the rule of constant growth. But migrant birds are mostly viewed as the original infection source [12,27]. Pathogens may be transmitted to new areas by migratory hosts, which leads to new host species' exposure and potential infection. ...
Depopulation of birds has been authenticated to be an effective measure in controlling avian influenza transmission. In this work, we establish a Filippov avian-only model incorporating a threshold policy control. We choose the index—the maximum between the infected threshold level $I_{T}$ I T and the product of the number of susceptible birds S and a ratio threshold value ξ —to decide on whether to trigger the control measures or not, which then leads to a discontinuous separation line and two pieces of sliding-mode domains. Meanwhile, one more sliding-mode domain gives birth to more complex dynamics. We investigate the global dynamical behavior of the Filippov model, including the real and/or virtual equilibria and the two sliding modes and their dynamics. The solutions will eventually stabilize at the real endemic equilibrium of the subsystem or the pseudoequilibria on the two sliding modes due to different threshold values. Therefore an effective and efficient threshold policy is essential to control the influenza by driving the number of infected birds below a certain level or at a previously given level.
... See Figs. 5 and 6 As seen in Fig. 5, the eight identified major migratory routes are mostly meridional and the majority of them extend to more than one continent (Shupeng and van Genderen 2008;Zhang et al. 2014). Wild birds such as waterfowls and cranes follow the Asian flyways in autumn, moving from the northern latitudes of Central and Eastern Asia toward the wintering grounds in China (e.g., Lake Qinghai and Yangtze River delta, see (Wang et al. 2018;Zhang et al. 2014). ...
... See Figs. 5 and 6 As seen in Fig. 5, the eight identified major migratory routes are mostly meridional and the majority of them extend to more than one continent (Shupeng and van Genderen 2008;Zhang et al. 2014). Wild birds such as waterfowls and cranes follow the Asian flyways in autumn, moving from the northern latitudes of Central and Eastern Asia toward the wintering grounds in China (e.g., Lake Qinghai and Yangtze River delta, see (Wang et al. 2018;Zhang et al. 2014). Particularly in China, a total of 53.6 million hectares of wetlands such as lakes, swamps, rivers as well as artificial wetlands provide breeding and wintering sites for several species including cranes, gulls, ducks, and geese (Wang et al. 2018). ...
... A recent study (Deng et al. 2019) shows that the Greater White-fronted Geese autumn migration starts from the Russian Arctic breeding sites in late September moving to wintering areas in southeast China in late October. These worldwide migrating pathways provide a possible natural avian carrier network which should be considered seriously in any mechanism Shupeng et al. 2008;Zhang et al. 2014) Content courtesy of Springer Nature, terms of use apply. Rights reserved. ...
In the first part, this work reports that during the global “anthropopause” period, that was imposed in March and April 2020 for limiting the spread of COVID-19, the concentrations of basic air pollutants over Europe were reduced by up to 70%. During May and June, the gradual lift of the stringent measures resulted in the recovery of these reductions with pollution concentrations approaching the levels before the lockdown by the end of June 2020. In the second part, this work examines the alleged correlations between the reported cases of COVID-19 and temperature, humidity and particulate matter for March and April 2020 in Europe. It was found that decreasing temperatures and relative humidity with increasing concentrations of particulate matter are correlated with an increase in the number of reported cases during these 2 months. However, when these calculations were repeated for May and June, we found a remarkable drop in the significance of the correlations which leads us to question the generally accepted inverse relation between pandemics and air temperature at least during the warmer months. Such a relationship could not be supported in our study for SARS-CoV-2 virus and the question remains open. In the third and last part of this work, we examine the question referring to the origin of pandemics. In this context we have examined the hypothesis that the observed climate warming in Siberia and the Arctic and the thawing of permafrost could result to the release of trapped in the permafrost pathogens in the atmosphere. We find that although such relations cannot be directly justified, they present a possible horrifying mechanism for the origin of viruses in the future during the developing global warming of our planet in the decades to come. Overall the findings of our study indicate that: (1) the reduction of anthropogenic emissions in Europe during the “anthropopause” period of March and April 2020 was significant, but when the lockdown measures were raised the concentrations of atmospheric pollutants quickly recovered to pre-pandemic levels and therefore any possible climatic feedbacks were negligible; (2) no robust relationship between atmospheric parameters and the spread of COVID-19 cases can be justified in the warmer part of the year and (3) more research needs to be done regarding the possible links between climate change and the release of new pathogens from thawing of permafrost areas.
