Multiple Transmission Pathways and Disease Dynamics in a Waterborne Pathogen Model

Multiple transmission pathways exist for many waterborne diseases, including cholera, Giardia, Cryptosporidium, and Campylobacter. Theoretical work exploring the effects of multiple transmission pathways on disease dynamics is incomplete. Here, we consider a simple ODE model that extends the classical SIR framework by adding a compartment (W) that tracks pathogen concentration in the water. Infected individuals shed pathogen into the water compartment, and new infections arise both through exposure to contaminated water, as well as by the classical SIR person–person transmission pathway. We compute the basic reproductive number (ℛ₀), epidemic growth rate, and final outbreak size for the resulting “SIWR” model, and examine how these fundamental quantities depend upon the transmission parameters for the different pathways. We prove that the endemic disease equilibrium for the SIWR model is globally stable. We identify the pathogen decay rate in the water compartment as a key parameter determining when the distinction between the different transmission routes in the SIWR model is important. When the decay rate is slow, using an SIR model rather than the SIWR model can lead to under-estimates of the basic reproductive number and over-estimates of the infectious period.     

Optimal Culling and Biocontrol in a Predator–Prey Model

Invasive species cause enormous problems in ecosystems around the world. Motivated by introduced feral cats that prey on bird populations and threaten to drive them extinct on remote oceanic islands, we formulate and analyze optimal control problems. Their novelty is that they involve both scalar and time-dependent controls. They represent different forms of control, namely the initial release of infected predators on the one hand and culling as well as trapping, infecting, and returning predators on the other hand. Combinations of different control methods have been proposed to complement their respective strengths in reducing predator numbers and thus protecting endangered prey. Here, we formulate and analyze an eco-epidemiological model, provide analytical results on the optimal control problem, and use a forward–backward sweep method for numerical simulations. By taking into account different ecological scenarios, initial conditions, and control durations, our model allows to gain insight how the different methods interact and in which cases they could be effective.     

The Dynamics of a SEIR–SIRC Antigenic Drift Influenza Model

We consider the dynamics of an influenza model with antigenic drift mechanism. Antigenic drift is an antigen mutation on the skin surface of the influenza virus that do not produce a new virus strain. The mutation produces the same virus but with slightly different antigens that cannot be recognized by the immune receptors formed by the previous infection. There are some type of influenza that involve the interaction between two populations such as human and animal. In this paper, we construct an influenza model with antigenic drift mechanism on the human population that has interaction with the animal population. The animal population is assumed to follow the SEIR epidemic model. Our model is motivated by the fact that some of the influenza cases in human come from the animal such as the swine and the avian. The transmission parameter that shows number of contact between the susceptible human and the infectious animals are important to study. The parameter plays an important role to detect the cycle of infection of the disease. The other important parameters are the seasonality degree, which shows the pathogen appearance and disappearance via annual migration, and the infection rate on the human population. We employ the bifurcation theory to analyze the behavior of the system and to detect the cycle of infection types when the parameters values are varied.     

Plankton community cycling and recovery after drought — dynamics in a basin on a flood plain

Lake Merrimajeel, a shallow swamp, is part of the Murray-Darling, a flood plain river system with high plankton diversity. It fluctuates drastically in water level and often dries out. The dynamics and seasonality of zooplankton in the face of these fluctuations and the effects of a total drawdown and refilling were monitored between February 1977 and January 1980. During this period thirty species of rotifers, thirty four of microcrustacea and several other species were recorded. Despite erratic fluctuations in water level, temperature and turbidity a community cycle from dominance by rotifers in summer/autumn and crustacea in winter/spring was maintained. The drawdown disturbed this cycle but it was reestablished the following year. Diversity and density reached a maximum just before the drawdown, during hot, turbid conditions. During this drying phase the waters remained relatively fresh and well oxygenated. Phyllopods were not recorded. The recovery phase was characterised by a group of rare species. It is postulated that these rare, colonising or successional species are dependent on a brief flush of rich organic material produced on flooding.The generally depressive effect of increased turbidity does not hold in this lake and many limnetic species were abundant during periods of high turbidity. It is suggested that turbidity may be tolerated or even be advantageous to some species, depending on the nature of the suspended material.The ability of species to lead a fugitive existence by temporarily colonising basins after drawdowns and refilling may be an important factor in producing the high diversity of plankton in flood plain river systems such as the Murray-Darling.     

