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In this paper a mathematical model is proposed for the interaction of the immune system with HIV viruses and malaria parasites in an individual host. It consists of a system of three coupled ordinary differential equations, which represents the rate of change in the concentration of malaria parasites, HIV viruses and immunity effector within a host, respectively. The theoretical model gives insight into the biological balance between pathogen replication and the immune response to the pathogen: persistence versus elimination of the pathogen, which determines the outcome of infection. Dynamical analysis shows that the outcomes of the interactions between the immune system of the host with either malaria parasites or HIV viruses are dramatic such as malaria infection promoting proliferation of HIV virus, HIV infection increasing the risk from malaria and the immune system of the host failing to keep the diseases under control, etc. The results provide a new perspective for understanding of the complexity mechanisms of the co-infection (or dual infection) with malaria and HIV in a host.

The within-host and between-host dynamics of malaria are linked in myriad ways, but most obviously by gametocytes, the parasite blood forms transmissible from human to mosquito. Gametocyte dynamics depend on those of non-transmissible blood forms, which stimulate immune responses, impeding transmission as well as within-host parasite densities. These dynamics can, in turn, influence antigenic diversity and recombination between genetically distinct parasites. Here, we embed a differential-equation model of parasite-immune system interactions within each of the individual humans represented in a discrete-event model of Plasmodium falciparum transmission, and examine the effects of human population turnover, parasite antigenic diversity, recombination, and gametocyte production on the dynamics of malaria. Our results indicate that the local persistence of P. falciparum increases with turnover in the human population and antigenic diversity in the parasite, particularly in combination, and that antigenic diversity arising from meiotic recombination in the parasite has complex differential effects on the persistence of founder and progeny genotypes. We also find that reductions in the duration of individual human infectivity to mosquitoes, even if universal, produce population-level effects only if near-absolute, and that, in competition, the persistence and prevalence of parasite genotypes with gametocyte production concordant with data exceed those of genotypes with higher gametocyte production. This new, integrated approach provides a framework for investigating relationships between pathogen dynamics within an individual host and pathogen dynamics within interacting host and vector populations.

Dispersal-assembly theories of species coexistence posit that environmental factors play no role in explaining community diversity and structure. Dispersal-assembly theories shed light on some aspects of community structure such as species-area and species-abundance relationships. However, species' environmental associations also affect these measures of community structure. Measurements of species' niche breadth and overlap address this influence. Using a new continuous measure of niche and a dispersal-assembly null model that maintains species' niche breadth and aggregation, we tested two hypotheses assessing the effects of habitat heterogeneity on the ability of dispersal-assembly theories to explain community niche structure. We found that in both homogenous and heterogeneous environments dispersal-assembly theories cannot fully explain observed niche structure. The performance of the dispersal-assembly null models was particularly poor in heterogeneous environments. These results indicate that non-dispersal based mechanisms are in part responsible for observed community structure and measures of community structure which include species' environmental associations should be used to test theories of species diversity.

In a series of models of Plasmodium falciparum dynamics, spontaneous local extinctions of the parasite sometimes occurred under steady, perennial-transmission conditions. These extinctions occurred only with extremely low mosquito densities or when the parameter describing the duration of human infection-blocking immunity was at its maximum value, and, simultaneously, those describing vector survivorship and the duration of human infectivity were at their minimum values. The range and frequency of extinctions increased with seasonal transmission, and decreased with the emergence of recombinant genotypes. Here we extend the immunity parameter up to levels that would describe a successful vaccine, and examine the combined influences of seasonality, genotype cross-reactivity, meiotic recombination, and human population turnover on parasite persistence. As Ross did 90 years ago, we conclude that malaria control programs that encompass several methods and targets of intervention are the most likely to succeed. Success is more likely if programs are cognizant of local circumstances of transmission, and, within that context, aim to reduce vector survivorship and human infectivity as well as augment human immunity.

