Within-host Dynamics Research Articles

Antibiotic Treatment, Duration of Infectiousness, and Disease Transmission

By curing infectious individuals, antibiotic therapy must sometimes limit the spread of contagious disease among hosts. But suppose that a diseased host stops transmitting infection due either to antibiotic cure or to non-therapeutic removal (e.g., isolation or mortality). An antibiotic`s suppression of within-host pathogen growth increases the likelihood of curing a single infection and may also reduce the probability of non-therapeutic removal. If antibiotic treatment relaxes the total rate of infection removal sufficiently to extend the average duration of infectiousness, between-host transmission can increase. That is, under some conditions, curing individuals with antibiotics can impact public health negatively (more new infections). To explore this counter-intuitive, but plausible effect, this paper assumes that a deterministic within-host dynamics drives the infectious host's time-dependent probability of pathogen transmission, as well as the probabilistic duration of the infectious period. At the within-host scale, the model varies (1) inoculum size, (2) bacterial self-regulation, (3) the time between infection and initiation of therapy, and (4) antibiotic efficacy. At the between-host scale the model varies (5) the size of groups randomly encountered in the infectious host’s environment. Results identify conditions where an antibiotic can increase duration of a host`s infectiousness, and consequently increase the expected number of new infections. At lower antibiotic efficacy, therapy might convert a rare, serious bacterial disease into a common, but treatable infection.

Disentangling the dynamical underpinnings of differences in SARS-CoV-2 pathology using within-host ecological models.

Health outcomes following infection with Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) are remarkably variable. The way the virus spreads inside hosts, and how this spread interacts with host immunity and physiology, is likely to determine variation in health outcomes. Decades of data and dynamical analyses of how other viruses spread and interact with host cells could shed light on SARS-CoV-2 within-host trajectories. We review how common axes of variation in within-host dynamics and emergent pathology (such as age and sex) might be combined with ecological principles to understand the case of SARS-CoV-2. We highlight pitfalls in application of existing theoretical frameworks relevant to the complexity of the within-host context and frame the discussion in terms of growing knowledge of the biology of SARS-CoV-2. Viewing health outcomes for SARS-CoV-2 through the lens of ecological models underscores the value of repeated measures on individuals, especially since many lines of evidence suggest important contingence on trajectory.

STABILITY OF A DELAYED ADAPTIVE IMMUNITY HIV INFECTION MODEL WITH SILENT INFECTED CELLS AND CELLULAR INFECTION

<abstract> In this paper we formulate a mathematical model to investigate the within-host HIV dynamics under the effect of both antibody and Cytotoxic T lymphocytes (CTL) immune responses. The model consists of five components: healthy CD$ 4^{+} $T cells, silent infected cells, active infected cells, free HIV particles, CTLs and antibodies. The healthy CD$ 4^{+} $T cells can be infected when they are contacted by (ⅰ) free HIV particles, (ⅱ) active infected cells, and (ⅲ) silent infected cells. The model is an improvement of some existing HIV infection models with both virus-to-cell (VTC) and cell-to-cell (CTC) transmissions by incorporating the incidence between the silent infected cells and healthy CD$ 4^{+} $T cells. The well-posedness of the model is established by showing that the solutions of the model are nonnegative and bounded. We have shown that the model has five equilibria and their existence is governed by five threshold parameters. We prove the global asymptotic stability of all equilibria by utilizing Lyapunov function and LaSalle's invariance principle. We have presented numerical simulations to illustrate the theoretical results. We have studied the effects of CTC transmission and time delays on the dynamical behavior of the system. We have shown that inclusion of time delay can significantly increase the concentration of the uninfected CD4$ ^{+} $ T cells and reduce the concentrations of the infected cells and free HIV particles. While the inclusion of CTC transmission decreases the concentration of the uninfected CD4$ ^{+} $ T cells and increases the concentrations of the infected cells and free HIV particles. </abstract>

MODELING THE WITHIN-HOST DYNAMICS OF CHOLERA: BACTERIAL-VIRAL-IMMUNE INTERACTION

<abstract> We present a mathematical model to investigate the within-host dynamics of cholera.We formulate a system of nonlinear differential equations to describe the evolution and interplay of the pathogenic bacteria at different stages, the viruses, and the immune response inside the human body.Our analysis shows that the basic reproduction number of this model is determined collectively by the bacterial, viral and immune reproduction numbers, and that the bacterial-viral-immune interaction shapes the complex dynamics of cholera infection within a human host. </abstract>

