Tree species respond to climate change at multiple scales,such as species physiological response at fine scale and species distribution (quantified by percent area) at broader spatial scale.At a given spatial scale,sp...Tree species respond to climate change at multiple scales,such as species physiological response at fine scale and species distribution (quantified by percent area) at broader spatial scale.At a given spatial scale,species physiological response and distribution can be correlated positively or negatively.The consistency of such correlation relationships at different spatial scales determines whether species responses derived from local scales can be extrapo-lated to broader spatial scales.In this study,we used a coupled modeling approach that coupled a plot-level ecosystem process model (LINKAGES) with a spatially explicit landscape model (LANDIS).We investigated species physio-logical responses and distribution responses to climate warming at the local,zonal and landscape scales respectively,and examined how species physiological response and distribution correlated at each corresponding scale and whether the correlations were consistent among these scales.The results indicate that for zonal and warming-sensitive species,the correlations between species physiological response and distribution are consistent at these spatial scales,and therefore the research results of vegetation response to climate warming at the local scale can be extrapolated to the zonal and landscape scales.By contrast,for zonal and warming-insensitive species the correlations among different spatial scales are consistent at some spatial scales but at other scales.The results also suggest that the results of azonal species at the local scale near their distribution boundaries can not be extrapolated simply to broader scales due to stronger responses to climate warming in those boundary regions.展开更多
Objective To investigate the anti-tumor effects in vitro and in vivo distribution of the human/murine chimeric antibody (D2C). Methods The CD71 positive target cells (K562, GEM and SMMC7721) and the effector cells, fr...Objective To investigate the anti-tumor effects in vitro and in vivo distribution of the human/murine chimeric antibody (D2C). Methods The CD71 positive target cells (K562, GEM and SMMC7721) and the effector cells, freshly isolated human PBMC, with the ratio of target cells to effector cells 1:50, were incubated in various dilutions of D2C antibody ( Ab) . Antibody dependent cytotoxicity (AD-CC) was tested by using an LDH-release assay. Instead of effector cells, complement was added to the target cells (GEM, SMMC-7721) with various dilutions of D2C Ab. A method of counting death cells was used in complement dependent cytotoxicity (CDC) assay. Tumor localization and distribution of the chimeric antibody (D2C) were observed by labeling the chimeric Ab with radioiodine(131I) and injecting it into nude mice (Balb/c nu/nu) transplanted with human hepatocellular carcinoma cells (SMMC-7721).Results A significant ADCC was observed with the increased concentration of the D2C Ab. Cytolysis of CD71-positive target cells by the D2C Ab was found in the presence of fresh rabbit complement. Labeled D2C administered by intraperitoneal as well as tumor regional injection, was visualized by SPECT. The distribution of D2C Ab in murine organs and tissues showed that non-specific binding was lower following tumor regional administration than when the antibody was administered by an intraperitoneal injection. The human/murine chimeric antibody (D2C) has in vitro anti-tumor effects and can exert its effects in specific tumor localization. Its distribution and local effects in vivo can be detected by radioimmunoimaging.Conclusion CD71 human/murine chimeric antibody showed marked killing of tumor cells in vitro, and specific recognition and high affinity binding to tumor tissue in vivo展开更多
On the basis of population balance a mathematical model is developed to describe the formation of polymer particle in styrene suspension polymerization. The characteristics of coalescence and breakage of droplets and ...On the basis of population balance a mathematical model is developed to describe the formation of polymer particle in styrene suspension polymerization. The characteristics of coalescence and breakage of droplets and the gel effect are analyzed in particular. Parameters of the models are estimated by experimental data on reaction conversion and particle size distribution. The results show that the model is suitable for predicting polymerization processes.展开更多
