Using a system of time-dynamical equations, we investigate how daily mobility indices, such as the homestay percentage above the pre-COVID normal (Formula: see text; or H-forcing), and the vaccinated ...percentage (Formula: see text; or V-forcing) impact the net reproductive rate (R0) of COVID-19 in ten island nations as a prototype, and then, extending it to 124 countries worldwide. Our H- and V-forcing model of R0 can explain the new trends in 106 countries. The disease transmission can be controlled by forcing down Formula: see text with an enforcement of continuous Formula: see text in Formula: see text of countries with Formula: see text vaccinated plus recovered, Formula: see text. The required critical Formula: see text decreases with increasing Formula: see text, dropping it down to Formula: see text with Formula: see text, and further down to Formula: see text with Formula: see text. However, the regulations on Formula: see text are context-dependent and country-specific. Our model gives insights into forecasting and controlling the disease's transmission behaviour when the effectiveness of the vaccines is a concern due to new variants, and/or there are delays in vaccination rollout programs.
Mathematical modeling provides a rigorous way to quantify immunological processes and discriminate between alternative mechanisms driving specific biological phenomena. It is typical that ...mathematical models of immunological phenomena are developed by modelers to explain specific sets of experimental data after the data have been collected by experimental collaborators. Whether the available data are sufficient to accurately estimate model parameters or to discriminate between alternative models is not typically investigated. While previously collected data may be sufficient to guide development of alternative models and help estimating model parameters, such data often do not allow to discriminate between alternative models. As a case study, we develop a series of power analyses to determine optimal sample sizes that allow for accurate estimation of model parameters and for discrimination between alternative models describing clustering of CD8 T cells around Plasmodium liver stages. In our typical experiments, mice are infected intravenously with Plasmodium sporozoites that invade hepatocytes (liver cells), and then activated CD8 T cells are transferred into the infected mice. The number of T cells found in the vicinity of individual infected hepatocytes at different times after T cell transfer is counted using intravital microscopy. We previously developed a series of mathematical models aimed to explain highly variable number of T cells per parasite; one of such models, the density-dependent recruitment (DDR) model, fitted the data from preliminary experiments better than the alternative models, such as the density-independent exit (DIE) model. Here, we show that the ability to discriminate between these alternative models depends on the number of parasites imaged in the analysis; analysis of about
n
=
50
parasites at 2, 4, and 8 h after T cell transfer will allow for over 95% probability to select the correct model. The type of data collected also has an impact; following T cell clustering around individual parasites over time (called as longitudinal (LT) data) allows for a more precise and less biased estimates of the parameters of the DDR model than that generated from a more traditional way of imaging individual parasites in different liver areas/mice (cross-sectional (CS) data). However, LT imaging comes at a cost of a need to keep the mice alive under the microscope for hours which may be ethically unacceptable. We finally show that the number of time points at which the measurements are taken also impacts the precision of estimation of DDR model parameters; in particular, measuring T cell clustering at one time point does not allow accurately estimating all parameters of the DDR model. Using our case study, we propose a general framework on how mathematical modeling can be used to guide experimental designs and power analyses of complex biological processes.
With the International Maritime Organization’s (IMO) International Convention for the Control and Management of Ships’ Ballast Water and Sediments now in force, determining abundance and distribution ...of phytoplankton inside ballast tanks is critical for successful ballast water management, particularly when assessing compliance. The relationship between the abundance and distribution of cells was examined to obtain the best representative sample of the entire phytoplankton community in ballast tanks, comparing three ballast water sampling techniques including in-line, in-tank, and Van Dorn bottle methods. Lloyd’s index, D
y
, and Gini index were applied to compare methods of sample collection and determine representativeness of samples and performance of sampling methods. Phytoplankton abundance trends from live microscopy counts using fluorescein diacetate (FDA) were also compared to those using a FlowCAM on preserved samples. The phytoplankton community showed a patchy distribution inside the ballast tank and this trend was observed across all voyages. The estimated marginal mean analysis showed that in hypothetical conditions (e.g., 702 m
3
of water in ballast tank and phytoplankton whole-tank abundance of 19,522 cells), the difference among the three methods was small. Conversely, statistical analysis performed on empiric abundances using a negative binomial regression model determined that the volume discharged during sampling of ballast water has an effect on the number of cells collected on a given voyage. Results of this study also confirmed that the in-line method may be a better method at collecting phytoplankton samples from ballast tanks than the in-tank or Van Dorn method, regardless of the time at which samples are collected. Finally, the number of living cells and the number of preserved cells showed similar trends for most of the voyages, despite fewer samples analyzed using FDA.
