Models of the within-host dynamics of persistent mycobacterial infections

The role of a programmatic immune response on the evolution of pathogen traits

In modelling pathogen evolution during epidemics, it is important to understand the interactions between within-host infection dynamics and between-host pathogen transmission. Multiscale models often assume an immune response that is highly responsive to pathogen dynamics. Empirical evidence, however, suggests that the immune response in acute infections is triggered and programmatic. This leads to somewhat more predictable infection trajectories where transition times and, consequently, the infectious window are non-exponentially distributed. Here, we develop a within-host model where the immune response is triggered by pathogen growth but otherwise develops independently, and use this to obtain analytic expressions for the infectious period and peak pathogen load. This allows us to model the basic reproductive number in terms of explicit functional relationships among within-host traits including the growth rate of the pathogen. We find that the dependence of pathogen load and the infectious window on within-host parameters constrains the evolution of the pathogen growth rate. At low growth rate, selection favours a higher pathogen load and therefore increasing pathogen growth rate. At high growth rates, selection for a longer infectious window trades off against selection against the effects of virulence. At intermediate growth rates the basic reproductive number is relatively insensitive to changes in the growth rate. The resulting "flat" region of the pathogen fitness landscape is due to the stability of the programmatic immune response in clearing the infection.

Combination anti-coronavirus therapies based on nonlinear mathematical models

Using nonlinear mathematical models and experimental data from laboratory and clinical studies, we have designed new combination therapies against COVID-19.

An investigation of tuberculosis progression revealing the role of macrophages apoptosis via sensitivity and bifurcation analysis

Mycobacterium tuberculosis infection features various disease outcomes: clearance, latency, active disease, and latent tuberculosis infection (LTBI) reactivation. Identifying the decisive factors for disease outcomes and progression is crucial to elucidate the macrophages-tuberculosis interaction and provide insights into therapeutic strategies. To achieve this goal, we first model the disease progression as a dynamical shift among different disease outcomes, which are characterized by various steady states of bacterial concentration. The causal mechanisms of steady-state transitions can be the occurrence of transcritical and saddle-node bifurcations, which are induced by slowly changing parameters. Transcritical bifurcation, occurring when the basic reproduction number equals to one, determines whether the infection clears or spreads. Saddle-node bifurcation is the key mechanism to create and destroy steady states. Based on these two steady-state transition mechanisms, we carry out two sample-based sensitivity analyses on transcritical bifurcation conditions and saddle-node bifurcation conditions. The sensitivity analysis results suggest that the macrophage apoptosis rate is the most significant factor affecting the transition in disease outcomes. This result agrees with the discovery that the programmed cell death (apoptosis) plays a unique role in the complex microorganism-host interplay. Sensitivity analysis narrows down the parameters of interest, but cannot answer how these parameters influence the model outcomes. To do this, we employ bifurcation analysis and numerical simulation to unfold various disease outcomes induced by the variation of macrophage apoptosis rate. Our findings support the hypothesis that the regulation mechanism of macrophage apoptosis affects the host immunity against tuberculosis infection and tuberculosis virulence. Moreover, our mathematical results suggest that new treatments and/or vaccines that regulate macrophage apoptosis in combination with weakening bacillary viability and/or promoting adaptive immunity could have therapeutic value.

Simulation modelling for immunologists

The immune system is inordinately complex with many interacting components determining overall outcomes. Mathematical and computational modelling provides a useful way in which the various contributions of different immunological components can be probed in an integrated manner. Here, we provide an introductory overview and review of mechanistic simulation models. We start out by briefly defining these types of models and contrasting them to other model types that are relevant to the field of immunology. We follow with a few specific examples and then review the different ways one can use such models to answer immunological questions. While our examples focus on immune responses to infection, the overall ideas and descriptions of model uses can be applied to any area of immunology.