Climate refugia can serve as a remnant habitat or stepping stones for species dispersal under climate warming.The largest freshwater lake by surface area,Lake Superior,USA and Canada,serves as a model system for under...Climate refugia can serve as a remnant habitat or stepping stones for species dispersal under climate warming.The largest freshwater lake by surface area,Lake Superior,USA and Canada,serves as a model system for understanding cooling-mediated local refugia,as its cool water temperatures and wave action have maintained shoreline habitats suitable for southern disjunct populations of arctic-alpine plants since deglaciation.Here,we seek to explain spatial patterns and environmental drivers of arctic-alpine plant refugia along Lake Superior’s shores,and assess future risk to refugia under moderate(+3.5℃)and warmest(+5.7℃)climate warming scenarios.First,we examined how the interactive effects of summer surface water temperatures and wind affected onshore temperatures,resulting in areas of cooler refugia.Second,we developed an ecological niche model for the presence of disjunct arctic-alpine refugia(pooling 1253 occurrences from 58 species)along the lake’s shoreline.Third,we fit species distribution models for 20 of the most common arctic-alpine disjunct species and predicted presence to identify refugia hotspots.Finally,we used the two climate warming scenarios to predict changes in the presence of refugia and disjunct hotspots.Bedrock type,elevation above water,inland distance,July land surface temperature from MODIS/Terra satellite and near-shore depth of water were the best predictors of disjunct occurrences.Overall,we predicted 2236 km of the shoreline(51%)as disjunct refugia habitat for at least one species under current conditions,but this was reduced to 20% and 7% with moderate(894 km)and warmest(313 km)climate change projections.展开更多
With the goal of model fitting species abundance distribution patterns of the tree,shrub and herb layers of the natural Toona ciliata community in Xingdoushan Nature Reserve,Enshi Autonomous Prefecture,Hubei Province,...With the goal of model fitting species abundance distribution patterns of the tree,shrub and herb layers of the natural Toona ciliata community in Xingdoushan Nature Reserve,Enshi Autonomous Prefecture,Hubei Province,we used the data collected from the field survey and employed different ecological niche models.The models tested were the broken stick model(BSM),the overlapping niche model(ONM)and the niche preemption model(NPM),as well as three statistic models,the log-series distribution model(LSD),the log-normal distribution model(LND)and the Weibull distribution model(WDM).To determine the fitted model most suitable to each layer,the fitting effects were judged by criteria of the lowest value of Akaike Information Criterion(AIC),Chi-square and the K-S values with no significant difference(P>0.05)between the theoretical predictions and observed species abundance distribution values.The result showed:(1)The fitting suitability and goodness of fit of the tree,shrub and herb layers by using the three ecological niche models were ranked as:NPM>BSM>ONM.Of the three statistical models,by accepting the fitting results of the three layers,WDM was the best fitting model,followed by LND.By rejecting the fitting tests of the herb layer,LSD had the worst fitting effect.The goodness of the statistical models was ranked as:WDM>LND>LSD.In general,the statistical models had better fitting results than the ecological models.(2)T.ciliata was the dominant species of the tree layer.The species richness and diversity of the herb layer were much higher than those of either the tree layer or the shrub layer.The species richness and diversity of the shrub layer were slightly higher than those of the tree layer.The community evenness accorded to the following order:herb>shrub>tree.Considering the fitting results of the different layers,different ecological niche models or statistical models with optimal goodness of fit and ecological significance can be given priority to in studying the species abundance distribution patterns of T.ciliata communities.展开更多
Species distribution models are increasing in popularity for mapping suitable habitat for species of management con- cern. Many investigators now recognize that extrapolations of these models with geographic informati...Species distribution models are increasing in popularity for mapping suitable habitat for species of management con- cern. Many investigators now recognize that extrapolations of these models with geographic information systems (GIS) might be sensitive to the environmental bounds of the data used in their development, yet there is no recommended best practice for "clamping" model extrapolations. We relied on two commonly used modeling approaches: classification and regression tree (CART) and maximum entropy (Maxent) models, and we tested a simple alteration of the model extrapolations, bounding ex- trapolations to the maximum and minimum values of primary environmental predictors, to provide a more realistic map of suit-able habitat of hybridized Africanized honey bees in the southwestern United States. Findings suggest that multiple models of bounding, and the most conservative bounding of species distribution models, like those presented here, should probably replace the unbounded or loosely bounded techniques currently used [Current Zoology 57 (5): 642-647,2011].展开更多