Caspase-1 and IL-1β Processing in a Teleost Fish

Interleukine-1β (IL-1β) is the most studied pro-inflammatory cytokine, playing a central role in the generation of systemic and local responses to infection, injury, and immunological challenges. In mammals, IL-1β is synthesized as an inactive 31 kDa precursor that is cleaved by caspase-1 generating a 17.5 kDa secreted active mature form. The caspase-1 cleavage site strictly conserved in all mammalian IL-1β sequences is absent in IL-1β sequences reported for non-mammalian vertebrates. Recently, fish caspase-1 orthologues have been identified in sea bass (Dicentrarchus labrax) and sea bream (Sparus aurata) but very little is known regarding their processing and activity. In this work it is shown that sea bass caspase-1 auto-processing is similar to that of the human enzyme, resulting in active p24/p10 and p20/p10 heterodimers. Moreover, the presence of alternatively spliced variants of caspase-1 in sea bass is reported. The existence of caspase-1 isoforms in fish and in mammals suggests that they have been evolutionarily maintained and therefore are likely to play a regulatory role in the inflammatory response, as shown for other caspases. Finally, it is shown that sea bass and avian IL-1β are specifically cleaved by caspase-1 at different but phylogenetically conserved aspartates, distinct from the cleavage site of mammalian IL-1β.     

Dynamics of Breakdown in a Low-Pressure Argon–Mercury Mixture in a Long Discharge Tube

Breakdown dynamics in the course of glow discharge ignition in a long discharge tube (80 cm in length and 25 mm in diameter) filled with argon at a pressure of 3–4 Torr and mercury vapor at room temperature was studied experimentally. Rectangular voltage pulses with amplitudes from 1 to 2.5 kV were applied to the tube anode, the cathode being grounded. Complex electrical and optical measurements of the breakdown dynamics were carried out. Breakdown begins with a primary discharge between the anode and the tube wall. In this stage, a jump in the anode current and a sharp decrease in the anode voltage are observed and prebreakdown ionization wave arises near the anode. The cathode current appears only after the ionization wave reaches the cathode. The wave propagation velocity was measured at different points along the tube axis. The wave emission spectrum contains Hg, Ar, and Ar⁺ lines. The intensities of these lines measured at a fixed point exhibit very different time behaviors. The effect of the tube shielding on the breakdown characteristics was examined. It is found that, at a sufficiently narrow gap between the shield and the tube, this effect can be substantial.     

Plankton and hydrography in a moderately eastern Adratic bay (Gruž Bay)

Gruž Bay (south-eastern Adriatic) is moderately eutrophicated, mostly by discharge from the karst river Ombla. Input of inorganic nitrogen might be attributed to enrichment from the open sea during strong and continuous north winds in winter 1988/89. Annual succession of primary producers, herbivores and decomposers was defined by seven stages and induced by specific physical-chemical characteristics. In the period April–August, biological production was mostly due to small size fractions of phytoplankton and zooplankton. Recycling of planktonic biomass occurred in September, of allochtonous organic matter in February and March.     

Characterization and Modulation of Glucose Uptake in a Human Blood–Brain Barrier Model

The blood–brain barrier (BBB) plays a key role in limiting and regulating glucose access to glial and neuronal cells. In this work glucose uptake on a human BBB cell model (the hCMEC/D3 cell line) was characterized. The influence of some hormones and diet components on glucose uptake was also studied. ³H-2-deoxy-d-glucose ([³H]-DG) uptake for hCMEC/D3 cells was evaluated in the presence or absence of tested compounds. [³H]-DG uptake was sodium- and energy-independent. [³H]-DG uptake was regulated by Ca²⁺ and calmodulin but not by MAPK kinase pathways. PKC, PKA and protein tyrosine kinase also seem to be involved in glucose uptake modulation. Progesterone and estrone were found to decrease ³H-DG uptake. Catechin and epicatechin did not have any effect, but their methylated metabolites increased [³H]-DG uptake. Quercetin and myricetin decreased [³H]-DG uptake, and glucuronic acid-conjugated quercetin did not have any effect. These cells expressed GLUT1, GLUT3 and SGLT1 mRNA.     