Brain pathological changes impair cognition early in disease etiology. There is an urgent need to understand aging-linked mechanisms of early memory loss to develop therapeutic strategies and prevent ...the development of cognitive impairment. Tusc2 is a mitochondrial-resident protein regulating Ca2+ fluxes to and from mitochondria impacting overall health. We previously reported that Tusc2−/− female mice develop chronic inflammation and age prematurely, causing age- and sex-dependent spatial memory deficits at 5 months old. Therefore, we investigated Tusc2-dependent mechanisms of memory impairment in 4-month-old mice, comparing changes in resident and brain-infiltrating immune cells. Interestingly, Tusc2−/− female mice demonstrated a pro-inflammatory increase in astrocytes, expression of IFN-γ in CD4+ T cells and Granzyme-B in CD8+T cells. We also found fewer FOXP3+ T-regulatory cells and Ly49G+ NK and Ly49G+ NKT cells in female Tusc2−/− brains, suggesting a dampened anti-inflammatory response. Moreover, Tusc2−/− hippocampi exhibited Tusc2- and sex-specific protein changes associated with brain plasticity, including mTOR activation, and Calbindin and CamKII dysregulation affecting intracellular Ca2+ dynamics. Overall, the data suggest that dysregulation of Ca2+-dependent processes and a heightened pro-inflammatory brain microenvironment in Tusc2−/− mice could underlie cognitive impairment. Thus, strategies to modulate the mitochondrial Tusc2- and Ca2+- signaling pathways in the brain should be explored to improve cognitive health.
Malaria, a disease caused by parasites of the Plasmodium genus, begins when Plasmodium-infected mosquitoes inject malaria sporozoites while searching for blood. Sporozoites migrate from the skin via ...blood to the liver, infect hepatocytes, and form liver stages which in mice 48 h later escape into blood and cause clinical malaria. Vaccine-induced activated or memory CD8 T cells are capable of locating and eliminating all liver stages in 48 h, thus preventing the blood-stage disease. However, the rules of how CD8 T cells are able to locate all liver stages within a relatively short time period remains poorly understood. We recently reported formation of clusters consisting of variable numbers of activated CD8 T cells around
(Py)-infected hepatocytes. Using a combination of experimental data and mathematical models we now provide additional insights into mechanisms of formation of these clusters. First, we show that a model in which cluster formation is driven exclusively by T-cell-extrinsic factors, such as variability in "attractiveness" of different liver stages, cannot explain distribution of cluster sizes in different experimental conditions. In contrast, the model in which cluster formation is driven by the positive feedback loop (i.e., larger clusters attract more CD8 T cells) can accurately explain the available data. Second, while both Py-specific CD8 T cells and T cells of irrelevant specificity (non-specific CD8 T cells) are attracted to the clusters, we found no evidence that non-specific CD8 T cells play a role in cluster formation. Third and finally, mathematical modeling suggested that formation of clusters occurs rapidly, within few hours after adoptive transfer of CD8 T cells, thus illustrating high efficiency of CD8 T cells in locating their targets in complex peripheral organs, such as the liver. Taken together, our analysis provides novel insights into and attempts to discriminate between alternative mechanisms driving the formation of clusters of antigen-specific CD8 T cells in the liver.
Marine calanoid copepods colonize new habitats, and some become invasive. Their fitness, measured by intrinsic growth rate and net reproductive rate, is partially driven by biochemical processes. ...Thus, it is a function of ambient temperature. Biochemical processes may not be approximated well by yearly mean temperature alone when temperature cycles yearly, largely. Higher order moments may also be important. The amplitude of yearly fluctuations of monthly and seasonal sea temperatures varies dramatically across the northern temperate regions. Thus, they can impact the fitness, thereby the colonization potential of copepods migrating across such region. To investigate this, we derive approximate metrics of periodic (yearly) fitness: the yearly intrinsic growth rate, and a weighted net reproductive rate. We use them to measure the persistence and the growth of an Allee-effect free, stage-structured, fast-maturing, small population of invasive copepods that reproduces year-round in habitats with yearly temperature cycles. We show that the yearly fitness increases substantially when a population is introduced from a habitat with large amplitude to that with small amplitude yearly fluctuating temperatures, given that their mean temperatures and other environmental and ecological factors are constant. The detected range-expansion of the modeled species matches the potential fitness gradient predicted by the metrics. The study leads to the question whether the gradient of the amplitudes of temperature between habitats with similar yearly mean temperatures impacts a class of fast-maturating calanoid copepods, colonizing new habitats, and becoming invasive.
•Fitness metrics were derived for fast-maturing copepods in cyclic temperatures.•Habitats with lower amplitude temperatures had increased copepod fitness.•Observed range-expansion matched the fitness gradient predicted by the metrics.•The amplitude gradient between different habitats impacts copepod invasibility.•This phenomenon may explain copepod invasion success on a global scale.