We incorporate a representation of Plasmodium falciparum recombination within a discrete-event model of malaria transmission. We simulate the introduction of a new parasite genotype into a human population in which another genotype has reached equilibrium prevalence and compare the emergence and persistence of the novel recombinant forms under differing cross-reactivity relationships between the genotypes. Cross-reactivity between the parental (initial and introduced) genotypes reduces the frequency of appearance of recombinants within three years of introduction from 100% to 14%, and delays their appearance by more than a year, on average. Cross-reactivity between parental and recombinant genotypes reduces the frequency of appearance to 36% and increases the probability of recombinant extinction following appearance from 0% to 83%. When a recombinant is cross-reactive with its parental types, its probability of extinction is influenced by cross-reactivity between the parental types in the opposite manner; that is, its probability of extinction after appearance decreases. Frequencies of P. falciparum outcrossing are mediated by frequencies of mixed-genotype infections in the host population, which are in turn mediated by the structure of cross-reactivity between parasite genotypes. The three leading hypotheses about how meiosis relates to oocyst production lead to quantitative, but no qualitative, differences in these results.

We incorporate stochastic, density-dependent seasonal recruitment in adult Anopheles mosquito populations in a discrete-event model of Plasmodium falciparum malaria transmission and find the probabilities of parasite extinction higher than with perennial transmission. Seasonal fluctuations in vector populations act to synchronize the dynamics of infection and immunity in host populations, leading to fluctuations in parasite prevalence greater than expected solely on the basis of high- and low-season vector densities. This synchronization also biases frequencies of infection with multiple parasite phenotypes or genotypes.

We present the first mathematical model of the within-host dynamics of a mixed-species malaria infection in a human: the blood-stage population dynamics of a dual infection with Plasmodium malariae and Plasmodium falciparum. Our results reproduce several important features of such infections in nature, including the asymmetry of species asexual-form densities, inter-specific suppression through interactions with the human immune system, and seasonal alternations in species prevalence. Most importantly, our results suggest that an existing P. malariae infection can reduce the peak parasitemia of a subsequent P. falciparum superinfection by as much as 50%. This result integrates numerous empirical observations and supports the hypothesis that clinical outcomes of P. falciparum infections may be influenced by the presence of a congener., (Copyright 1999 Academic Press.)

We analyzed point-prevalence data from 19 recent studies of human populations in which either Plasmodium ovale or Plasmodium vivax co-occur with Plasmodium falciparum and Plasmodium malariae. Although the only statistical interactions among, sympatric congeners are pairwise, the frequencies of mixed-species infections relative to standard hypotheses of species sampling independence show no strong relation to overall malaria prevalence. The striking difference between the P. falciparum-P. malariae-P. ovale and the P. falciparum-P. malariae-P. vivax data is that the first typically shows a statistical surplus of mixed-species infections and the second a deficit. This suggests that the number of Plasmodium species present in a human population may be less important in determining the frequencies of mixed-species infections than is the identity of those species.

We extend our basic discrete-event model of Plasmodium falciparum malaria to encompass circumstances in which multiple phenotypic variants of the parasite circulate within interacting human and mosquito populations, and we compare a version in which variants behave independently to one in which they interact through shared host immune responses. Relative to the standard hypothesis of statistical independence, frequencies of mixed-phenotype infection in humans were as expected in the independent-immunity version and much less than expected in the cross-immunity version; in both versions, however, such frequencies in mosquitoes were much greater than expected.

We use a simple model of the blood-stage infection dynamics of the malaria parasite Plasmodium falciparum to consider the adaptive significance of different rates of conversion from its pathogenic, asexual stages to its transmissible, sexual forms. We find that maximize transmissivity in single-strain infections are generally greater than the highest rates reported for in vitro cultures and are several times those for which the behavior of the model is consistent with clinical profiles of infection dynamics. When two strains that share a common immune agent coinfect a host through simultaneous inoculation or sequential superinfection, however, a strain with a lower, clinically-consistent value of the conversion rate inhibits the transmissivity of one with the higher value optimal for single-strain infection. Hence we suggest that "apparent" competition by way of a common immune response might be responsible for selection of the former.