Information limitation and the dynamics of coupled ecological systems

The dynamics of large ecological systems result from vast numbers of interactions between individual organisms. Here, we develop mathematical theory to show that the rate of such interactions is inherently limited by the ability of organisms to gain information about one another. This phenomenon, which we call 'information limitation', is likely to be widespread in real ecological systems and can dictate both the rates of ecological interactions and long-run dynamics of interacting populations. We show how information limitation leads to sigmoid interaction rate functions that can stabilize antagonistic interactions and destabilize mutualistic ones; as a species or type becomes rare, information on its whereabouts also becomes rare, weakening coupling with consumers, pathogens and mutualists. This can facilitate persistence of consumer-resource systems, alter the course of pathogen infections within a host and enhance the rates of oceanic productivity and carbon export. Our findings may shed light on phenomena in many living systems where information drives interactions.

Development of a Computational Model of Abscess Formation

In some bacterial infections, the immune system cannot eliminate the invading pathogen. In these cases, the invading pathogen is successful in establishing a favorable environment to survive and persist in the host organism. For example, S. aureus bacteria survive in organ tissues employing a set of mechanisms that work in a coordinated and highly regulated way allowing: (1) efficient impairment of the immune response; and (2) protection from the immune cells and molecules. S. aureus secretes several proteins including coagulases and toxins that drive abscess formation and persistence. Unless staphylococcal abscesses are surgically drained and treated with antibiotics, disseminated infection and septicemia produce a lethal outcome. Within this context, this paper develops a simple mathematical model of abscess formation incorporating characteristics that we judge important for an abscess to be formed. Our aim is to build a mathematical model that reproduces some characteristics and behaviors that are observed in the process of abscess formation.

Mathematical model for the growth of Mycobacterium tuberculosis in the granuloma

In this work we formulate a model for the population dynamics of Mycobacterium tuberculosis (Mtb), the causative agent of tuberculosis (TB). Our main interest is to assess the impact of the competition among bacteria on the infection prevalence. For this end, we assume that Mtb population has two types of growth. The first one is due to bacteria produced in the interior of each infected macrophage, and it is assumed that is proportional to the number of infected macrophages. The second one is of logistic type due to the competition among free bacteria released by the same infected macrophages. The qualitative analysis and numerical results suggests the existence of forward, backward and S-shaped bifurcations when the associated reproduction number R0 of the Mtb is less unity. In addition, qualitative analysis of the model shows that there may be up to three bacteria-present equilibria, two locally asymptotically stable, and one unstable.

Model-based inference from multiple dose, time course data reveals Wolbachia effects on infection profiles of type 1 dengue virus in Aedes aegypti

Infection is a complex and dynamic process involving a population of invading microbes, the host and its responses, aimed at controlling the situation. Depending on the purpose and level of organization, infection at the organism level can be described by a process as simple as a coin toss, or as complex as a multi-factorial dynamic model; the former, for instance, may be adequate as a component of a population model, while the latter is necessary for a thorough description of the process beginning with a challenge with an infectious inoculum up to establishment or elimination of the pathogen. Experimental readouts in the laboratory are often static, snapshots of the process, assayed under some convenient experimental condition, and therefore cannot comprehensively describe the system. Different from the discrete treatment of infection in population models, or the descriptive summarized accounts of typical lab experiments, in this manuscript, infection is treated as a dynamic process dependent on the initial conditions of the infectious challenge, viral growth, and the host response along time. Here, experimental data is generated for multiple doses of type 1 dengue virus, and pathogen levels are recorded at different points in time for two populations of mosquitoes: either carrying endosymbiont bacteria Wolbachia or not. A dynamic microbe/host-response mathematical model is used to describe pathogen growth in the face of a host response like the immune system, and to infer model parameters for the two populations of insects, revealing a slight—but potentially important—protection conferred by the symbiont.