... In this article we have used a mathematical dynamical model to reversely deduce, in two hypothetical cases, the number of people infected with COVID-19 on the Diamond Princess cruise ship from January 20 to February 20, 2020, the peak time of infection, the number of the infections caused by the Hong Kong passenger, and the basic reproduction number, information which can provide the theoretical basis for understanding the spread of the epidemic and developing effective control measures. The results reported in this paper demonstrate that a dynamical model which incorporates a transmission mechanism can be a very useful method for predicting the spread of a disease, especially when actual data are scarce [22][23][24][25]. ...
As of July 21, 2020, the coronavirus SARS-CoV-2 had spread to almost all countries around the world and caused more than 14.8 million confirmed cases, owing to its high transmissibility and fast rate of spread. Of the infected locations, the Diamond Princess cruise ship is special in that it is an isolated system with a population highly concentrated in a limited space, providing particularly favorable conditions for the transmission of the novel coronavirus-associated pneumonia, COVID-19. The Japanese government's emergency measures for controlling the spread of COVID-19 on the cruise ship have also been questioned. In this paper we develop a homogeneous mixed difference system to describe the mechanism of transmission of COVID-19 on the cruise ship, reverse-predict the epidemic transmission trend from January 20 to February 20, 2020, including the daily number of infected people and the peak time of infection, estimate the range of the basic reproduction number of virus transmission on the cruise ship, and assess the effects of prevention and control measures. It is concluded that the isolation of people, along with rapid and comprehensive detection of infections, play an important role in controlling the epidemic. In fact, the Japanese government's emergency measures did have a certain effect on limiting the spread of COVID-19, but the number of infected people could have been reduced by at least 60% if all personnel on the cruise ship had been tested and isolated promptly as early as February 5.
... Domestic animals provide a further source of zoonotic pathogens and can also act as hosts for pathogens of wild animals that can then spread more easily into the human population from our close contact with domestic stock. For instance, in the case of the 2013 avian flu (H7N9) outbreak in Southeast Asia, flu strains from wild birds likely combined with flu strains in domestic birds before moving into the human population through people's close contact with backyard poultry (Zhang et al. 2014). Figure 2 illustrates some of the human activities that are unwittingly increasing the likelihood of spillover events and the development of pandemic diseases. ...
... 3-6. Finally, we conclude this work together with biological implications in Sec. 7. Zhang et al., 2014]. Migratory hosts may transmit pathogens to new areas, leading to the exposure and potential infection of new host species [Altizer et al., 2011]. ...
Culling birds has always been an effective method to control the spread of avian influenza. Here, we introduce a Filippov avian-only model with culling of both susceptible and infected birds. The Filippov-type model is formulated by considering that no control strategy is taken if the number of infected birds is less than an infected threshold level [Formula: see text]; further, we cull infected birds once the number of infected birds exceeds [Formula: see text]; meanwhile, we cull susceptible birds if the number of susceptible birds exceeds a susceptible threshold level [Formula: see text]. The global dynamical behavior of the Filippov system, including the existence and stability of various types of equilibria, the existence of the sliding mode and its dynamics, together with bifurcation analyses with regard to local sliding bifurcations, is investigated. It is shown that model solutions ultimately converge to the positive equilibrium that lies in the region above [Formula: see text], or below [Formula: see text], or on [Formula: see text], as we vary the susceptible and infected threshold values [Formula: see text] and [Formula: see text]. Our results indicate that proper combinations of the susceptible and infected threshold values based on the threshold policy can maintain the number of infected birds either below a certain threshold level or at a previously given level.
