Models for transmission of disease with immigration of infectives

Simple models for disease transmission that include immigration of infective individuals and variable population size are constructed and analyzed. A model with a general contact rate for a disease that confers no immunity admits a unique endemic equilibrium that is globally stable. A model with mass action incidence for a disease in which infectives either die or recover with permanent immunity has the same qualitative behavior. This latter result is proved by reducing the system to an integro-differential equation. If mass action incidence is replaced by a general contact rate, then the same result is proved locally for a disease that causes fatalities. Threshold-like results are given, but in the presence of immigration of infectives there is no disease-free equilibrium. A considerable reduction of infectives is suggested by the incorporation of screening and quarantining of infectives in a model for HIV transmission in a prison system.     

The effect of immigration on genetic control

Summary Immigration by wild type flies into an established compound chromosome control zone was studied in the laboratory using discrete generation population cages. Immigration rates of less than 10 % per generation by virgin migrants were unlikely to disrupt the zone. However, the zone could be disrupted by immigration rates of 0.5 % if the migrants had mated. The curvilinear relationship between the number of generations to fixation of the migrant genotype and the immigration rate suggested a possible equilibrium between immigration rate and the maintenance of a control zone. -The importance of the results to the strategy of a particular control program is emphasized, as is the need for an integrated multi-disciplinary approach to insect pest management.     

The effect of immigration on genetic control.

The effect of immigration of already inseminated females into the target area of a genetic control programme is analyzed. The sterile male technique and the use of cytoplasmically incompatible males are handled as special cases of the integrated genetical system proposed by Laven and Aslamakhan. For the sterile male technique explicit formulae are given for the critical immigration rate below which genetic control may be successful. If a strain is available which is advantageous to man, the integrated genetical system may be used to replace rather than to control the target population. An explicit formula is derived for the immigration level which can be sustained by a strain of a given fertility. In comparing the sterile male technique with the use of cytoplasmically incompatible males for control it is concluded that the former is to be chosen since the release rates of males necessary for population suppression would cause population replacement due to the unavoidable escape of even a very few females.     

Modelling the effect of immigration on drinking behaviour

A drinking model with immigration is constructed. For the model with problem drinking immigration, the model admits only one problem drinking equilibrium. For the model without problem drinking immigration, the model has two equilibria, one is problem drinking-free equilibrium and the other is problem drinking equilibrium. By employing the method of Lyapunov function, stability of all kinds of equilibria is obtained. Numerical simulations are also provided to illustrate our analytical results. Our results show that alcohol immigrants increase the difficulty of the temperance work of the region.     

The effect of emigration and immigration on the dynamics of a discrete-generation population

The recent paper of Sinha and Parthasarathy investigated the effect of modifying the Ricker and logistic population models to simulate the effects of immigration to, and emigration from, the population. Immigration of a fixed number of individuals was shown to reduce the probability of observing chaos in the Ricker model but not the logistic one. Here, isocline analysis is used to investigate why these effects occur. The stabilization effect for the Ricker equation occurs over a wide range of values of the immigration parameter. There are no values of the parameter, however, which increase the stability of the logistic equation substantially. In contrast density-dependent immigration is found to destabilize both the Ricker and logistic models. Density-dependent emigration serves to reduce the propensity of both models to exhibit chaos.     

The effect of temperature on potassium equilibria in chick embryo muscle

The effect of temperature upon the exchange rates between intra- and extracellular potassium in chick embryo muscle was determined by the use of radioactive potassium. The temperature coefficient of at least four-fifths of the cell potassium is large. At temperatures below 15 degrees C., potassium is lost from the cell and is regained on warming. The results suggest the possibility that 20 per cent or less of the cell potassium may differ from the rest by being more rapidly exchangeable with the medium.     

The effect of perceived cultural and material threats on ethnic preferences in immigration attitudes

This paper shows that cultural and material threats exist side by side, serving different psychological functions, and that they manifest in differential attitudes towards immigrants from different ethnic or racial origins. While culturally threatened individuals prefer immigrants akin to themselves, as opposed to those from different races and cultures, the materially threatened prefer immigrants who are different from themselves who can be expected not to compete for the same resources. We test our hypotheses using multilevel structural equation modelling, based on data from twenty countries in the 2002 wave of the European Social Survey. The disaggregation of these two types of perceived threat reveals responsiveness to the race of immigrants that is otherwise masked by pooling the two threat dimensions.     

Bottlenecks in large populations: the effect of immigration on population viability

We model a large population that is subject to successive short bottlenecks, in order to investigate the impact of different extents of immigration on the change in genetic load and on viability. A first simple genetic model uncovers the opposite effects of immigration on fitness according to the type of deleterious mutations considered: immigration increases fitness if the genetic load is comprised of mildly deleterious mutations, whereas it decreases fitness if it is comprised of lethals. When considering both types of mutations and adding explicit stochastic demographic considerations, in which bottlenecks are engendered by random catastrophes, the global impact of immigration on viability is dependent upon a balance between its opposite effects on the two components of the genetic load and on demographic stochasticity. In this context, immigration tends to increase the probability of extinction if occurring preferentially when population density is high, while it decreases extinction if occurring preferentially towards low-density populations.     

