Andreas Handel

A review of mathematical models of influenza A infections within a host or cell culture: lessons learned and challenges ahead.

Most mathematical models used to study the dynamics of influenza A have thus far focused on the between-host population level, with the aim to inform public health decisions regarding issues such as drug and social distancing intervention strategies, antiviral stockpiling or vaccine distribution. Here, we investigate mathematical modeling of influenza infection spread at a different scale; namely that occurring within an individual host or a cell culture. We review the models that have been developed in the last decades and discuss their contributions to our understanding of the dynamics of influenza infections. We review kinetic parameters (e.g., viral clearance rate, lifespan of infected cells) and values obtained through fitting mathematical models, and contrast them with values obtained directly from experiments. We explore the symbiotic role of mathematical models and experimental assays in improving our quantitative understanding of influenza infection dynamics. We also discuss the challenges in developing better, more comprehensive models for the course of influenza infections within a host or cell culture. Finally, we explain the contributions of such modeling efforts to important public health issues, and suggest future modeling studies that can help to address additional questions relevant to public health.

Neuraminidase Inhibitor Resistance in Influenza: Assessing the Danger of Its Generation and Spread

Neuraminidase Inhibitors (NI) are currently the most effective drugs against influenza. Recent cases of NI resistance are a cause for concern. To assess the danger of NI resistance, a number of studies have reported the fraction of treated patients from which resistant strains could be isolated. Unfortunately, those results strongly depend on the details of the experimental protocol. Additionally, knowing the fraction of patients harboring resistance is not too useful by itself. Instead, we want to know how likely it is that an infected patient can generate a resistant infection in a secondary host, and how likely it is that the resistant strain subsequently spreads. While estimates for these parameters can often be obtained from epidemiological data, such data is lacking for NI resistance in influenza. Here, we use an approach that does not rely on epidemiological data. Instead, we combine data from influenza infections of human volunteers with a mathematical framework that allows estimation of the parameters that govern the initial generation and subsequent spread of resistance. We show how these parameters are influenced by changes in drug efficacy, timing of treatment, fitness of the resistant strain, and details of virus and immune system dynamics. Our study provides estimates for parameters that can be directly used in mathematical and computational models to study how NI usage might lead to the emergence and spread of resistance in the population. We find that the initial generation of resistant cases is most likely lower than the fraction of resistant cases reported. However, we also show that the results depend strongly on the details of the within-host dynamics of influenza infections, and most importantly, the role the immune system plays. Better knowledge of the quantitative dynamics of the immune response during influenza infections will be crucial to further improve the results.

Towards a quantitative understanding of the within-host dynamics of influenza A infections.

Although the influenza A virus has been extensively studied, a quantitative understanding of the infection dynamics is still lacking. To make progress in this direction, we designed several mathematical models and compared them with data from influenza A infections of mice. We find that the immune response (IR) plays an important part in the infection dynamics. Both an innate and an adaptive IR are required to provide adequate explanation of the data. In contrast, regrowth of epithelial cells did not seem to be an important mechanism on the time scale of the infection. We also find that different model variants for both innate and adaptive responses fit the data well, indicating the need for additional data to allow further model discrimination.

The role of compensatory mutations in the emergence of drug resistance.

Pathogens that evolve resistance to drugs usually have reduced fitness. However, mutations that largely compensate for this reduction in fitness often arise. We investigate how these compensatory mutations affect population-wide resistance emergence as a function of drug treatment. Using a model of gonorrhea transmission dynamics, we obtain generally applicable, qualitative results that show how compensatory mutations lead to more likely and faster resistance emergence. We further show that resistance emergence depends on the level of drug use in a strongly nonlinear fashion. We also discuss what data need to be obtained to allow future quantitative predictions of resistance emergence.

Molecular evolution and emergence of avian gammacoronaviruses

Abstract Coronaviruses, which are single stranded, positive sense RNA viruses, are responsible for a wide variety of existing and emerging diseases in humans and other animals. The gammacoronaviruses primarily infect avian hosts. Within this genus of coronaviruses, the avian coronavirus infectious bronchitis virus (IBV) causes a highly infectious upper-respiratory tract disease in commercial poultry. IBV shows rapid evolution in chickens, frequently producing new antigenic types, which adds to the multiple serotypes of the virus that do not cross protect. Rapid evolution in IBV is facilitated by strong selection, large population sizes and high genetic diversity within hosts, and transmission bottlenecks between hosts. Genetic diversity within a host arises primarily by mutation, which includes substitutions, insertions and deletions. Mutations are caused both by the high error rate, and limited proof reading capability, of the viral RNA-dependent RNA-polymerase, and by recombination. Recombination also generates new haplotype diversity by recombining existing variants. Rapid evolution of avian coronavirus IBV makes this virus extremely difficult to diagnose and control, but also makes it an excellent model system to study viral genetic diversity and the mechanisms behind the emergence of coronaviruses in their natural host.

Heterogeneous Adaptive Trajectories of Small Populations on Complex Fitness Landscapes

Background Small populations are thought to be adaptively handicapped, not only because they suffer more from deleterious mutations but also because they have limited access to new beneficial mutations, particularly those conferring large benefits. Methodology/Principal Findings Here, we test this widely held conjecture using both simulations and experiments with small and large bacterial populations evolving in either a simple or a complex nutrient environment. Consistent with expectations, we find that small populations are adaptively constrained in the simple environment; however, in the complex environment small populations not only follow more heterogeneous adaptive trajectories, but can also attain higher fitness than the large populations. Large populations are constrained to near deterministic fixation of rare large-benefit mutations. While such determinism speeds adaptation on the smooth adaptive landscape represented by the simple environment, it can limit the ability of large populations from effectively exploring the underlying topography of rugged adaptive landscapes characterized by complex environments. Conclusions Our results show that adaptive constraints often faced by small populations can be circumvented during evolution on rugged adaptive landscapes.