... viral aerosols, and exposure to environments contaminated with the virus [2]- [4]. Human cases of A(H7N9) infection have occurred since 2013, during the annual winter-spring epidemics in mainland China [5], [6]. After peaking in 2013-2014, the human infection cohort in subsequent epidemics was generally smaller [7], but it sharply increased in the fifth epidemic wave in December 2016 [8]. ...
Numerous studies have demonstrated that exposure to live poultry or live poultry markets is the significant risk factor for human infection with avian influenza A(H7N9). However, the specific live poultry markets that are major infection sources for A(H7N9) human cases have not been explored in detail. In this study, we extract data associated with poultry farms, live poultry markets and farmers' markets from Baidu Map using the JavaScript language and then construct the live poultry transport network. From this, we establish our A(H7N9) transmission model over the network based upon probabilistic discrete-time Markov chain. On the basis of the obtained network and model, we propose spatiotemporal backward detection and forward transmission algorithms to detect the most likely infection sources and to compute the first arrival times of the infection sources. Our simulations use these algorithms to identify the specific locations of the infection sources, the first arrival times of the infection sources and the most likely transmission map of the A(H7N9) virus along the live poultry transport network. The results reveal that, in addition to the hazards posed by the live poultry markets, backyard poultry also contributed to A(H7N9) human infections; this risk source was significant especially in the newly affected provinces, in the fifth wave of infection. In particular, by analyzing the temperature characteristics at a given location when the infection source arrived, we find that the risk of human infection with the influenza A(H7N9) virus was high under 9°C~19°C; moderate under 0°C~9°C or 19°C~25°C; and low for temperatures <; 0°C or >25°C. Our results suggest that strengthening the supervision of the live poultry market system and immunizing poultry at both live poultry markets and the backyard poultry operations under the high risk temperature band of 9°C~19°C, will be able to significantly contribute to the control of avian influenza A(H7N9) in the future.
... Zhang et al. [13] analyzed the source of infection of avian influenza A (H7N9). According to theirs analysis, the most probable transmission route of avian influenza A (H7N9) is that migratory birds carry the virus and transmit it to local birds through physical space transitions, which then transmit the virus to poultry and to human with direct or indirect contact with poultry. ...
... Their total numbers of birds, poultry, and human at any time are denoted by ( ), ( ), and ℎ ( ), respectively. The concentration of viruses in the environment is denoted by ( ), and the average number of viruses that causes a H7N9 individual case is called an infectious unit (IU) [13,18]. The infectivity of virus in the environment to birds, poultry, or humans is more affected by the temperature, and we will consider it is periodic. ...
... It is easy to see that system (13) always has the disease-free ...
H7N9 virus in the environment plays a role in the dynamics of avian influenza A (H7N9). A nationwide poultry vaccination with H7N9 vaccine program was implemented in China in October of 2017. To analyze the effect of vaccination and environmental virus on the development of avian influenza A (H7N9), we establish an avian influenza A (H7N9) transmission model with vaccination and seasonality among human, birds, and poultry. The basic reproduction number for the prevalence of avian influenza is obtained. The global stability of the disease-free equilibrium and the existence of positive periodic solution are proved by the comparison theorem and the asymptotic autonomous system theorem. Finally, we use numerical simulations to demonstrate the theoretical results. Simulation results indicate that the risk of H7N9 infection is higher in colder environment. Vaccinating poultry can significantly reduce human infection.
... Liu and Fang [11] constructed a SIR-SIR mathematical model, and parameters in the model were estimated. Zhang et al. [12] and Xing et al. [13] carried out the data fitting and the sensitivity analysis for the source factors and recurrence factors, respectively. eir analyses are based on two four-populations models, including migratory birds, resident birds, domestic poultry, and humans, involving the virus in environment. ...