Analysis of a within-host HIV/HTLV-I co-infection model with immunity

Human immunodeficiency virus (HIV) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses that attack the immune cells and impair their functions. Both HIV and HTLV-I can be transmitted between individuals through direct contact with certain body fluids from infected individuals. Therefore, a person can be co-infected with both viruses. HIV causes acquired immunodeficiency syndrome, while HTLV-I is the causative agent for adult T-cell leukemia and HTLV-I-associated myelopathy/tropical spastic paraparesis. Several mathematical models have been developed in the literature to describe the within-host dynamics of HIV and HTLV-I mono-infections. However, modeling a within-host dynamics of HIV/HTLV-I co-infection has not been involved. In the present paper, we are concerned to formulate and analyze a new HIV/HTLV co-infection model under the effect of Cytotoxic T lymphocytes (CTLs) immune response. The model describes the interaction between susceptible CD4+T cells, silent HIV-infected cells, active HIV-infected cells, silent HTLV-infected cells, Tax-expressing HTLV-infected cells, free HIV particles, HIV-specific CTLs and HTLV-specific CTLs. The HIV can spread by two routes of transmission, virus-to-cell and cell-to-cell. On the other side, HTLV-I has two modes of transmission, (i) horizontal transmission via direct cell-to-cell contact, and (ii) vertical transmission through mitotic division of Tax-expressing HTLV-infected cells. The well-posedness of the model is established by showing that the solutions of the model are nonnegative and bounded. We define a set of threshold parameters which govern the existence and stability of all equilibria of the model. We explore the global asymptotic stability of all equilibria by utilizing Lyapunov function and LaSalle's invariance principle. We have presented numerical simulations to justify the applicability and effectiveness of the theoretical results. In addition, we evaluate the effect of HTLV-I infection on the HIV dynamics and vice versa.

How mechanistic in silico modelling can improve our understanding of TB disease and treatment.

TB is one of the top 10 causes of death worldwide and the leading cause of death from a single infectious agent. Decreasing the length of time for TB treatment is an important step towards the goal of reducing mortality. Mechanistic in silico modelling can provide us with the tools to explore gaps in our knowledge, with the opportunity to model the complicated within-host dynamics of the infection, and simulate new treatment strategies. Significant insight has been gained using this form of modelling when applied to other diseases - much can be learned in infection research from these advances.

Gene Expression Variation of Candidate Endogenous Control Genes Across Latitudinal Populations of the Bank Vole (Clethrionomys glareolus)

The bank vole has become an important species for the study of gene expression changes underlying evolutionary adaptation, within-host dynamics and resistance to pathogens, or response to pollutants. RT–qPCR is an optimized method for the rapid and accurate measuring gene expression, but it relies on the use of reference genes (RGs) as endogenous controls to normalize mRNA levels of the target genes. Contrary to the common practice, the expression level of the housekeeping genes traditionally used as RGs cannot be assumed stable across different species and experimental settings. Furthermore, compared to model laboratory species, there are potentially additional sources of variation when collecting gene expression data from natural populations with unknown genetic and environmental backgrounds. Thus, rigorous determination of RGs in natural populations of the bank vole was necessary to facilitate gene expression studies in this emerging model species. Therefore, we evaluated the expression variation of 10 RG candidates in spleen samples of bank voles spanning a broad latitudinal range across Europe, using four approaches. Ube2d2a, Ppia and Tbp were consistently identified as the least variable genes, followed by Rn18s, Ywhaz and Rplp0. The combinations Ube2d2a and Ppia or Ube2d2a and Tbp were identified to be sufficient for the normalization. In contrast, the traditional housekeeping genes Actb, Gapdh, Sdha and Tuba1a displayed large expression variation and are not recommended as internal controls. Our results underscore the need of a systematic evaluation of appropriate reference genes to each particular experimental system and provide a useful starting point for further studies.

Modelling within-host macrophage dynamics in influenza virus infection

Human respiratory disease associated with influenza virus infection is of significant public health concern. Macrophages, as part of the front line of host innate cellular defence, have been shown to play an important role in controlling viral replication. However, fatal outcomes of infection, as evidenced in patients infected with highly pathogenic viral strains, are often associated with prompt activation and excessive accumulation of macrophages. Activated macrophages can produce a large amount of pro-inflammatory cytokines, which leads to severe symptoms and at times death. However, the mechanism for rapid activation and excessive accumulation of macrophages during infection remains unclear. It has been suggested that the phenomena may arise from complex interactions between macrophages and influenza virus. In this work, we develop a novel mathematical model to study the relationship between the level of macrophage activation and the level of viral load in influenza infection. Our model combines a dynamic model of viral infection, a dynamic model of macrophages and the essential interactions between the virus and macrophages. Our model predicts that the level of macrophage activation can be negatively correlated with the level of viral load when viral infectivity is sufficiently high. We further identify that temporary depletion of resting macrophages in response to viral infection is a major driver in our model for the negative relationship between the level of macrophage activation and viral load, providing new insight into the mechanisms that regulate macrophage activation. Our model serves as a framework to study the complex dynamics of virus-macrophage interactions and provides a mechanistic explanation for existing experimental observations, contributing to an enhanced understanding of the role of macrophages in influenza viral infection.