Vultures provide invaluable ecosystem services and play an important role in ecosystem balancing. The number of native vultures in India has declined in the past. Acquiring present knowledge of their habitat spread is...Vultures provide invaluable ecosystem services and play an important role in ecosystem balancing. The number of native vultures in India has declined in the past. Acquiring present knowledge of their habitat spread is essential to manage and prevent such a decline. It is envisaged that ongoing climate crisis may further cause change in habitat suitability and impact the existing population. Therefore, this study in Central India—a vulture stronghold, is aimed at predicting habitat changes in the short and long term and present the data statistically and graphically by using Species Distribution Model. MaxEnt software was chosen for its advantages over other models, like using presence-only data and performing well with incomplete data, small sample sizes and gaps, etc. Global Climate Model ensemble(CCSM4, HadGEM2 AO and MIROC5), was used to get better prediction. Fourteen robust models(AUC 0.864 0.892) were developed using data from over 1000 locations of seven vulture species over two seasons together. Selected climatic and other environmental variables were used to predict the current habitat. Future prediction was based on climatic variables only. The most important variables influencing the distribution were precipitation(bio 15, bio 18, bio 19) and temperature(bio 3, bio 5). Forest and water bodies were the major influencers within land use-landcover in the current prediction. At finer scale, while extremely suitable habitat area decreased and highly suitable area increased over time, the total suitable area marginally increased in 2050 but decreased in 2070. For broader consideration, net loss in suitable area was 5% in 2050 and 7.17% in 2070(RCP4.5). Similarly, in the RCP8.5 this was 6% in 2050 and 7.3% in 2070. The data generated can be used in conservation planning and management and thus protecting the vultures from any future threat.展开更多
The mechanisms responsible for species replacement during ecological successions is a long-standing and open debate. In this study, we examined the distribution of the Sardinian warbler Sylvia melanocephala along two ...The mechanisms responsible for species replacement during ecological successions is a long-standing and open debate. In this study, we examined the distribution of the Sardinian warbler Sylvia melanocephala along two grassland-to-forest gradients, one in a high-diversity area (Albera-Aspres chain in Catalonia: eight Sylvia warbler species) and one in a low-diversity area (Mount Hymittos in Greece: four species). In Catalonia, distribution models suggested that the apparent exclusion of S. melanocephala from the open and forest ends of the gradient may be explained entirely by the preference of S. melanocephala for mid-successional shrublands. However, a joint analysis of both data sets revealed that: 1) S. melanocephala was more evenly dis- tributed along the vegetation gradient in Greece, suggesting ecological release in the low-diversity area; and 2) a distribution model assuming interspecific competition (based on the distribution of Sylvia species showing a negative co-occurrence pattern with S. melanocephala) had a significantly higher predictive ability than a distribution model based on habitat variables alone. Our study supports the view that species turnover along ecological gradients generally results from a combination of intrinsic preferences and interspecific competition [Current Zoology 57 (3): 307-317, 2011].展开更多
Crop damages by wildlife is a frequent form of human-wildlife conflict. Identifying areas where the risk of crop damages is highest is pivotal to set up preventive measures and reduce conflict. Species distribution mo...Crop damages by wildlife is a frequent form of human-wildlife conflict. Identifying areas where the risk of crop damages is highest is pivotal to set up preventive measures and reduce conflict. Species distribution models are routinely used to predict species distribution in response of environmental changes. The aim of this paper was assessing whether species distribution models can allow to identify the areas most at risk of crop damages, helping to set up management strategies aimed at the mitigation of human-wildlife conflicts. We obtained data on wild boar Sus scrofa damages to crops in the Alta Murgia National Park, Southern Italy, and related them to landscape features, to identify areas where the risk of wild boar damages is highest. We used MaxEnt to build species distribution models. We identified the spatial scale at which landscape mostly affects the distribution damages, and optimized the regularization parameter of models, through an information-theoretic approach based on AIC. Wild boar damages quickly increased in the period 2007-2011; cereals and legtmaes were the crops more affected. Large areas of the park have a high risk of wild boar damages. The risk of damages was related to low cover of urban areas or olive grows, intermediate values of forest cover, and high values of shrubland cover within a 2-km radius. Temporally independent validation data demonstrated that models can successfully predict damages in the future. Species distribution models can accurately identify the areas most at risk of wildlife damages, as models calibrated on data collected during only a subset of years correctly predicted damages in the subsequent year [Current Zoology 60 (2): 170-179, 2014].展开更多