... In [17], we established a SEM-SIR eco-epidemiological model incorporating the mutation factor, focused on the disease control measures and the production protection, and then both the global dynamic properties and the disease control suggestions are given. Observed from the reported cases and the following spatiotemporal distributions, also inspired by [12,13], we formulate here a SEV-SIR model with a class of the virus in environment and analyze it dynamically and also concern about disease control and production protection. ...
In 2013 in mainland China, a novel avian influenza virus H7N9 began to infect humans and had aroused severe fatality in the infected humans, followed by the annual outbreaks. By methods of GIS and kriging interpolation, we get the geographical distributions. We obtain the longitudinal characteristics of these outbreaks based on statistics and diagrams. After these spatiotemporal distributions, an eco-epidemiological model is established and analyzed. In this model, the general incidence functions, the factor of fully killed infected poultry, and the virus in environment are taken into account. Theoretical analysis shows that the endemic will be formed to a large extent once the H7N9 avian influenza virus exists in poultry. On the basis of dynamics, we explore the possible disease control measures by numerical simulations. Simulations indicate that measures of vaccination in poultry and stopping live poultry transactions are the primary choices for disease control in humans, and strengthened inhibition effects and environmental disinfections can effectively control the outbreak.
... Pantin-Jackwood et al. [3] showed that quail and chickens are susceptible to infection, shed large amounts of virus, and are likely important in the spread of the virus to humans, and it is therefore conceivable that passerine birds may serve as vectors for transmission of H7N9 virus to domestic poultry [4]. Zhang et al. [5] concluded that migrant birds are the original infection source. Many authors investigated the epidemic model which describes the transmission of avian influenza among birds and humans [8][9][10][11][12][13][14][15]. ...
In order to analyze the spread of avian influenza A (H7N9), we construct an avian influenza transmission model from poultry (including poultry farm, backyard poultry farm, live-poultry wholesale market, and wet market) to human according to poultry transport network. We obtain the threshold value for the prevalence of avian influenza A (H7N9) and also give the existence and number of the boundary equilibria and endemic equilibria in different conditions. We can see that poultry transport network plays an important role in controlling avian influenza A (H7N9). Finally, numerical simulations are presented to illustrate the effects of poultry in different places on avian influenza. In order to reduce human infections in China, our results suggest that closing the retail live-poultry market or preventing the poultry of backyard poultry farm into the live-poultry market is feasible in a suitable condition.
... General speaking, environment toxins contain some kind of pathogens discharged by infected individuals, which has a negative effect on respiratory organs and the cardiovascular system, such as the avian influenza H7N9 (Zhang et al. 2014), pulmonary emphysema, asthma, and tuberculosis (Brauer et al. 2007;Wang et al. 2016). The emergence of environmental toxins can lead to the decline and finally failure of lung functions. ...
To study the effects of an environmental toxin, such as fine particles in hazy weather, on the spread of infectious diseases, we derive a toxin-dependent dynamic model that incorporates the birth rate with the toxin-dependent switching mode, the mortality rate, and infection rate with the toxin-dependent saturation effect. We analyze the model by showing the positive invariance, existence and stability of equilibria, and bifurcations. Numerical simulation is adopted to verify the mathematical results and exhibit transcritical and Hopf bifurcations. Our theoretical results show that there exists a threshold value of the environmental toxin: if the environmental toxin concentration is lower than the threshold, the system has a disease-free equilibrium and an interior equilibrium; if the environmental toxin concentration is higher than the threshold, the system has the extinction equilibrium. For the case where the disease-induced death is ignored, we show the global stability results. Numerical simulations clearly show that the environmental toxin facilitates the spread of infectious diseases. This study provides a theoretical basis for uncovering the impact of toxins on the spread of infectious diseases and for guiding the decision making by disease control agencies and governments.
