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Journal of Mathematical Biology Dec 2021It has been suggested, without rigorous mathematical analysis, that the classical vaccine-induced herd immunity threshold (HIT) assuming a homogeneous population can be...
It has been suggested, without rigorous mathematical analysis, that the classical vaccine-induced herd immunity threshold (HIT) assuming a homogeneous population can be substantially higher than the minimum HIT obtained when considering population heterogeneities. We investigated this claim by developing, and rigorously analyzing, a vaccination model that incorporates various forms of heterogeneity and compared it with a model that considers a homogeneous population. By employing a two-group vaccination model in heterogeneous populations, we theoretically established conditions under which heterogeneity leads to different HIT values, depending on the relative values of the contact rates for each group, the type of mixing between the groups, the relative vaccine efficacy, and the relative population size of each group. For example, under biased random mixing assumption and when vaccinating a given group results in disproportionate prevention of higher transmission per capita, we show that it is optimal to vaccinate that group before vaccinating the other groups. We also found situations, under biased assortative mixing assumption, where it is optimal to vaccinate more than one group. We show that regardless of the form of mixing between the groups, the HIT values assuming a heterogeneous population are always lower than the HIT values obtained from a corresponding model with a homogeneous population. Using realistic numerical examples and parametrization (e.g., assuming assortative mixing together with vaccine efficacy of 95% and the value of the basic reproduction number, [Formula: see text], of the model set at [Formula: see text] 2.5), we demonstrate that the HIT value generated from a model that considers population heterogeneity (e.g., biased assortative mixing) is significantly lower (40%) compared with a HIT value of 63% obtained if the model uses homogeneous population.
Topics: Basic Reproduction Number; Immunity, Herd; Population Density; Vaccination; Vaccine Efficacy
PubMed: 34878609
DOI: 10.1007/s00285-021-01686-z -
Mathematical Biosciences and... Jan 2024Epidemiologists have used the timing of the peak of an epidemic to guide public health interventions. By determining the expected peak time, they can allocate resources...
Epidemiologists have used the timing of the peak of an epidemic to guide public health interventions. By determining the expected peak time, they can allocate resources effectively and implement measures such as quarantine, vaccination, and treatment at the right time to mitigate the spread of the disease. The peak time also provides valuable information for those modeling the spread of the epidemic and making predictions about its future trajectory. In this study, we analyze the time needed for an epidemic to reach its peak by presenting a straightforward analytical expression. Utilizing two epidemiological models, the first is a generalized $ SEIR $ model with two classes of latent individuals, while the second incorporates a continuous age structure for latent infections. We confirm the conjecture that the peak occurs at approximately $ T\sim(\ln N)/\lambda $, where $ N $ is the population size and $ \lambda $ is the largest eigenvalue of the linearized system in the first model or the unique positive root of the characteristic equation in the second model. Our analytical results are compared to numerical solutions and shown to be in good agreement.
Topics: Humans; Epidemics; Quarantine; Public Health; Population Density
PubMed: 38454709
DOI: 10.3934/mbe.2024126 -
Journal of Insect Science (Online) Jul 2023Until now, little is known about the population structure and mobility of temperate dung beetles including the rainbow scarab, Phanaeus vindex (MacLeay 1819), although...
Until now, little is known about the population structure and mobility of temperate dung beetles including the rainbow scarab, Phanaeus vindex (MacLeay 1819), although this knowledge is essential for their conservation as pastures become increasingly rare and the landscape fragmented by monocultures and urbanization. Here, we estimated population size, longevity, and dispersal within and between pastures. For 3 yr, we life-trapped beetles every week on 2 adjacent farms in SE Michigan, determined their sex, male morph, and size, and marked their elytra with individual tattoo patterns before releasing them. We marked a total of 470 rainbow scarabs of which 14 were recaptured once and 2 were recaptured twice. The sex ratio was not significantly sex-biased but fluctuated between months with no apparent uniformity between years. While the minor to major male ratios were unbiased in 2019 and 2020, they were marginally minor-biased in 2021. The gross population estimates for the 2 farms were 458-491 and 217 rainbow scarabs, respectively. Beetles traveled distances of up to 178 m within farms. No beetles dispersed between farms. One large female was recaptured after 338 days documenting the first cold hardiness and long lifespan of a cold-temperate dung beetle species in the wild. The low population estimates on both farms indicate 2 vulnerable populations with no or extremely limited connectivity. Supplementary funding for the land stewardship of small-scale cattle farmers could stabilize populations of native dung beetles and maintain their ecosystem services.
Topics: Male; Female; Animals; Cattle; Coleoptera; Ecosystem; Michigan; Population Density; Feces
PubMed: 37399115
DOI: 10.1093/jisesa/iead050 -
Scientific Reports Apr 2022The time period between 560 and 360 ka (MIS14 to MIS11) was critical for the evolution of the Neanderthal lineage and the appearance of Levallois technology in Europe....