Infection is usually assayed as a static observation of a pathogen within a host; it is, nevertheless, a dynamic process that cannot be described from a single time point and arbitrary conditions. Results based on the usual methods are a snapshot of a convenient laboratory condition; a more comprehensive data set is required to describe the entire process of infection from inoculation of the host with a microorganism to establishment of a systemic infection, or elimination of the threat by the host. We design an experiment that takes into account increasing pathogen challenges to a mosquito host and viral levels along time; we use a dynamic mathematical model to analyze the resulting data set. The entire framework is used to compare susceptibility to dengue virus of Aedes aegypti mosquitoes either carrying the Wolbachia symbiont or not. Instead of a simple pairwise comparison, we are able to compare infection profiles and parameters associated to host immune processes in this insect-symbiont-virus system.

A review of computational and mathematical modeling contributions to our understanding of Mycobacterium tuberculosis within-host infection and treatment

Tuberculosis (TB) is an ancient and deadly disease characterized by complex host-pathogen dynamics playing out over multiple time and length scales and physiological compartments. Computational modeling can be used to integrate various types of experimental data and suggest new hypotheses, mechanisms, and therapeutic approaches to TB. Here, we offer a first-time comprehensive review of work on within-host TB models that describe the immune response of the host to infection, including the formation of lung granulomas. The models include systems of ordinary and partial differential equations and agent-based models as well as hybrid and multi-scale models that are combinations of these. Many aspects of M. tuberculosis infection, including host dynamics in the lung (typical site of infection for TB), granuloma formation, roles of cytokine and chemokine dynamics, and bacterial nutrient availability have been explored. Finally, we survey applications of these within-host models to TB therapy and prevention and suggest future directions to impact this global disease.

Mathematical modelling of bacterial resistance to multiple antibiotics and immune system response

Resistance of developed bacteria to antibiotic treatment is a very important issue, because introduction of any new antibiotic is after a little while followed by the formation of resistant bacterial isolates in the clinic. The significant increase in clinical resistance to antibiotics is a troubling situation especially in nosocomial infections, where already defenseless patients can be unsuccessful to respond to treatment, causing even greater health issue. Nosocomial infections can be identified as those happening within 2 days of hospital acceptance, 3 days of discharge or 1 month of an operation. They influence 1 out of 10 patients admitted to hospital. Annually, this outcomes in 5000 deaths only in UK with a cost to the National Health Service of a billion pounds. Despite these problems, antibiotic therapy is still the most common method used to treat bacterial infections. On the other hand, it is often mentioned that immune system plays a major role in the progress of infections. In this context, we proposed a mathematical model defining population dynamics of both the specific immune cells produced according to the properties of bacteria by host and the bacteria exposed to multiple antibiotics synchronically, presuming that resistance is gained through mutations due to exposure to antibiotic. Qualitative analysis found out infection-free equilibrium point and other equilibrium points where resistant bacteria and immune system cells exist, only resistant bacteria exists and sensitive bacteria, resistant bacteria and immune system cells exist. As a result of this analysis, our model highlights the fact that when an individual’s immune system weakens, he/she suffers more from the bacterial infections which are believed to have been confined or terminated. Also, these results was supported by numerical simulations.

Understanding PGE2, LXA4 and LTB4 balance during Mycobacterium tuberculosis infection through mathematical model

Infection of humans with Mycobacterium tuberculosis (Mtb) results in diverse outcomes that range from acute disease to establishment of persistence and to even clearance of the pathogen. These different outcomes represent the combined result of host heterogeneity on the one hand, and virulence properties of the infecting strain of pathogen on the other. From the standpoint of the host, the balance between PGE2, LXA4 and LTB4 represents at least one of the factors that dictates the eventual pathophysiology. We therefore built an ODE model to describe the host-pathogen interaction and studied the local stability properties of the system, to obtain the parametric conditions that lead to different disease outcomes. We then modulated levels of the pro- and anti-inflammatory lipid mediators to better understand the convergence between host phenotype and factors that relate to virulence properties of the pathogen. Global sensitivity analysis, using the variance-based method of extended Fourier Amplitude Sensitivity Test (eFAST), revealed that disease severity was indeed defined by combined effects of phenotypic variability at the level of both host and pathogen. Interestingly here, [PGE2] was found to act as a switch between bacterial clearance and acute disease. Our mathematical model suggests that development of more effective treatments for tuberculosis will be contingent upon a better understanding of how the intrinsic variability at the level of both host and pathogen contribute to influence the nature of interactions between these two entities.