It has been proposed that microbial predator and prey densities are related through sublinear power laws. We revisited previously published biomass and abundance data and fitted Power‐law Biomass ...Scaling Relationships (PBSRs) between marine microzooplankton predators (Z) and phytoplankton prey (P), and marine viral predators (V) and bacterial prey (B). We analysed them assuming an error structure given by Type II regression models which, in contrast to the conventional Type I regression model, accounts for errors in both the independent and the dependent variables. We found that the data support linear relationships, in contrast to the sublinear relationships reported by previous authors. The scaling exponent yields an expected value of 1 with some spread in different datasets that was well‐described with a Gaussian distribution. Our results suggest that the ratios Z/P, and V/B are on average invariant, in contrast to the hypothesis that they systematically decrease with increasing P and B, respectively, as previously thought.
We consider the problem of estimating the time needed for species colonization. The analysis is based upon the known population dynamic models by Dennis with minor modification to the Allee effect ...description, which allows us to obtain an analytical expression for the colonization time. For the stochastic counterpart of the models in diffusion approximation, we (1) propose the description of immigration stochasticity, (2) provide the estimates of time required for the population to overcome strong demographic Allee effect, and (3) consider the numerical results for mean colonization time and its uncertainty. Strong Allee effect strictly disallows populations at small immigration rates to colonize new habitats, unless the stochasticity in immigration, environment, or demography is present, or incorporated into the model. Immigration stochasticity, complementing with environmental and demographic stochasticity, enables the populations to overcome the Allee threshold even at low values of propagule pressure.
•We derive several models of Allee effect from the basic one by Dennis (1989).•We propose a definition of colonization time (CT) and substantiate it.•We give analytical estimates of CT for several deterministic and stochastic models.•We perform a detailed numerical study of CT for a number of stochastic models.•We show that CT depends on the type of stochasticity in the model.
Many commercial ships will soon begin to use treatment systems to manage their ballast water and reduce the global transfer of harmful aquatic organisms and pathogens in accordance with upcoming ...International Maritime Organization regulations. As a result, rapid and accurate automated methods will be needed to monitoring compliance of ships' ballast water. We examined two automated particle counters for monitoring organisms ≥50μm in minimum dimension: a High Resolution Laser Optical Plankton Counter (HR-LOPC), and a Flow Cytometer with digital imaging Microscope (FlowCAM), in comparison to traditional (manual) microscopy considering plankton concentration, size frequency distributions and particle size measurements. The automated tools tended to underestimate particle concentration compared to standard microscopy, but gave similar results in terms of relative abundance of individual taxa. For most taxa, particle size measurements generated by FlowCAM ABD (Area Based Diameter) were more similar to microscope measurements than were those by FlowCAM ESD (Equivalent Spherical Diameter), though there was a mismatch in size estimates for some organisms between the FlowCAM ABD and microscope due to orientation and complex morphology. When a single problematic taxon is very abundant, the resulting size frequency distribution curves can become skewed, as was observed with Asterionella in this study. In particular, special consideration is needed when utilizing automated tools to analyse samples containing colonial species. Re-analysis of the size frequency distributions with the removal of Asterionella from FlowCAM and microscope data resulted in more similar curves across methods with FlowCAM ABD having the best fit compared to the microscope, although microscope concentration estimates were still significantly higher than estimates from the other methods. The results of our study indicate that both automated tools can generate frequency distributions of particles that might be particularly useful if correction factors can be developed for known differences in well-studied aquatic ecosystems.
•A High Resolution-LOPC and a FlowCAM were evaluated for ballast water monitoring.•Both instruments underestimated density compared to microscopy.•Size measurements can be affected by organism orientation and complex morphology.•Both tools might be particularly useful when working with a known community.
The metabolic theory of ecology (MTE) has explained the taxonomic richness of ectothermic species as an inverse function of habitat mean temperature. Extending this theory, we show that yearly ...temperature cycles reduce metabolic rates of taxa having short generation times. This reduction is due to Jensen’s inequality, which results from a nonlinear dependency of metabolic rate of organisms on temperature. It leads to a prediction that relatively lower species richness is found in habitats with larger amplitudes of yearly temperature cycles where mean temperatures and other conditions are similar. We show that metabolically driven generation time of a taxon also relates functionally to species richness, and similarly, its yearly cycles reduce richness. We test these hypotheses on marine calanoid copepods with 46,377 records of data collected by scientific cruise surveys in Mediterranean regions, across which the temperature amplitudes vary dramatically. We test both bio-energetic and phenomenological effects of temperature cycles on richness in 86 1° × 1° latitudinal and longitudinal spatial units. The models incorporated the effect of both periodic fluctuations and mean temperature explained 21.6% more variation in the data, with lower AIC, compared to models incorporated only the mean temperature. The study also gives insight into the basis of energetic-equivalence rule in MTE determining richness, which can be governed by generation time of taxon. The results of this study lead to the proposition that amplitude of yearly temperature cycles may contribute to both the longitudinal and the latitudinal differences in species richness and show how the metabolic theory can explain macro-ecological patterns arising from yearly temperature cycles.
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