In this paper, based on a class of multi-group epidemic models of SEIR type with bilinear incidences, we introduce a vaccination compartment, leading to multi-group SVEIR model. We establish that the global dynamics a...In this paper, based on a class of multi-group epidemic models of SEIR type with bilinear incidences, we introduce a vaccination compartment, leading to multi-group SVEIR model. We establish that the global dynamics are completely determined by the basic reproduction number R0V which is defined by the spectral radius of the next generation matrix. Our proofs of global stability of the equilibria utilize a graph-theoretical approach to the method of Lyapunov functionals. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccines to obtain immunity or the possibility for them to be infected before acquiring immunity is neglected in each group, this condition will be satisfied and the disease can always be eradicated by suitable vaccination strategies. This may lead to over evaluation for the effect of vaccination.展开更多
基金Under the auspices of International Partnership Program of Chinese Academy of Sciences (No.KZCX2-YW-T06)Key Direction in Knowledge Innovation Programs of Chinese Academy of Sciences (No.KZCX2-YW-444)Major State Basic Research Development Program of China (No.2009CB421101)
文摘Tree species respond to climate change at multiple scales,such as species physiological response at fine scale and species distribution (quantified by percent area) at broader spatial scale.At a given spatial scale,species physiological response and distribution can be correlated positively or negatively.The consistency of such correlation relationships at different spatial scales determines whether species responses derived from local scales can be extrapo-lated to broader spatial scales.In this study,we used a coupled modeling approach that coupled a plot-level ecosystem process model (LINKAGES) with a spatially explicit landscape model (LANDIS).We investigated species physio-logical responses and distribution responses to climate warming at the local,zonal and landscape scales respectively,and examined how species physiological response and distribution correlated at each corresponding scale and whether the correlations were consistent among these scales.The results indicate that for zonal and warming-sensitive species,the correlations between species physiological response and distribution are consistent at these spatial scales,and therefore the research results of vegetation response to climate warming at the local scale can be extrapolated to the zonal and landscape scales.By contrast,for zonal and warming-insensitive species the correlations among different spatial scales are consistent at some spatial scales but at other scales.The results also suggest that the results of azonal species at the local scale near their distribution boundaries can not be extrapolated simply to broader scales due to stronger responses to climate warming in those boundary regions.
基金National Sciences Foundation of China(No.39970693)
文摘Objective To investigate the anti-tumor effects in vitro and in vivo distribution of the human/murine chimeric antibody (D2C). Methods The CD71 positive target cells (K562, GEM and SMMC7721) and the effector cells, freshly isolated human PBMC, with the ratio of target cells to effector cells 1:50, were incubated in various dilutions of D2C antibody ( Ab) . Antibody dependent cytotoxicity (AD-CC) was tested by using an LDH-release assay. Instead of effector cells, complement was added to the target cells (GEM, SMMC-7721) with various dilutions of D2C Ab. A method of counting death cells was used in complement dependent cytotoxicity (CDC) assay. Tumor localization and distribution of the chimeric antibody (D2C) were observed by labeling the chimeric Ab with radioiodine(131I) and injecting it into nude mice (Balb/c nu/nu) transplanted with human hepatocellular carcinoma cells (SMMC-7721).Results A significant ADCC was observed with the increased concentration of the D2C Ab. Cytolysis of CD71-positive target cells by the D2C Ab was found in the presence of fresh rabbit complement. Labeled D2C administered by intraperitoneal as well as tumor regional injection, was visualized by SPECT. The distribution of D2C Ab in murine organs and tissues showed that non-specific binding was lower following tumor regional administration than when the antibody was administered by an intraperitoneal injection. The human/murine chimeric antibody (D2C) has in vitro anti-tumor effects and can exert its effects in specific tumor localization. Its distribution and local effects in vivo can be detected by radioimmunoimaging.Conclusion CD71 human/murine chimeric antibody showed marked killing of tumor cells in vitro, and specific recognition and high affinity binding to tumor tissue in vivo
文摘On the basis of population balance a mathematical model is developed to describe the formation of polymer particle in styrene suspension polymerization. The characteristics of coalescence and breakage of droplets and the gel effect are analyzed in particular. Parameters of the models are estimated by experimental data on reaction conversion and particle size distribution. The results show that the model is suitable for predicting polymerization processes.
基金supported by the Natural Sciences and Engineering Research Council of Canada(RGPIN-2019-06040).