Mathematical modeling on bacterial resistance to multiple antibiotics caused by spontaneous mutations

We formulate a mathematical model that describes the population dynamics of bacteria exposed to multiple antibiotics simultaneously, assuming that acquisition of resistance is through mutations due to antibiotic exposure. Qualitative analysis reveals the existence of a free-bacteria equilibrium, resistant-bacteria equilibrium and an endemic equilibrium where both bacteria coexist.

Latent Tuberculosis: Models, Computational Efforts and the Pathogen's Regulatory Mechanisms during Dormancy

Latent tuberculosis is a clinical syndrome that occurs after an individual has been exposed to the Mycobacterium tuberculosis (Mtb) Bacillus, the infection has been established and an immune response has been generated to control the pathogen and force it into a quiescent state. Mtb can exit this quiescent state where it is unresponsive to treatment and elusive to the immune response, and enter a rapid replicating state, hence causing infection reactivation. It remains a gray area to understand how the pathogen causes a persistent infection and it is unclear whether the organism will be in a slow replicating state or a dormant non-replicating state. The ability of the pathogen to adapt to changing host immune response mechanisms, in which it is exposed to hypoxia, low pH, nitric oxide (NO), nutrient starvation, and several other anti-microbial effectors, is associated with a high metabolic plasticity that enables it to metabolize under these different conditions. Adaptive gene regulatory mechanisms are thought to coordinate how the pathogen changes their metabolic pathways through mechanisms that sense changes in oxygen tension and other stress factors, hence stimulating the pathogen to make necessary adjustments to ensure survival. Here, we review studies that give insights into latency/dormancy regulatory mechanisms that enable infection persistence and pathogen adaptation to different stress conditions. We highlight what mathematical and computational models can do and what they should do to enhance our current understanding of TB latency.

Novel methods for quantifying individual host response to infectious pathogens for genetic analyses

We propose two novel approaches for describing and quantifying the response of individual hosts to pathogen challenge in terms of infection severity and impact on host performance. The first approach is a direct extension of the methodology for estimating group tolerance (the change in performance with respect to changes in pathogen burden in a host population) to the level of individuals. The second approach aims to capture the dynamic aspects of individual resistance and tolerance over the entire time course of infections. In contrast to the first approach, which provides a means to disentangle host resistance from tolerance, the second approach focuses on the combined effects of both characteristics. Both approaches provide new individual phenotypes for subsequent genetic analyses and come with specific data requirements. In particular, both approaches rely on the availability of repeated performance and pathogen burden measurements of individuals over the time course of one or several episodes of infection. Consideration of individual tolerance also highlights some of the assumptions hidden within the concept of group tolerance, indicating where care needs to be taken in trait definition and measurement.

Mathematical modeling of pulmonary tuberculosis therapy: Insights from a prototype model with rifampin

There is a critical need for improved and shorter tuberculosis (TB) treatment. Current in vitro models of TB, while valuable, are poor predictors of the antibacterial effect of drugs in vivo. Mathematical models may be useful to overcome the limitations of traditional approaches in TB research. The objective of this study was to set up a prototype mathematical model of TB treatment by rifampin, based on pharmacokinetic, pharmacodynamic and disease submodels. The full mathematical model can simulate the time-course of tuberculous disease from the first day of infection to the last day of therapy. Therapeutic simulations were performed with the full model to study the antibacterial effect of various dosage regimens of rifampin in lungs. The model reproduced some qualitative and quantitative properties of the bactericidal activity of rifampin observed in clinical data. The kill curves simulated with the model showed a typical biphasic decline in the number of extracellular bacteria consistent with observations in TB patients. Simulations performed with more simple pharmacokinetic/pharmacodynamic models indicated a possible role of a protected intracellular bacterial compartment in such a biphasic decline. This modeling effort strongly suggests that current dosage regimens of RIF may be further optimized. In addition, it suggests a new hypothesis for bacterial persistence during TB treatment.