Threshold dynamics of a general delayed within-host viral infection model with humoral immunity and two modes of virus transmission

In this paper, a general viral infection model with humoral immunity is investigated. The model describes the interaction of uninfected target cells, infected cells, free viruses and humoral immune response, incorporating two virus transmission modes and intracellular delay. Some reasonable hypothesises are made for the general incidence rates. Through stability analysis of equilibria under these hypothesises, the model exhibits threshold dynamics with respect to the immune-inactivated reproduction rate \begin{document}$ \mathfrak{R}_0 $\end{document} and the immune-activated reproduction rate \begin{document}$ \mathfrak{R}_1 $\end{document} . The theoretical results and corresponding numerical simulations show that the intracellular latency, both of virus-to-cell infection and cell-to-cell infection have direct effects on the global dynamics of the general viral infection model. Our results improve and generalize some known results on within-host virus dynamics.

Modeling within-host viral dynamics: The role of CTL immune responses in the evolution of drug resistance

To study the emergence and evolution of drug resistance during treatment of HIV infection, we study a mathematical model with two strains, one drug-sensitive and the other drug-resistant, by incorporating cytotoxic T lymphocyte (CTL) immune response. The reproductive numbers for each strain with and without the CTL immune response are obtained and shown to determine the stability of the steady states. By sensitivity analysis, we evaluate how the changes of parameters influence the reproductive numbers. The model shows that CTL immune response can suppress the development of drug resistance. There is a dynamic relationship between antiretroviral drug administration, the prevalence of drug resistance, the total level of viral production, and the strength of immune responses. We further investigate the scenario under which the drug-resistant strain can outcompete the wild-type strain. If drug efficacy is at an intermediate level, the drug-resistant virus is likely to arise. The slower the immune response wanes, the slower the drug-resistant strain grows. The results suggest that immunotherapy that aims to enhance immune responses, combined with antiretroviral drug treatment, may result in a functional control of HIV infection.

Development of New Tuberculosis Drugs: Translation to Regimen Composition for Drug-Sensitive and Multidrug-Resistant Tuberculosis.

Tuberculosis (TB) kills more people than any other infectious disease. Challenges for developing better treatments include the complex pathology due to within-host immune dynamics, interpatient variability in disease severity and drug pharmacokinetics-pharmacodynamics (PK-PD), and the growing emergence of resistance. Model-informed drug development using quantitative and translational pharmacology has become increasingly recognized as a method capable of drug prioritization and regimen optimization to efficiently progress compounds through TB drug development phases. In this review, we examine translational models and tools, including plasma PK scaling, site-of-disease lesion PK, host-immune and bacteria interplay, combination PK-PD models of multidrug regimens, resistance formation, and integration of data across nonclinical and clinical phases.We propose a workflow that integrates these tools with computational platforms to identify drug combinations that have the potential to accelerate sterilization, reduce relapse rates, and limit the emergence of resistance.

Host age alters disease life history. A case study in zooplankton and a castrating pathogen

Host age alters disease life history. A case study in zooplankton and a castrating pathogen

A data-based mathematical modelling study to quantify the effects of ciprofloxacin and ampicillin on the within-host dynamics of Salmonella enterica during treatment and relapse.

Antibiotic therapy has drastically reduced the mortality and sequelae of bacterial infections. From naturally occurring to chemically synthesized, different classes of antibiotics have been successfully used without detailed knowledge of how they affect bacterial dynamics in vivo. However, a proportion of patients receiving antimicrobial therapy develop recrudescent infections post-treatment. Relapsing infections are attributable to incomplete clearance of bacterial populations following antibiotic administration; the metabolic profile of this antibiotic-recalcitrant bacterial subpopulation, the spatio-temporal context of its emergence and the variance of antibiotic-bacterial interactions in vivo remain unclear. Here, we develop and apply a mechanistic mathematical model to data from a study comparing the effects of ciprofloxacin and ampicillin on the within-host dynamics of Salmonella enterica serovar Typhimurium in murine infections. Using the inferential capacity of our model, we show that the antibiotic-recalcitrant bacteria following ampicillin, but not ciprofloxacin, treatment belong to a non-replicating phenotype. Aligning with previous studies, we independently estimate that the lymphoid tissues and spleen are important reservoirs of non-replicating bacteria. Finally, we predict that post-treatment, the progenitors of the non-growing and growing bacterial populations replicate and die at different rates. Ultimately, the liver, spleen and mesenteric lymph nodes are all repopulated by progenitors of the previously non-growing phenotype in ampicillin-treated mice.