What is the best control strategy for multiple infectious disease outbreaks

Effective control of infectious disease outbreaks is an important public health goal. In a number of recent studies, it has been shown how different intervention measures like travel restrictions, school closures, treatment and prophylaxis might allow us to control outbreaks of diseases, such as SARS, pandemic influenza and others. In these studies, control of a single outbreak is considered. It is, however, not clear how one should handle a situation where multiple outbreaks are likely to occur. Here, we identify the best control strategy for such a situation. We further discuss ways in which such a strategy can be implemented to achieve additional public health objectives.

Exploring the role of the immune response in preventing antibiotic resistance

For many bacterial infections, drug resistant mutants are likely present by the time antibiotic treatment starts. Nevertheless, such infections are often successfully cleared. It is commonly assumed that this is due to the combined action of drug and immune response, the latter facilitating clearance of the resistant population. However, most studies of drug resistance emergence during antibiotic treatment focus almost exclusively on the dynamics of bacteria and the drug and neglect the contribution of immune defenses. Here, we develop and analyze several mathematical models that explicitly include an immune response. We consider different types of immune responses and investigate how each impacts the emergence of resistance. We show that an immune response that retains its strength despite a strong drug-induced decline of bacteria numbers considerably reduces the emergence of resistance, narrows the mutant selection window, and mitigates the effects of non-adherence to treatment. Additionally, we show that compared to an immune response that kills bacteria at a constant rate, one that trades reduced killing at high bacterial load for increased killing at low bacterial load is sometimes preferable. We discuss the predictions and hypotheses derived from this study and how they can be tested experimentally.

Antiviral resistance and the control of pandemic influenza: The roles of stochasticity, evolution and model details

Antiviral drugs, most notably the neuraminidase inhibitors, are an important component of control strategies aimed to prevent or limit any future influenza pandemic. The potential large-scale use of antiviral drugs brings with it the danger of drug resistance evolution. A number of recent studies have shown that the emergence of drug-resistant influenza could undermine the usefulness of antiviral drugs for the control of an epidemic or pandemic outbreak. While these studies have provided important insights, the inherently stochastic nature of resistance generation and spread, as well as the potential for ongoing evolution of the resistant strain have not been fully addressed. Here, we study a stochastic model of drug resistance emergence and consecutive evolution of the resistant strain in response to antiviral control during an influenza pandemic. We find that taking into consideration the ongoing evolution of the resistant strain does not increase the probability of resistance emergence; however, it increases the total number of infecteds if a resistant outbreak occurs. Our study further shows that taking stochasticity into account leads to results that can differ from deterministic models. Specifically, we find that rapid and strong control cannot only contain a drug sensitive outbreak, it can also prevent a resistant outbreak from occurring. We find that the best control strategy is early intervention heavily based on prophylaxis at a level that leads to outbreak containment. If containment is not possible, mitigation works best at intermediate levels of antiviral control. Finally, we show that the results are not very sensitive to the way resistance generation is modeled.

Dominant protection from HLA-linked autoimmunity by antigen-specific regulatory T cells

Susceptibility and protection against human autoimmune diseases, including type I diabetes, multiple sclerosis, and Goodpasture disease, is associated with particular human leukocyte antigen (HLA) alleles. However, the mechanisms underpinning such HLA-mediated effects on self-tolerance remain unclear. Here we investigate the molecular mechanism of Goodpasture disease, an HLA-linked autoimmune renal disorder characterized by an immunodominant CD4+ T-cell self-epitope derived from the α3 chain of type IV collagen (α3135–145). While HLA-DR15 confers a markedly increased disease risk, the protective HLA-DR1 allele is dominantly protective in trans with HLA-DR15 (ref. 2). We show that autoreactive α3135–145-specific T cells expand in patients with Goodpasture disease and, in α3135–145-immunized HLA-DR15 transgenic mice, α3135–145-specific T cells infiltrate the kidney and mice develop Goodpasture disease. HLA-DR15 and HLA-DR1 exhibit distinct peptide repertoires and binding preferences and present the α3135–145 epitope in different binding registers. HLA-DR15-α3135–145 tetramer+ T cells in HLA-DR15 transgenic mice exhibit a conventional T-cell phenotype (Tconv) that secretes pro-inflammatory cytokines. In contrast, HLA-DR1-α3135–145 tetramer+ T cells in HLA-DR1 and HLA-DR15/DR1 transgenic mice are predominantly CD4+Foxp3+ regulatory T cells (Treg cells) expressing tolerogenic cytokines. HLA-DR1-induced Treg cells confer resistance to disease in HLA-DR15/DR1 transgenic mice. HLA-DR15+ and HLA-DR1+ healthy human donors display altered α3135–145-specific T-cell antigen receptor usage, HLA-DR15-α3135–145 tetramer+ Foxp3− Tconv and HLA-DR1-α3135–145 tetramer+ Foxp3+CD25hiCD127lo Treg dominant phenotypes. Moreover, patients with Goodpasture disease display a clonally expanded α3135–145-specific CD4+ T-cell repertoire. Accordingly, we provide a mechanistic basis for the dominantly protective effect of HLA in autoimmune disease, whereby HLA polymorphism shapes the relative abundance of self-epitope specific Treg cells that leads to protection or causation of autoimmunity.