The time period between 560 and 360 ka (MIS14 to MIS11) was critical for the evolution of the Neanderthal lineage and the appearance of Levallois technology in Europe. The shifts in the distribution of the human populations, driven by cyclical climate changes, are generally accepted to have played major roles in both processes. We used a dataset of palaeoclimate maps and a species distribution model to reconstruct the changes in the area of Western Europe with suitable environmental conditions for humans during 11 time intervals of the MIS14 to MIS 11 period. Eventually, the maximum sustainable human population within the suitable area during each time interval was estimated by extrapolating the relationship observed between recent hunter-gatherer population density and net primary productivity and applying it to the past. Contrary to common assumptions, our results showed the three Mediterranean Peninsulas were not the only region suitable for humans during the glacial periods. The estimated total sustainable population of Western Europe from MIS14 to MIS11 oscillated between 13,000 and 25,000 individuals. These results offer a new theoretical scenario to develop models and hypotheses to explain cultural and biological evolution during the Middle Pleistocene in Western Europe.
Topics: Animals; Climate Change; Europe; Hominidae; Humans; Neanderthals; Population Density
PubMed: 35484382
DOI: 10.1038/s41598-022-10642-w -
Oecologia Jan 2022Spatial capture-recapture modelling (SCR) is a powerful tool for estimating density, population size, and space use of elusive animals. Here, we applied SCR modelling to...
Spatial capture-recapture modelling (SCR) is a powerful tool for estimating density, population size, and space use of elusive animals. Here, we applied SCR modelling to non-invasive genetic sampling (NGS) data to estimate red fox (Vulpes vulpes) densities in two areas of boreal forest in central (2016-2018) and southern Norway (2017-2018). Estimated densities were overall lower in the central study area (mean = 0.04 foxes per km in 2016, 0.10 in 2017, and 0.06 in 2018) compared to the southern study area (0.16 in 2017 and 0.09 in 2018). We found a positive effect of forest cover on density in the central, but not the southern study area. The absence of an effect in the southern area may reflect a paucity of evidence caused by low variation in forest cover. Estimated mean home-range size in the central study area was 45 km [95%CI 34-60] for females and 88 km [69-113] for males. Mean home-range sizes were smaller in the southern study area (26 km [16-42] for females and 56 km [35-91] for males). In both study areas, detection probability was session-dependent and affected by sampling effort. This study highlights how SCR modelling in combination with NGS can be used to efficiently monitor red fox populations, and simultaneously incorporate ecological factors and estimate their effects on population density and space use.
Topics: Animals; Female; Foxes; Male; Norway; Population Density; Probability
PubMed: 34859281
DOI: 10.1007/s00442-021-05087-3 -
Scientific Reports Jun 2022Thriving under high population density is considered a major feature of urban exploiter species. Nevertheless, population density appears to be a surprisingly overlooked...
Thriving under high population density is considered a major feature of urban exploiter species. Nevertheless, population density appears to be a surprisingly overlooked factor in urban ecology studies. High population numbers observed in urban species might promote pathogen transmission and negatively affect health or condition, thus requiring investments in immunocompetence. The feral pigeon Columba livia domestica is an example of a successful city-dweller, found in great abundance in large cities across the globe. We investigated the effects of population density on induced immune response (phytohaemagglutinin skin test) and body condition (blood haemoglobin concentration and size-corrected body mass) in 120 feral pigeons, captured along population density gradient in Łódź (central Poland). We found that stronger immune response was associated with higher population density, but was not related to physiological condition and physiological stress (heterophil/lymphocyte ratio). Moreover, condition indices were not associated with population density. However, since pigeon population density was highly correlated with the level of habitat urbanization, we cannot exclude that any density-dependent effects may be mediated by habitat variation. Our results indicate that urban environment, via population density, might exert different selective pressures on immunocompetence and body condition in this successful urban exploiter.
Topics: Adaptation, Physiological; Animals; Columbidae; Immunity; Population Density; Urbanization
PubMed: 35650222
DOI: 10.1038/s41598-022-12910-1 -
Proceedings. Biological Sciences Dec 2020Animals living at high population densities commonly experience greater exposure to disease, leading to increased parasite burdens. However, social animals can benefit...
Animals living at high population densities commonly experience greater exposure to disease, leading to increased parasite burdens. However, social animals can benefit immunologically and hygienically from cooperation, and individuals may alter their socio-spatial behaviour in response to infection, both of which could counteract density-related increases in exposure. Consequently, the costs and benefits of sociality for disease are often uncertain. Here, we use a long-term study of a wild European badger population () to investigate how within-population variation in host density determines infection with multiple parasites. Four out of five parasite taxa exhibited consistent spatial hotspots of infection, which peaked among badgers living in areas of low local population density. Combined movement, survival, spatial and social network analyses revealed that parasite avoidance was the likely cause of this negative density dependence, with possible roles for localized mortality, encounter-dilution effects, and micronutrient-enhanced immunity. These findings demonstrate that animals can organize their societies in space to minimize parasite infection, with important implications for badger behavioural ecology and for the control of badger-associated diseases.
Topics: Animals; Movement; Mustelidae; Population Density; Symbiosis
PubMed: 33323092
DOI: 10.1098/rspb.2020.2655 -
Theoretical Population Biology Dec 2022This study deals with the problem of the population shrinking in habitats affected by aging and excessive migration outflows. First, a control-oriented population...