文摘Climate refugia can serve as a remnant habitat or stepping stones for species dispersal under climate warming.The largest freshwater lake by surface area,Lake Superior,USA and Canada,serves as a model system for understanding cooling-mediated local refugia,as its cool water temperatures and wave action have maintained shoreline habitats suitable for southern disjunct populations of arctic-alpine plants since deglaciation.Here,we seek to explain spatial patterns and environmental drivers of arctic-alpine plant refugia along Lake Superior’s shores,and assess future risk to refugia under moderate(+3.5℃)and warmest(+5.7℃)climate warming scenarios.First,we examined how the interactive effects of summer surface water temperatures and wind affected onshore temperatures,resulting in areas of cooler refugia.Second,we developed an ecological niche model for the presence of disjunct arctic-alpine refugia(pooling 1253 occurrences from 58 species)along the lake’s shoreline.Third,we fit species distribution models for 20 of the most common arctic-alpine disjunct species and predicted presence to identify refugia hotspots.Finally,we used the two climate warming scenarios to predict changes in the presence of refugia and disjunct hotspots.Bedrock type,elevation above water,inland distance,July land surface temperature from MODIS/Terra satellite and near-shore depth of water were the best predictors of disjunct occurrences.Overall,we predicted 2236 km of the shoreline(51%)as disjunct refugia habitat for at least one species under current conditions,but this was reduced to 20% and 7% with moderate(894 km)and warmest(313 km)climate change projections.
基金Public Welfare Research Project of Department of Science and Technology in Hubei Province(40 2012DBA40001)Scientific Research Project of Department of Education in Hubei Province(B20160555)
文摘With the goal of model fitting species abundance distribution patterns of the tree,shrub and herb layers of the natural Toona ciliata community in Xingdoushan Nature Reserve,Enshi Autonomous Prefecture,Hubei Province,we used the data collected from the field survey and employed different ecological niche models.The models tested were the broken stick model(BSM),the overlapping niche model(ONM)and the niche preemption model(NPM),as well as three statistic models,the log-series distribution model(LSD),the log-normal distribution model(LND)and the Weibull distribution model(WDM).To determine the fitted model most suitable to each layer,the fitting effects were judged by criteria of the lowest value of Akaike Information Criterion(AIC),Chi-square and the K-S values with no significant difference(P>0.05)between the theoretical predictions and observed species abundance distribution values.The result showed:(1)The fitting suitability and goodness of fit of the tree,shrub and herb layers by using the three ecological niche models were ranked as:NPM>BSM>ONM.Of the three statistical models,by accepting the fitting results of the three layers,WDM was the best fitting model,followed by LND.By rejecting the fitting tests of the herb layer,LSD had the worst fitting effect.The goodness of the statistical models was ranked as:WDM>LND>LSD.In general,the statistical models had better fitting results than the ecological models.(2)T.ciliata was the dominant species of the tree layer.The species richness and diversity of the herb layer were much higher than those of either the tree layer or the shrub layer.The species richness and diversity of the shrub layer were slightly higher than those of the tree layer.The community evenness accorded to the following order:herb>shrub>tree.Considering the fitting results of the different layers,different ecological niche models or statistical models with optimal goodness of fit and ecological significance can be given priority to in studying the species abundance distribution patterns of T.ciliata communities.
文摘Species distribution models are increasing in popularity for mapping suitable habitat for species of management con- cern. Many investigators now recognize that extrapolations of these models with geographic information systems (GIS) might be sensitive to the environmental bounds of the data used in their development, yet there is no recommended best practice for "clamping" model extrapolations. We relied on two commonly used modeling approaches: classification and regression tree (CART) and maximum entropy (Maxent) models, and we tested a simple alteration of the model extrapolations, bounding ex- trapolations to the maximum and minimum values of primary environmental predictors, to provide a more realistic map of suit-able habitat of hybridized Africanized honey bees in the southwestern United States. Findings suggest that multiple models of bounding, and the most conservative bounding of species distribution models, like those presented here, should probably replace the unbounded or loosely bounded techniques currently used [Current Zoology 57 (5): 642-647,2011].