Dynamic models of immune responses: what is the ideal level of detail?

Background

One of the goals of computational immunology is to facilitate the study of infectious diseases. Dynamic modeling is a powerful tool to integrate empirical data from independent sources, make novel predictions, and to foresee the gaps in the current knowledge. Dynamic models constructed to study the interactions between pathogens and hosts' immune responses have revealed key regulatory processes in the infection.

Optimum complexity and dynamic modeling

We discuss the usability of various deterministic dynamic modeling approaches to study the progression of infectious diseases. The complexity of these models is dependent on the number of components and the temporal resolution in the model. We comment on the specific use of simple and complex models in the study of the progression of infectious diseases.

Conclusions

Models of sub-systems or simplified immune response can be used to hypothesize phenomena of host-pathogen interactions and to estimate rates and parameters. Nevertheless, to study the pathogenesis of an infection we need to develop models describing the dynamics of the immune components involved in the progression of the disease. Incorporation of the large number and variety of immune processes involved in pathogenesis requires tradeoffs in modeling.

Applying predator-prey theory to modelling immune-mediated, within-host interspecific parasite interactions

Predator-prey models are often applied to the interactions between host immunity and parasite growth. A key component of these models is the immune system's functional response, the relationship between immune activity and parasite load. Typically, models assume a simple, linear functional response. However, based on the mechanistic interactions between parasites and immunity we argue that alternative forms are more likely, resulting in very different predictions, ranging from parasite exclusion to chronic infection. By extending this framework to consider multiple infections we show that combinations of parasites eliciting different functional responses greatly affect community stability. Indeed, some parasites may stabilize other species that would be unstable if infecting alone. Therefore hosts' immune systems may have adapted to tolerate certain parasites, rather than clear them and risk erratic parasite dynamics. We urge for more detailed empirical information relating immune activity to parasite load to enable better predictions of the dynamic consequences of immune-mediated interspecific interactions within parasite communities.

Unravelling the relationship between animal growth and immune response during micro-parasitic infections

Background

Both host genetic potentials for growth and disease resistance, as well as nutrition are known to affect responses of individuals challenged with micro-parasites, but their interactive effects are difficult to predict from experimental studies alone.

Methodology/Principal Findings

Here, a mathematical model is proposed to explore the hypothesis that a host's response to pathogen challenge largely depends on the interaction between a host's genetic capacities for growth or disease resistance and the nutritional environment. As might be expected, the model predicts that if nutritional availability is high, hosts with higher growth capacities will also grow faster under micro-parasitic challenge, and more resistant animals will exhibit a more effective immune response. Growth capacity has little effect on immune response and resistance capacity has little effect on achieved growth. However, the influence of host genetics on phenotypic performance changes drastically if nutrient availability is scarce. In this case achieved growth and immune response depend simultaneously on both capacities for growth and disease resistance. A higher growth capacity (achieved e.g. through genetic selection) would be detrimental for the animal's ability to cope with pathogens and greater resistance may reduce growth in the short-term.

Significance

Our model can thus explain contradicting outcomes of genetic selection observed in experimental studies and provides the necessary biological background for understanding the influence of selection and/or changes in the nutritional environment on phenotypic growth and immune response.