Investigation of Lysozyme–Antilysozyme Interactions in a Model Tetrahymena–EscherichiaCommunity

Lysozyme and antilysozyme activities present in a wide range of microorganisms determine the so-called lysozyme–antilysozyme system of hydrobionts, which greatly contribute to the formation of aquatic biocenoses. However, the mechanism of the functioning of this system in natural freshwater communities remains obscure. The experimental investigation of lysozyme–antilysozyme interactions in a model Tetrahymena–Escherichiacommunity showed that the antilysozyme activity of Escherichia colileads to incomplete phagocytosis, thus enhancing bacterial survival in a mixed culture with infusoria. The selection and reproduction of bacterial cells resistant to grazing by infusoria determine the character of host–parasite interactions and allow bacteria to survive. It was demonstrated that the antilysozyme activity of microorganisms, which is responsible for bacterial persistency in natural biocenoses, is involved in the maintenance of protozoa–bacteria communities in bodies of water.     

Dynamics of a Prey–Predator System with Herd Behaviour in Both and Strong Allee Effect in Prey

Biophysics - This paper mainly deals with the prey?predator dynamics where both the prey and predator exhibit herd behavior. Positivity, boundedness, some extinction criteria, stability of...     

Dynamics analysis of a predator–prey system with harvesting prey and disease in prey species

In this paper, a predator–prey system with harvesting prey and disease in prey species is given. In the absence of time delay, the existence and stability of all equilibria are investigated. In the presence of time delay, some sufficient conditions of the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analysing the corresponding characteristic equation, and the properties of Hopf bifurcation are given by using the normal form theory and centre manifold theorem. Furthermore, an optimal harvesting policy is investigated by applying the Pontryagin's Maximum Principle. Numerical simulations are performed to support our analytic results.     

Mode Transitions in a Model Reaction–Diffusion System Driven by Domain Growth and Noise

Pattern formation in many biological systems takes place during growth of the underlying domain. We study a specific example of a reaction-diffusion (Turing) model in which peak splitting, driven by domain growth, generates a sequence of patterns. We have previously shown that the pattern sequences which are presented when the domain growth rate is sufficiently rapid exhibit a mode-doubling phenomenon. Such pattern sequences afford reliable selection of certain final patterns, thus addressing the robustness problem inherent of the Turing mechanism. At slower domain growth rates this regular mode doubling breaks down in the presence of small perturbations to the dynamics. In this paper we examine the breaking down of the mode doubling sequence and consider the implications of this behaviour in increasing the range of reliably selectable final patterns.     

A Jump-Growth Model for Predator–Prey Dynamics: Derivation and Application to Marine Ecosystems

This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master equation, we derive a deterministic equation for the macroscopic dynamics, which we call the deterministic jump-growth equation, and a linear Fokker–Planck equation for the stochastic fluctuations. The McKendrick–von Foerster equation, used in previous studies, is shown to be a first-order approximation, appropriate in equilibrium systems where predators are much larger than their prey. The model has a power-law steady state consistent with the approximate constancy of mass density in logarithmic intervals of body mass often observed in marine ecosystems. The behaviours of the stochastic process, the deterministic jump-growth equation, and the McKendrick–von Foerster equation are compared using numerical methods. The numerical analysis shows two classes of attractors: steady states and travelling waves.     

Dynamics induced by delay in a nutrient–phytoplankton model with diffusion

In this paper, a nutrient–phytoplankton model described by a couple of reaction-diffusion equations with delay is studied analytically and numerically. The aim of this research is to provide an understanding of the impact of delay on the nutrient–phytoplankton dynamics. Significantly, the delay can not only induce instability of a positive equilibrium, but also promote the formation of patchiness (an irregular pattern) via Hopf bifurcation. However, if the delay does not exist, the positive equilibrium is always globally asymptotically stable when it exists. In addition, the numerical analysis indicates that the input rate and the loss rate of nutrient also play an important role in the growth of phytoplankton, which supports that eutrophic conditions may be a significant reason inducing phytoplankton blooms. Numerical results are consistent with the analytical results.     

Regional Endothermy in a Coral Reef Fish?