We present a set of simple mathematical models to investigate interactions between malaria parasites and the human immune system and the differentiation of parasites from asexual, pathogenic into sexual, transmissible blood stages. Each model represents a different combination of empirically based hypotheses, and salient behaviors of each fit criteria developed from clinical data. In all models, however, higher gametocyte conversion rates result in lower peak asexual-form densities. Therefore, to the extent that asexual-form densities are associated with disease symptoms, interventions that stimulate gametocytogenesis should produce unexpected clinical benefits.

We develop discrete-event simulation models using a single "timeline" variable to represent the Plasmodium falciparum lifecycle in individual hosts and vectors within interacting host and vector populations. Where they are comparable our conclusions regarding the relative importance of vector mortality and the durations of host immunity and parasite development are congruent with those of classic differential-equation models of malaria, epidemiology. However, our results also imply that in regions with intense perennial transmission, the influence of mosquito mortality on malaria prevalence in humans may be rivaled by that of the duration of host infectivity.

We develop a system of ordinary differential equations to model the dynamics of the blood-stages of the malaria parasite, Plasmodium falciparum. Variants of the model allow the study of a set of hypotheses about the interaction of the parasite with the host immune system, in particular with regard to the stimulation of the immune response and the regulation of the rate of conversion from the pathogenic, asexual to the transmissible, sexual blood stage. The values of several parameters of our models can be estimated from previous empirical work. Although the dynamics of the variants differ somewhat, in each variant some set of values of the three unconstrained parameters, different from one variant to the next, produces a range of behaviours quantitatively consistent with those reported from clinical studies. Some parameter values produce infections which quickly terminate, while others approach a chronic equilibrium level or produce oscillations, with repeated severe peaks separated by periods of undetectable parasitemia. We examine these and several other distinctions that might be used to assess model variants and focus further empirical research., (Copyright 1997 Academic Press Limited.)

We analyzed point-prevalence data from 35 recent studies of human populations in which Plasmodium falciparum and one other Plasmodium species were the reported causes of malaria infections. For the P. falciparum-Plasmodium vivax pair, higher overall prevalence in a human population is associated with fewer mixed-species infections than expected on the basis of the product of individual species prevalences. This is not true for P. falciparum-Plasmodium malariae.

Mixed-pathogen infections of vectors rarely are considered in the epidemiological literature, although they may occur in nature. A review of published reports shows that many Anopheles species are capable of carrying sporozoites of > 1 Plasmodium species, of doing so simultaneously in field conditions, and of acquiring and transmitting these in experimental situations. Mixed-species infections in mosquito populations occur at frequencies greater than or equal to the product of the constituent species prevalences, whereas human populations have apparent mixed-species infections at frequencies less than or equal to their corresponding expected values. We present a model for the accumulation of parasite infections over the lifespan of a mosquito that explains this surplus of mixed-species infections. However, the expected frequencies of mixed infections on the basis of our model are greater than those found in nature, indicating that the sampling by mosquitoes of Plasmodium species from human malaria infections may not be random.

Systematic data are not available with regard to the anticipated appropriate responses of arterial PCO2 to primary alterations in plasma bicarbonate concentration. In the present study, we attempted to rigorously characterize the ventilatory response to chronic metabolic acid-base disturbances of graded severity in the dog. Animals with metabolic acidosis produced by prolonged HCl feeding and metabolic alkalosis of three different modes of generation, i.e., diuretics (ethacrynic acid or chlorothiazide), gastric drainage, and administration of deoxycorticosterone acetate (alone or in conjunction with oral sodium bicarbonate), were examined. The results indicate the existence of a significant and highly predictable ventilatory response to chronic metabolic acid-base disturbances. Moreover, the magnitude of the ventilatory response appears to be uniform throughout a wide spectrum of chronic metabolic acid-base disorders extending from severe metabolic acidosis to severe metabolic alkalosis; on average, arterial PCO2 is expected to change by 0.74 Torr for a 1-meq/l chronic change in plasma bicarbonate concentration of metabolic origin. Furthermore, the data suggest that the ventilatory response to chronic metabolic alkalosis is independent of the particular mode of generation.