Acute or chronic? Within-host models with immune dynamics, infection outcome, and parasite evolution

There is ample theoretical and experimental evidence that virulence evolution depends on the immune response of the host. In this article, we review a number of recent studies that attempt to explicitly incorporate the dynamics of the immune system (instead of merely representing it by a single black box parameter) in models for the evolution of parasite virulence. A striking observation is that the type of infection (acute or chronic) is invariably considered to be a constraint that model assumptions have to satisfy rather than as a potential outcome of the interaction of the parasite with its host's immune system. We argue that avoiding making assumptions about the type of infection will lead to a better understanding of infectious diseases, even though a number of fundamental and technical problems remain. Dynamical modeling of the immune system opens a wide range of perspectives: for understanding how the immune system eradicates a parasite (which it does for most pathogens but not for all, HIV being a notorious example of a virus that is not completely eliminated), for studying multiple infections through concomitant immunity, for understanding the emergence and evolution of the immune system in animals, and for evolutionary epidemiology in general (e.g., predicting evolutionary consequences of new therapies and public health policies). We conclude by discussing new approaches based on embedded (or nested) models and identify future perspectives for the modeling of infectious diseases.

Cellular responses to MPT-51, GlcB and ESAT-6 among MDR-TB and active tuberculosis patients in Brazil

Multi-drug resistant pulmonary tuberculosis (MDR-TB) may result from either insufficiency of the host cellular immune response or mycobacterial mechanisms of resistance. Mycobacterium tuberculosis-specific CD8+ and CD4+ T lymphocytes from MDR-TB patients are poorly studied. The aim of this study was to evaluate CD4+IFN-gamma+, CD4+IL-10+, CD8(+)IFN-gamma+ and CD8+IL-10+ cell populations by flow cytometry in non-resistant TB and multi-drug resistant tuberculosis (MDR-TB) patients from mid-central Brazil after stimulation with MPT-51, GlcB and ESAT-6 recombinant antigens from M. tuberculosis in comparison to tuberculin skin test negative (TST) healthy individuals. Non-resistant TB patients present specific cellular responses (CD4 and CD8, both IFN-gamma and IL-10) to GlcB, MPT-51 and ESAT-6; while MDR-TB patients present only CD8+IFN-gamma+ responses to ESAT-6 and CD8+IL-10+ responses to GlcB and ESAT-6. The results show that MDR-TB patients present impaired specific CD4 IFN-gamma and IL-10 responses and increased/normal specific CD8 IFN-gamma and IL-10 responses. This suggests an important role for CD8 function in these patients.

Modeling intercellular interactions in early Mycobacterium infection

Infection with Mycobacterium tuberculosis (Mtb) is characterized by localized, roughly spherical lesions within which the pathogen interacts with host cells. Containment of the infection or progression of disease depends on the behavior of individual cells, which, in turn, depends on the local molecular environment and on contact with neighboring cells. Modeling can help us understand the nonlinear interactions that drive the overall dynamics in this system. Early events in infection are particularly important, as are spatial effects and inherently stochastic processes. We describe a model of early Mycobacterium infection using the CyCells simulator, which was designed to capture these effects. We relate CyCells simulations of the model to several experimental observations of individual components of the response to Mtb.

Mycobacterium tuberculosis as viewed through a computer

Mathematical models are emerging as important tools in the study of microbiology. As an illustrative example, we present results from several models each generated to study the interaction of Mycobacterium tuberculosis and the immune system. Different mathematical models were formulated on the basis of assumptions regarding system-component interactions, enabling us to explore specific aspects at diverse biological scales (e.g. intracellular, cell-cell interactions, and cell population dynamics). In addition, we were able to examine both temporal and spatial aspects. At each scale, there were consistent themes that emerged as determinative in infection outcome. Factors we identified include both host and microbial characteristics. The use of the models lies in generating hypotheses that can then be tested experimentally. Here, we outline the primary host and bacterial factors that we have identified as key mechanisms that contribute to the success of M. tuberculosis as a human pathogen. Our goal is to stimulate experimentation and foster collaborations between theoretical and experimental scientists.