Although a few pelagic species exhibit regional endothermy, most fish are regarded as ectotherms. However, we document significant regional endothermy in a benthic reef fish. Individual steephead parrotfish, Chlorurus microrhinos (Labridae, formerly Scaridae) were tagged and their internal temperatures were monitored for a 24 h period using active acoustic telemetry. At night, on the reef, C. microrhinos were found to maintain a consistent average peritoneal cavity temperature 0.16 ± 0.005 °C (SE) warmer than ambient. Diurnal internal temperatures were highly variable for individuals monitored on the reef, while in tank-based trials, peritoneal cavity temperatures tracked environmental temperatures. The mechanisms responsible for a departure of the peritoneal cavity temperature from environmental temperature occurred in C. microrhinos are not yet understood. However, the diet and behavior of the species suggests that heat in the peritoneal cavity may result primarily from endogenous thermogenesis coupled with physiological heat retention mechanisms. The presence of limited endothermy in C. microrhinos indicates that a degree of uncertainty may exist in the manner that reef fish respond to their thermal environment. At the very least, they do not always appear to respond to environmental temperatures as neutral thermal vessels and do display limited, but significant, visceral warming.     

Dynamics of Inorganic Nitrogen in Nitrate and Glucose-amended Alkaline–saline Soil

Induction of assimilatory NO ₃ ⁻ reduction through the application of an easily decomposable substrate in alkaline–saline soils of the former lake Texcoco (Mexico) resulted in a fast immobilization of NO ₃ ⁻ in excess of N required for metabolic activity and the release of large concentrations of NO ₂ ⁻ and smaller amounts of NH ₄ ⁺ . We postulated that this was regulated by the amounts of NO ₃ ⁻ and glucose added, and affected by the specific characteristics of soil from the former lake Texcoco. This was investigated by spiking soils of different electrolytic conductivity (EC) 56.0 dS m⁻¹ (soil A of Texcoco) and 11.6 dS m⁻¹ (soil B of Texcoco) with different concentrations of NO ₃ ⁻ and glucose while dynamics of CO₂, NH ₄ ⁺ , NO ₂ ⁻ and NO ₃ ⁻ were monitored in an aerobic incubation for 7 days. For comparison reasons (control) an agricultural soil with low EC (0.3 dS m⁻¹) was included as well. In the agricultural soil, 67% of the added glucose mineralized within 7 days, but only 15% in soil A of Texcoco and 20% in soil B of Texcoco. The application of NO ₃ ⁻ to the agricultural soil added with glucose increased cumulative production of CO₂ 1.2 times, 1.5 times in soil A of Texcoco and 1.8 times in soil B of Texcoco. Concentration of NO ₂ ⁻ increased to > 100 mg NO ₂ ⁻ -N kg⁻¹ when 1000 mg glucose-C kg⁻¹ and 500 mg NO ₃ ⁻ -N kg⁻¹ were added to soil A and B of Texcoco, but remained < 3 mg NO ₂ ⁻ -N kg⁻¹ in the agricultural soil. The ratio between the cumulative production of CO₂ and the decrease in concentration of NO ₃ ⁻ was approximately one in soil A and B of Texcoco, but 10 in the agricultural soil after 3 days. It was found that micro-organisms in the alkaline–saline soil of the former lake Texcoco were capable of immobilizing large quantities of NO ₃ ⁻ when an easy decomposable substrate was available in excess of what might be required for metabolic activity while producing large concentrations of NO ₂ ⁻ , but these phenomena were absent in an agricultural soil. In soil of Texcoco, concentrations of NO ₂ ⁻ and NH ₄ ⁺ increased with increased salinity and availability of NO ₃ ⁻ . This ability to remove large quantities of NO ₃ ⁻ under these conditions and then utilize it at a later time might benefit micro-organisms of the N limited alkaline–saline soils of Texcoco.     

A Mathematical Model for Simultaneous Spatio-Temporal Dynamics of Calcium and Inositol 1,4,5-Trisphosphate in Madin–Darby Canine Kidney Epithelial Cells

The landmark paper by Hirose et al. (Hirose, K., Kadowaki, S., Tanabe, M., Takeshima, H., Iino, M., Science 284:1527–1530, 1999) presented experimental investigations to show that not only can calcium upregulate IP₃, but that it can also have an inhibitory effect on IP₃. In this paper, we present a preliminary model, which is consistent with these experiments. This model includes positive and negative feedback between calcium and IP₃ and is able to reproduce more precisely the data presented in Hirose et al. (Hirose, K., Kadowaki, S., Tanabe, M., Takeshima, H., Iino, M., Science 284:1527–1530, 1999). In the second part of the paper, the intracellular and intercellular calcium movement in Madin–Darby canine kidney epithelial cells is investigated. With the aid of the model we are able to identify the aspects of IP₃ and calcium signalling, which should be studied further experimentally before refining the model.