Stability of a delay-distributed HIV infection model with silent infected cell-to-cell spread and CTL-mediated immunity

In this paper, we formulate a mathematical model to investigate a within-host HIV dynamics under the effect of cytotoxic T lymphocytes immune response. The model incorporates two modes of transmission, virus-to-cell (VTC) and cell-to-cell (CTC). The CTC infection is due to the contact of healthy CD $$4^{+}$$ T cells with (i) silent HIV-infected cells, and (ii) active HIV-infected cells. The model integrates three types of distributed time delays. We show that the model is well posed and it has three equilibria. The existence and stability of equilibria are governed by two threshold parameters. We prove the global asymptotic stability of all equilibria by utilizing Lyapunov function and LaSalle’s invariance principle. We have presented numerical simulations to illustrate the theoretical results. We have studied the effects of CTC transmission and time delays on the dynamical behavior of the system. We have shown that inclusion of time delay can significantly increase the concentration of healthy CD4 $$^{+}$$ T cells and reduce the concentrations of infected cells and free HIV particles. While the inclusion of CTC transmission decreases the concentration of healthy CD4 $$^{+}$$ T cells and increases the concentrations of infected cells and free HIV particles.

An age-structured model for coupling within-host and between-host dynamics in environmentally-driven infectious diseases.

In this paper, an age-structured epidemic model for coupling within-host and between-host dynamics in environmentally-driven infectious diseases is investigated. The model is described by a mixed system of ordinary and partial differential equations which is constituted by the within-host virus infectious fast time ordinary system and the between-host disease transmission slow time age-structured system. The isolated fast system has been investigated in previous literatures, and the main results are introduced. For the isolated slow system, the basic reproduction number Rb0, the positivity and ultimate boundedness of solutions are obtained, the existence of equilibria, the local stability of equilibria, and the global stability of disease-free equilibrium are established. We see that when Rb0 ≤ 1 the system only has the disease-free equilibrium which is globally asymptotically stable, and when Rb0 > 1 the system has a unique endemic equilibrium which is local asymptotically stable. With regard to the coupled slow system, the basic reproduction number Rb, the positivity and boundedness of solutions and the existence of equilibria are firstly obtained. Particularly, the coupled slow system can exist two positive equilibria when Rb < 1 and a unique endemic equilibrium when Rb > 1. When Rb < 1 the disease-free equilibrium is local asymptotically stable, and when Rb > 1 and an additional condition is satisfied the unique endemic equilibrium is local asymptotically stable. When there exist two positive equilibria, under an additional condition the local asymptotic stability of a positive equilibrium and the instability of other positive equilibrium also are established. The numerical examples show that the additional condition may be removed. The research shows that the coupled slow age-structured system has more complex dynamical behavior than the corresponding isolated slow system.

Global analysis of an environmental disease transmission model linking within-host and between-host dynamics

In this paper, a multi-scale mathematical model for environmentally transmitted diseases is proposed which couples the pathogen-immune interaction inside the human body with the disease transmission at the population level. The model is based on the nested approach that incorporates the infection-age-structured immunological dynamics into an epidemiological system structured by the chronological time, the infection age and the vaccination age. We conduct detailed analysis for both the within-host and between-host disease dynamics. Particularly, we derive the basic reproduction number R0 for the between-host model and prove the uniform persistence of the system. Furthermore, using carefully constructed Lyapunov functions, we establish threshold-type results regarding the global dynamics of the between-host system: the disease-free equilibrium is globally asymptotically stable when R0 < 1, and the endemic equilibrium is globally asymptotically stable when R0 > 1. We explore the connection between the within-host and between-host dynamics through both mathematical analysis and numerical simulation. We show that the pathogen load and immune strength at the individual level contribute to the disease transmission and spread at the population level. We also find that, although the between-host transmission risk correlates positively with the within-host pathogen load, there is no simple monotonic relationship between the disease prevalence and the individual pathogen load.