The dynamics of acute inflammation

When the body is infected, it mounts an acute inflammatory response to rid itself of the pathogens and restore health. Uncontrolled acute inflammation due to infection is defined clinically as sepsis and can culminate in organ failure and death. We consider a three-dimensional ordinary differential equation model of inflammation consisting of a pathogen, and two inflammatory mediators. The model reproduces the healthy outcome and diverse negative outcomes, depending on initial conditions and parameters. We analyze the various bifurcations between the different outcomes when key parameters are changed and suggest various therapeutic strategies. We suggest that the clinical condition of sepsis can arise from several distinct physiological states, each of which requires a different treatment approach.

Evidence for positive selection on Mycobacterium tuberculosis within patients

BACKGROUND

While the pathogenesis and epidemiology of tuberculosis are well studied, relatively little is known about the evolution of the infectious agent Mycobacterium tuberculosis, especially at the within-host level. The insertion sequence IS6110 is a genetic marker that is widely used to track the transmission of tuberculosis between individuals. This and other markers may also facilitate our understanding of the disease within patients.

RESULTS

This article presents three lines of evidence supporting the action of positive selection on M. tuberculosis within patients. The arguments are based on a comparison between empirical findings from molecular epidemiology, and population genetic models of evolution. Under the hypothesis of neutrality of genotypes, 1) the mutation rate of the marker IS6110 is unusually high, 2) the time it takes for substitutions to occur within patients is too short, and 3) the amount of polymorphism within patients is too low.

CONCLUSIONS

Empirical observations are explained by the action of positive selection during infection, or alternatively by very low effective population sizes. I discuss the possible roles of antibiotic treatment, the host immune system and extrapulmonary dissemination in creating opportunities for positive selection.

Dynamic optimization of host defense, immune memory, and post-infection pathogen levels in mammals

When attacked by pathogens, higher vertebrates produce specific immune cells that fight against them. We here studied the host's optimal schedule of specific immune cell production. The damage caused by the pathogen increases with the pathogen amount in the host integrated over time. On the other hand, there is also a cost incurred by the production of specific immune cells, not only in terms of the energy needed to produce and maintain the cells, but also with respect to damages sustained by the host's body as a result of immune activity. The optimal strategy of the host is the one that minimizes the total cost, defined as a weighted sum of the damage caused by pathogens and the costs caused by the specific immune cells. The problem is solved by using Pontryagin's maximum principle and dynamic programming. The optimal defense schedule is typically as follows: In the initial phase after infection, immune cells are produced at the fastest possible rate. The amount of pathogen increases temporarily but is eventually suppressed. When the pathogen amount is suppressed to a sufficiently low level, the immune cell number decreases and converges to a low steady level, which is maintained by alternately switching between fastest production and no production. We examine the effect of time delay required to have fully active immune cells by comparing cases with different number of rate limiting steps before producing immune cells. We examine the effect of the duration of time (time delay) required before full-scale production of active immune cells by comparing cases with different numbers of rate-limiting steps before immune-cell production. We also discuss the role of immune memory based on the results of the optimal immune reaction.

Within-host parasite dynamics, emerging trade-off, and evolution of virulence with immune system

Virulence is an evolutionary paradox because parasites never benefit from their host's death. The adaptive explanation of virulence is classically based upon the existence of physiological constraints that create a trade-off between parasites' epidemiological traits (virulence, transmissibility, and clearance). Here we develop an epidemiological model where infections are dynamic processes and we demonstrate how these dynamics generate a trade-off between emerging epidemiological parameters. We then study how host's immune strength modifies this trade-off and hence influences virulence evolution. We found that in acute infections, where parasites are engaged in a race with immune cells, immunity restrains more the duration of the infection than its intensity. As a consequence parasites evolve to provoke more virulent but shorter infections in strongly immunized hosts.