Micropuncture studies were carried out in the rat to evaluate the in situ distensibility characteristics of the proximal and distal tubules under a variety of experimental conditions. In the first phase, we determined the response of tubular diameter (D) to changes in tubular pressure (P) induced by partially obstructing single tubules. The response observed under these conditions (i.e., when interstitial pressure is presumed to be constant) has been defined as the compliance of the tubule. Over the range of tubular pressures studied (10-35 mm Hg for the proximal tubule, 5-25 mm Hg for the distal tubule) the compliance characteristics of the proximal and distal tubule were found to be markedly different; the proximal tubular pressure-diameter relationship was linear, DeltaD/DeltaP = 0.45 mum/mm Hg, whereas the distal pressure-diameter relationship was curvilinear, DeltaD/DeltaP = c(-0.1xP+2.2). In the second phase we used the compliance data to construct a series of theoretical pressure-diameter curves that define the response of the tubule to increments in interstitial as well as intratubular pressure. These curves indicate that changes in distal diameter should provide a sensitive index of a rise in interstitial pressure under conditions in which the transtubular pressure gradient is increased by a small amount, but that proximal diameter should provide a more sensitive index of changes in interstitial pressure when the transtubular pressure gradient is increased by a large amount. In subsequent experiments in which furosemide was administered, we observed that the pressure-diameter relationships for both the proximal and distal tubule were indistinguishable from the compliance curves, a finding consistent with the interpretation that interstitial pressure was not appreciably changed from control. By contrast, when mannitol was administered, both proximal and distal tubular pressure-diameter relationships were significantly altered in a fashion consistent with a large increase in interstitial pressure. Neither with furosemide nor mannitol administration did it appear likely that significant changes in tubular compliance could account for the observed behavior of the tubule.Finally, we propose that a knowledge of tubular compliance will be useful in exploring the interrelationships between tubular and peritubular pressures, tubular anatomy, and transtubular ionic permeability. Recent studies linking changes in the geometry of lateral intercellular spaces of the tubule to changes in passive ion movement suggest that an investigation of such anatomical-functional correlates should be productive.

Many fluid-transporting epithelia possess dead-end, long, and narrow channels opening in the direction to which fluid is being transported (basal infoldings, lateral intercellular spaces, etc.). These channels have been thought to possess geometrical significance as standing-gradient flow systems, in which active solute transport into the channel makes the channel contents hypertonic and permits water-to-solute coupling. However, some secretory epithelia (choroid plexus, Malpighian tubule, rectal gland, etc.) have "backwards" channels opening in the direction from which fluid is being transported. It is shown that these backwards channels can function as standing-gradient flow systems in which solute transport out of the channel makes the channel contents hypotonic and results in coupled water flow into the channel mouth. The dependence of the transported osmolarity (isotonic or hypertonic) on channel radius, length, and other parameters is calculated for backwards channels for values of these parameters in the physiological range. In addition to backwards channels' being hypotonic rather than hypertonic, they are predicted to differ from "forwards" channels in that some restrictions are imposed by the problem of solute exhaustion, and in the presence of a sweeping-in effect on other solutes which limits the solutes that may be transported.

At the ultrastructural level, epithelia performing solute-linked water transport possess long, narrow channels open at one end and closed at the other, which may constitute the fluid transport route (e.g., lateral intercellular spaces, basal infoldings, intracellular canaliculi, and brush-border microvilli). Active solute transport into such folded structures would establish standing osmotic gradients, causing a progressive approach to osmotic equilibrium along the channel's length. The behavior of a simple standing-gradient flow system has therefore been analyzed mathematically because of its potential physiological significance. The osmolarity of the fluid emerging from the channel's open end depends upon five parameters: channel length, radius, and water permeability, and solute transport rate and diffusion coefficient. For ranges of values of these parameters encountered experimentally in epithelia, the emergent osmolarity is found by calculation to range from isotonic to a few times isotonic; i.e., the range encountered in epithelial absorbates and secretions. The transported fluid becomes more isotonic as channel radius or solute diffusion coefficient is decreased, or as channel length or water permeability is increased. Given appropriate parameters, a standing-gradient system can yield hypertonic fluids whose osmolarities are virtually independent of transport rate over a wide range, as in distal tubule and avian salt gland. The results suggest that water-to-solute coupling in epithelia is due to the ultrastructural geometry of the transport route.