文摘Vultures provide invaluable ecosystem services and play an important role in ecosystem balancing. The number of native vultures in India has declined in the past. Acquiring present knowledge of their habitat spread is essential to manage and prevent such a decline. It is envisaged that ongoing climate crisis may further cause change in habitat suitability and impact the existing population. Therefore, this study in Central India—a vulture stronghold, is aimed at predicting habitat changes in the short and long term and present the data statistically and graphically by using Species Distribution Model. MaxEnt software was chosen for its advantages over other models, like using presence-only data and performing well with incomplete data, small sample sizes and gaps, etc. Global Climate Model ensemble(CCSM4, HadGEM2 AO and MIROC5), was used to get better prediction. Fourteen robust models(AUC 0.864 0.892) were developed using data from over 1000 locations of seven vulture species over two seasons together. Selected climatic and other environmental variables were used to predict the current habitat. Future prediction was based on climatic variables only. The most important variables influencing the distribution were precipitation(bio 15, bio 18, bio 19) and temperature(bio 3, bio 5). Forest and water bodies were the major influencers within land use-landcover in the current prediction. At finer scale, while extremely suitable habitat area decreased and highly suitable area increased over time, the total suitable area marginally increased in 2050 but decreased in 2070. For broader consideration, net loss in suitable area was 5% in 2050 and 7.17% in 2070(RCP4.5). Similarly, in the RCP8.5 this was 6% in 2050 and 7.3% in 2070. The data generated can be used in conservation planning and management and thus protecting the vultures from any future threat.
文摘The mechanisms responsible for species replacement during ecological successions is a long-standing and open debate. In this study, we examined the distribution of the Sardinian warbler Sylvia melanocephala along two grassland-to-forest gradients, one in a high-diversity area (Albera-Aspres chain in Catalonia: eight Sylvia warbler species) and one in a low-diversity area (Mount Hymittos in Greece: four species). In Catalonia, distribution models suggested that the apparent exclusion of S. melanocephala from the open and forest ends of the gradient may be explained entirely by the preference of S. melanocephala for mid-successional shrublands. However, a joint analysis of both data sets revealed that: 1) S. melanocephala was more evenly dis- tributed along the vegetation gradient in Greece, suggesting ecological release in the low-diversity area; and 2) a distribution model assuming interspecific competition (based on the distribution of Sylvia species showing a negative co-occurrence pattern with S. melanocephala) had a significantly higher predictive ability than a distribution model based on habitat variables alone. Our study supports the view that species turnover along ecological gradients generally results from a combination of intrinsic preferences and interspecific competition [Current Zoology 57 (3): 307-317, 2011].
文摘Crop damages by wildlife is a frequent form of human-wildlife conflict. Identifying areas where the risk of crop damages is highest is pivotal to set up preventive measures and reduce conflict. Species distribution models are routinely used to predict species distribution in response of environmental changes. The aim of this paper was assessing whether species distribution models can allow to identify the areas most at risk of crop damages, helping to set up management strategies aimed at the mitigation of human-wildlife conflicts. We obtained data on wild boar Sus scrofa damages to crops in the Alta Murgia National Park, Southern Italy, and related them to landscape features, to identify areas where the risk of wild boar damages is highest. We used MaxEnt to build species distribution models. We identified the spatial scale at which landscape mostly affects the distribution damages, and optimized the regularization parameter of models, through an information-theoretic approach based on AIC. Wild boar damages quickly increased in the period 2007-2011; cereals and legtmaes were the crops more affected. Large areas of the park have a high risk of wild boar damages. The risk of damages was related to low cover of urban areas or olive grows, intermediate values of forest cover, and high values of shrubland cover within a 2-km radius. Temporally independent validation data demonstrated that models can successfully predict damages in the future. Species distribution models can accurately identify the areas most at risk of wildlife damages, as models calibrated on data collected during only a subset of years correctly predicted damages in the subsequent year [Current Zoology 60 (2): 170-179, 2014].
文摘In this paper, based on a class of multi-group epidemic models of SEIR type with bilinear incidences, we introduce a vaccination compartment, leading to multi-group SVEIR model. We establish that the global dynamics are completely determined by the basic reproduction number R0V which is defined by the spectral radius of the next generation matrix. Our proofs of global stability of the equilibria utilize a graph-theoretical approach to the method of Lyapunov functionals. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccines to obtain immunity or the possibility for them to be infected before acquiring immunity is neglected in each group, this condition will be satisfied and the disease can always be eradicated by suitable vaccination strategies. This may lead to over evaluation for the effect of vaccination.