Models of CD8+ responses: 1. What is the antigen-independent proliferation program

Recent experimental results show that even brief stimulation with antigen can cause antigen-specific CD8 T-cells to undergo sustained proliferation followed by differentiation into memory cells. These results show that the dynamics of these immune responses are not governed by constant monitoring of antigen levels, but rather that following stimulation immune cells commit to a "program". At present relatively little is known about the program which governs CD8 cell proliferation and differentiation. For example, we do not know whether the program is completely specified by the initial encounter of a T cell with antigen, or whether it subsequently can be modified by the amount of antigen present. Nor do we know whether the entire program for T cell proliferation and differentiation resides within the T cell itself, or whether some component(s) of the program are determined by cells or molecules external to the CD8 cell. In this paper we construct simple mathematical models which incorporate antigen-independent proliferation and differentiation of CD8 cells during acute infections. We use these models to determine what characteristics the program must have in order to be consistent with the existing data on the dynamics of CD8 responses, and in particular to answer the questions posed above. Our results suggest that the program is not completely defined by the initial encounter of T cell with antigen but may be augmented by exposure to antigen in a brief window shortly after infection; furthermore, parts of the program may reside external to the T-cells. Finally we examine some of the consequences of the "program" for pathogen-host coevolution.

The immunoepidemiology of nematode parasites of farmed animals: a mathematical approach

The population dynamics of farmed animals are controlled by humans, and often involve high host densities, which encourage higher parasite burdens than would be usual in wild animals. As a result, the immunity to reinfection acquired by the host is an important determinant of parasite population dynamics. For example, lambs are highly susceptible to gastrointestinal nematodes as they begin to graze, but develop an immunity that accounts for the observed within-year variation in parasite load and pasture contamination. In the longer term, control measures are compromised by the development of parasite strains resistant to chemotherapy, focusing attention on the development of 'natural' measures, including the selection for resistant hosts and the development of antiparasite vaccines. Mick Roberts here considers the immunoepidemiology of parasites of farmed animals on three levels: the interaction between the parasite and the host's immune system determining the individual's level of protection; the development of acquired immunity determining the within-year parasite population dynamics; and the long-term effects of control measures on the between-year parasite population dynamics.

Dynamics of co-infection with M. Tuberculosis and HIV-1

Since 1985, there has been a renewed epidemic of tuberculosis (TB) that was previously thought to be in check. There is evidence to believe the main factor for this resurgence has been the human immunodeficiency virus (HIV). Co-infection with HIV and M. Tuberculosis has profound implications for the course of both diseases. This study represents a first attempt to understand how the introduction of an opportunistic infection, namely Mycobacterium tuberculosis, the bacteria that causes TB, affects the dynamic interaction of HIV-1 and the immune system. We create a mathematical model using ordinary differential equations to describe the interaction of HIV and TB with the immune system. It is known that infection with TB can decrease the CD4(+) T cell counts-a key marker of AIDS progression; thus, it shortens survival in HIV infected individuals. Another main marker for HIV progression is the viral load. If this load is increased due to the presence of opportunistic infections, the disease progression is much more rapid. We also explore the effects of drug treatment on the TB infection in the doubly-infected patient.

A bacterial cytokine

Viable cells of Micrococcus luteus secrete a factor, which promotes the resuscitation and growth of dormant, nongrowing cells of the same organism. The resuscitation-promoting factor (Rpf) is a protein, which has been purified to homogeneity. In picomolar concentrations, it increases the viable cell count of dormant M. luteus cultures at least 100-fold and can also stimulate the growth of viable cells. Rpf also stimulates the growth of several other high G+C Gram-positive organisms, including Mycobacterium avium, Mycobacterium bovis (BCG), Mycobacterium kansasii, Mycobacterium smegmatis, and Mycobacterium tuberculosis. Similar genes are widely distributed among high G+C Gram-positive bacteria; genome sequencing has uncovered examples in Mycobacterium leprae and Mb. tuberculosis and others have been detected by hybridization in Mb. smegmatis, Corynebacterium glutamicum, and Streptomyces spp. The mycobacterial gene products may provide different targets for the detection and control of these important pathogens. This report is thus a description of a proteinaceous autocrine or paracrine bacterial growth factor or cytokine.