The influence of immigration on demography of sympatric voles

We studied the influence of immigration on the dynamics ofMicrotus ochrogaster Wagner, 1842 andM. pennsylvanicus Ord, 1815 populations in alfalfa, bluegrass, and tallgrass prairie in east-central Illinois for 25 years. The numbers of immigrants in a site were positively correlated with overall population densities of the species in the vicinity of the study sites and within the study site. Population density of the other species was not correlated with immigration of either species. Immigrants did not differ significantly from residents with respect to sex-ratio and reproductive condition. Persistence of immigrantM. pennsylvanicus was lower than that of resident adults in all three habitats, while that of immigrantM. ochrogaster was lower than that of resident adults in alfalfa, where the species was most abundant. Neither the absolute number of immigrants nor the proportion of the population composed of immigrants indicated an effect of immigrants on among- and within-habitat differences in demography and population fluctuations of either species. Immigrants may have been an important factor in maintenance ofM. pennsylvanicus in alfalfa, a low-quality habitat, but the influence of immigration on the dynamics of populations inhabiting other habitats was insubstantial.     

Species-sorting may explain an apparent minimal effect of immigration on freshwater bacterial community dynamics

Long distance atmospheric transport of bacterial cells is often implied as a driver of the apparent cosmopolitan distribution of bacterial taxa. Surprisingly, efforts to measure immigration in bacterial communities are rare. An 8-week time series of within-lake bacterial community composition and atmospheric deposition rates and composition were used to estimate the influence of immigration on bacterial community dynamics in two north temperate lakes. Characterization of bacterial community dynamics using automated ribosomal intergenic spacer analysis suggested moderate overlap in composition between the lakes and atmospherically deposited cells. However, taxa that appeared to be delivered by atmospheric deposition had a relatively minor influence on lake bacterial community dynamics. The weak influence of immigrating bacterial taxa suggests that a species-sorting concept best describes aquatic bacterial metacommunity dynamics.     

A theory of complex multiple equilibria. The effect of poly-U concentration on the binding of deoxyadenosine

A grand-partition function method employed previously for the study of cooperative binding of nucleosides to polynucleotides is generalized to include the effect of changes in the polymer concentration, as well as the effect of changes in the nucleoside concentration. This method is applied to compute isotherms for the binding of deoxyadenosine by polyuridylic acid at various total concentrations of polyuridylic acid. It is found that these isotherms are extremely insensitive to the polymer concentration, as commonly assumed heretofore, and as demonstrated experimentally (to some degree) by Davies and Davidson. However, the conclusion inferred by Davies and Davidson that the complexes must be unimolecular in polyuridylic acid is now seen to be clearly unwarranted, though it remains still a viable possibility, until data over a much wider range of polyuridylic acid concentrations become available.     

The effect of temperature on the oxygen equilibria of fish hemoglobins in relation to environmental thermal variability

• 1. We have measured the temperature dependence of the oxygen equilibria of blood and hemoglobin solutions from four neotropical and three temperate zone fishes.
• 2. Significant differences exist in the heats of oxygenation of the bloods but not the hemoglobin solutions from different species.
• 3. The differences in thermal sensitivity of the oxygenation of the bloods appear to depend on differences in intracellular pH, organic phosphates and other ligand-linked variables and not the intrinsic enthalpies of the oxygenation of the hemoglobins themselves.

     

Lipase reaction in AOT-isooctane reversed micelles: effect of water on equilibria

The effect of water on equilibria for hydrolytic reaction in reversed micelles has been investigated using lipase as a model enzyme. The effect of water on equilibria has been ignored for hydrolase reactions in an aqueous phase. In a reversed micellar system, however, the equilibrium of the lipase reaction was changed when water was added during the hydrolytic reaction. Furthermore, equilibrium fractional conversion is affected by the initial water concentration, being shifted to higher values with higher water concentrations, with other reaction conditions being held constant, indicating that the reaction should be regarded as a two-substrate process. Equations corresponding to a two-substrate, second-order reversible model are derived and used for further analysis. The progress curves predicted from the rate equations agree very well with the experimental results under various reaction conditions. The values of the molar ratio of water to surfactant (R) which maximize the initial reaction rate and maximum fractional conversion is predictable from the derived rate equations and the resulting relationship between R and the kinetic constants.     

Controlling the number of HIV infectives in a mobile population

The spread of the human immunodeficiency virus (HIV) depends prominently on the migration of people between different regions. An important consequence of this population mobility is that HIV control strategies that are optimal in a regional sense may not be optimal in a national sense. We formulate various mathematical control problems for HIV spread in mobile heterosexual populations, and show how optimal regional control strategies can be obtained that minimize the national spread of HIV. We apply the cross-entropy method to solve these highly multi-modal and non-linear optimization problems. We demonstrate the effectiveness of the method via a range of experiments and illustrate how the form of the optimal control function depends on the mathematical model used for the HIV spread.