AN IMMUNO-EPIDEMIOLOGICAL VECTOR–HOST MODEL WITH WITHIN-VECTOR VIRAL KINETICS

A current challenge for disease modeling and public health is understanding pathogen dynamics across scales since their ecology and evolution ultimately operate on several coupled scales. This is particularly true for vector-borne diseases, where within-vector, within-host, and between vector–host populations all play crucial roles in diversity and distribution of the pathogen. Despite recent modeling efforts to determine the effect of within-host virus-immune response dynamics on between-host transmission, the role of within-vector viral dynamics on disease spread is overlooked. Here, we formulate an age-since-infection-structured epidemic model coupled to nonlinear ordinary differential equations describing within-host immune-virus dynamics and within-vector viral kinetics, with feedbacks across these scales. We first define the within-host viral-immune response and within-vector viral kinetics-dependent basic reproduction number [Formula: see text] Then we prove that whenever [Formula: see text] the disease-free equilibrium is locally asymptotically stable, and under certain biologically interpretable conditions, globally asymptotically stable. Otherwise, if [Formula: see text] it is unstable and the system has a unique positive endemic equilibrium. In the special case of constant vector to host inoculum size, we show the positive equilibrium is locally asymptotically stable and the disease is weakly uniformly persistent. Furthermore, numerical results suggest that within-vector-viral kinetics and dynamic inoculum size may play a substantial role in epidemics. Finally, we address how the model can be utilized to better predict the success of control strategies such as vaccination and drug treatment.

Mathematical modelling of the role of mucosal vaccine on the within-host dynamics of Chlamydia trachomatis

A mathematical model of the within-host replicative dynamics of C. trachomatis infection and its interactions with the immune system, in the presence of a mucosal vaccine, is presented. Our aim is to estimate the requisite efficacy of an efficacious mucosal vaccine that could promote a stable disease-free state in vivo. Sensitivity analysis was used to quantify how variability in the model parameters influence the value of the disease threshold R0. This shows that the two most important factors to be considered for achieving a disease-free state state in vivo, based on their influence on R0, are the efficacy of the Chlamydia vaccine, and the rate at which the humoral immune response protects healthy epithelial cells from infection. Numerical simulations of the model show that a vaccine with a minimum efficacy of 86% may be required for the in vivo control of Chlamydia burden. Such effective but imperfect Chlamydia vaccine could confer long-term protective immunity to genital Chlamydia infections. Conditions under which lower vaccine efficacies may suffice are also explored.

Global analysis of a reaction–diffusion blood-stage malaria model with immune response

Malaria is one of the most dangerous diseases that threatens people’s lives around the world. In this paper, we study a reaction-diffusion model for the within-host dynamics of malaria infection with an antibody immune response. The model is given by a system of partial differential equations (PDEs) to describe the blood-stage of malaria life cycle. It addresses the interactions between uninfected red blood cells, antibodies, and three types of infected red blood cells, namely ring-infected red blood cells, trophozoite-infected red blood cells and schizont-infected red blood cells. Moreover, the model contains a parameter to measure the efficacy of isoleucine starvation and its effect on the growth of malaria parasites. We show the basic properties of the model. We compute all equilibria and derive the thresholds from the conditions of existence of malaria equilibrium points. We prove the global stability of all equilibrium points based on choosing suitable Lyapunov functionals. We use the characteristic equations to verify the local instability of equilibrium points. We finally execute numerical simulations to validate the theoretical results and highlight some important observations. The results indicate that isoleucine starvation can have a critical impact on the stability of equilibrium points. When the efficacy of isoleucine starvation is high, it switches the system from the infection state to the malaria-free state. The presence of an antibody immune response does not lead to the elimination of malaria infection, but it suppresses the growth of malaria parasites and increases the amount of healthy red blood cells.

Evaluating the contributions of purifying selection and progeny-skew in dictating within-host Mycobacterium tuberculosis evolution.

The within-host evolutionary dynamics of tuberculosis (TB) remain unclear, and underlying biological characteristics render standard population genetic approaches based upon the Wright-Fisher model largely inappropriate. In addition, the compact genome combined with an absence of recombination is expected to result in strong purifying selection effects. Thus, it is imperative to establish a biologically relevant evolutionary framework incorporating these factors in order to enable an accurate study of this important human pathogen. Further, such a model is critical for inferring fundamental evolutionary parameters related to patient treatment, including mutation rates and the severity of infection bottlenecks. We here implement such a model and infer the underlying evolutionary parameters governing within-patient evolutionary dynamics. Results demonstrate that the progeny skew associated with the clonal nature of TB severely reduces genetic diversity and that the neglect of this parameter in previous studies has led to significant mis-inference of mutation rates. As such, our results suggest an underlying de novo mutation rate that is considerably faster than previously inferred, and a progeny distribution differing significantly from Wright-Fisher assumptions. This inference represents a more appropriate evolutionary null model, against which the periodic effects of positive selection, associated with drug-resistance for example, may be better assessed.