This study deals with the problem of the population shrinking in habitats affected by aging and excessive migration outflows. First, a control-oriented population dynamics model was proposed that catches the effect of depopulation. The model also includes the effect of spatial interaction-driven migration flows on population size. The resulting model is a non-homogeneous ordinary differential equation. It includes such phenomena that are important from the control point of view, such as the influence of migration costs on population dynamics, the impact of aging on population size, or the effect of the habitats' carrying capacity on migration flows. Based on the model, controllability conditions are formulated and a control strategy was developed that is meant to avoid the depopulation of the habitat. The control method acts on the migration costs to achieve the control goal and requires only population size measurements. Simulation measurements are presented in the paper to show the effectiveness of the proposed modeling and control methods.
Topics: Population Dynamics; Population Density; Computer Simulation; Ecosystem; Conservation of Natural Resources
PubMed: 36379299
DOI: 10.1016/j.tpb.2022.11.002 -
The Journal of Animal Ecology Nov 2022Harvest of wild organisms is an important component of human culture, economy, and recreation, but can also put species at risk of extinction. Decisions that guide...
Harvest of wild organisms is an important component of human culture, economy, and recreation, but can also put species at risk of extinction. Decisions that guide successful management actions therefore rely on the ability of researchers to link changes in demographic processes to the anthropogenic actions or environmental changes that underlie variation in demographic parameters. Ecologists often use population models or maximum sustained yield curves to estimate the impacts of harvest on wildlife and fish populations. Applications of these models usually focus exclusively on the impact of harvest and often fail to consider adequately other potential, often collinear, mechanistic drivers of the observed relationships between harvest and demographic rates. In this study, we used an integrated population model and long-term data (1973-2016) to examine the relationships among hunting and natural mortality, the number of hunters, habitat conditions, and population size of blue-winged teal Spatula discors, an abundant North American dabbling duck with a relatively fast-paced life history strategy. Over the last two and a half decades of the study, teal abundance tripled, hunting mortality probability increased slightly ( ), and natural mortality probability increased substantially ( ) at greater population densities. We demonstrate strong density-dependent effects on natural mortality and fecundity as population density increased, indicative of compensatory harvest mortality and compensatory natality. Critically, an analysis that only assessed the relationship between survival and hunting mortality would spuriously indicate depensatory mortality due to multicollinearity between abundance, natural mortality and hunting mortality. Our findings demonstrate that models that only consider the direct effect of hunting on survival or natural mortality can fail to accurately assess the mechanistic impact of hunting on population dynamics due to multicollinearity among demographic drivers. This multicollinearity limits inference and may have strong impacts on applied management actions globally.
Topics: Animals; Humans; Conservation of Natural Resources; Ducks; Fishes; Population Density; Population Dynamics; Hunting; Animals, Wild
PubMed: 36054772
DOI: 10.1111/1365-2656.13807 -
MBio Jun 2022Quorum sensing (QS) is a mechanism of cell-cell communication that connects gene expression to environmental conditions (e.g., cell density) in many bacterial species,...
Quorum sensing (QS) is a mechanism of cell-cell communication that connects gene expression to environmental conditions (e.g., cell density) in many bacterial species, mediated by diffusible signal molecules. Current functional studies focus on qualitatively distinct QS ON/OFF states. In the context of density sensing, this view led to the adoption of a "quorum" analogy in which populations sense when they are above a sufficient density (i.e., "quorate") to efficiently turn on cooperative behaviors. This framework overlooks the potential for intermediate, graded responses to shifts in the environment. In this study, we tracked QS-regulated protease () expression and showed that Pseudomonas aeruginosa can deliver a graded behavioral response to fine-scale variation in population density, on both the population and single-cell scales. On the population scale, we saw a graded response to variation in population density (controlled by culture carrying capacity). On the single-cell scale, we saw significant bimodality at higher densities, with separate OFF and ON subpopulations that responded differentially to changes in density: a static OFF population of cells and increasing intensity of expression among the ON population of cells. Together, these results indicate that QS can tune gene expression to graded environmental change, with no critical cell mass or "quorum" at which behavioral responses are activated on either the individual-cell or population scale. In an infection context, our results indicate there is not a hard threshold separating a quorate "attack" mode from a subquorate "stealth" mode. Bacteria can be highly social, controlling collective behaviors via cell-cell communication mechanisms known as quorum sensing (QS). QS is now a large research field, yet a basic question remains unanswered: what is the environmental resolution of QS? The notion of a threshold, or "quorum," separating coordinated ON and OFF states is a central dogma in QS, but recent studies have shown heterogeneous responses at a single cell scale. Using Pseudomonas aeruginosa, we showed that populations generate graded responses to environmental variation through shifts in the proportion of cells responding and the intensity of responses. In an infection context, our results indicate that there is not a hard threshold separating a quorate "attack" mode and a subquorate "stealth" mode.
Topics: Bacteria; Gene Expression Regulation, Bacterial; Population Density; Pseudomonas aeruginosa; Quorum Sensing
PubMed: 35583321
DOI: 10.1128/mbio.00745-22