BACKGROUND: Accurate estimation of the effective reproductive number ([Formula: see text]) of epidemic outbreaks is of central relevance to public health policy and decision making. We present estimateR, an R package for the estimation of the reproductive number through time from delayed observations of infection events. Such delayed observations include confirmed cases, hospitalizations or deaths. The package implements the methodology of Huisman et al. but modularizes the [Formula: see text] estimation procedure to allow easy implementation of new alternatives to the currently available methods. Users can tailor their analyses according to their particular use case by choosing among implemented options. RESULTS: The estimateR R package allows users to estimate the effective reproductive number of an epidemic outbreak based on observed cases, hospitalization, death or any other type of event documenting past infections, in a fast and timely fashion. We validated the implementation with a simulation study: estimateR yielded estimates comparable to alternative publicly available methods while being around two orders of magnitude faster. We then applied estimateR to empirical case-confirmation incidence data for COVID-19 in nine countries and for dengue fever in Brazil; in parallel, estimateR is already being applied (i) to SARS-CoV-2 measurements in wastewater data and (ii) to study influenza transmission based on wastewater and clinical data in other studies. In summary, this R package provides a fast and flexible implementation to estimate the effective reproductive number for various diseases and datasets. CONCLUSIONS: The estimateR R package is a modular and extendable tool designed for outbreak surveillance and retrospective outbreak investigation. It extends the method developed for COVID-19 by Huisman et al. and makes it available for a variety of pathogens, outbreak scenarios, and observation types. Estimates obtained with estimateR can be interpreted directly or used to inform more complex epidemic models (e.g. for forecasting) on the value of [Formula: see text].

Bacteria have adaptive immunity against viruses (phages) in the form of CRISPR-Cas immune systems. Currently, 6 types of CRISPR-Cas systems are known and the molecular study of three of these has revealed important molecular differences. It is unknown if and how these molecular differences change the outcome of phage infection and the evolutionary pressure the CRISPR-Cas systems faces. To determine the importance of these molecular differences, we model a phage outbreak entering a population defending exclusively with a type I/II or a type III CRISPR-Cas system. We show that for type III CRISPR-Cas systems, rapid phage extinction is driven by the probability to acquire at least one resistance spacer. However, for type I/II CRISPR-Cas systems, rapid phage extinction is characterized by an a threshold-like behaviour: any acquisition probability below this threshold leads to phage survival whereas any acquisition probability above it, results in phage extinction. We also show that in the absence of autoimmunity, high acquisition rates evolve. However, when CRISPR-Cas systems are prone to autoimmunity, intermediate levels of acquisition are optimal during a phage outbreak. As we predict an optimal probability of spacer acquisition 2 factors of magnitude above the one that has been measured, we discuss the origin of such a discrepancy. Finally, we show that in a biologically relevant parameter range, a type III CRISPR-Cas system can outcompete a type I/II CRISPR-Cas system with a slightly higher probability of acquisition.

Large-scale serological testing in the population is essential to determine the true extent of the current SARS-CoV-2 pandemic. Serological tests measure antibody responses against pathogens and use predefined cutoff levels that dichotomize the quantitative test measures into sero-positives and negatives and use this as a proxy for past infection. With the imperfect assays that are currently available to test for past SARS-CoV-2 infection, the fraction of seropositive individuals in serosurveys is a biased estimator of the cumulative incidence and is usually corrected to account for the sensitivity and specificity. Here we use an inference method-referred to as mixture-model approach-for the estimation of the cumulative incidence that does not require to define cutoffs by integrating the quantitative test measures directly into the statistical inference procedure. We confirm that the mixture model outperforms the methods based on cutoffs, leading to less bias and error in estimates of the cumulative incidence. We illustrate how the mixture model can be used to optimize the design of serosurveys with imperfect serological tests. We also provide guidance on the number of control and case sera that are required to quantify the test's ambiguity sufficiently to enable the reliable estimation of the cumulative incidence. Lastly, we show how this approach can be used to estimate the cumulative incidence of classes of infections with an unknown distribution of quantitative test measures. This is a very promising application of the mixture-model approach that could identify the elusive fraction of asymptomatic SARS-CoV-2 infections. An R-package implementing the inference methods used in this paper is provided. Our study advocates using serological tests without cutoffs, especially if they are used to determine parameters characterizing populations rather than individuals. This approach circumvents some of the shortcomings of cutoff-based methods at exactly the low cumulative incidence levels and test accuracies that we are currently facing in SARS-CoV-2 serosurveys.

There is an error in the caption for Fig 1, "Instantaneous reproductive number as estimated by the method of Cori et al. vs. cohort reproductive number estimated by Wallinga and Teunis" sentence four.

Estimation of the effective reproductive number Rt is important for detecting changes in disease transmission over time. During the Coronavirus Disease 2019 (COVID-19) pandemic, policy makers and public health officials are using Rt to assess the effectiveness of interventions and to inform policy. However, estimation of Rt from available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make recommendations. For near real-time estimation of Rt, we recommend the approach of Cori and colleagues, which uses data from before time t and empirical estimates of the distribution of time between infections. Methods that require data from after time t, such as Wallinga and Teunis, are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for retrospective analyses of how individuals infected at different time points contributed to the spread. We advise caution when using methods derived from the approach of Bettencourt and Ribeiro, as the resulting Rt estimates may be biased if the underlying structural assumptions are not met. Two key challenges common to all approaches are accurate specification of the generation interval and reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems in Rt estimation.

Disease tolerance is a defense strategy against infections that aims at maintaining host health even at high pathogen replication or load. Tolerance mechanisms are currently intensively studied with the long-term goal of exploiting them therapeutically. Because tolerance-based treatment imposes less selective pressure on the pathogen it has been hypothesised to be "evolution-proof". However, the primary public health goal is to reduce the incidence and mortality associated with a disease. From this perspective, tolerance-based treatment bears the risk of increasing the prevalence of the disease, which may lead to increased mortality. We assessed the promise of tolerance-based treatment strategies using mathematical models. Conventional treatment was implemented as an increased recovery rate, while tolerance-based treatment was assumed to reduce the disease-related mortality of infected hosts without affecting recovery. We investigated the endemic phase of two types of infections: acute and chronic. Additionally, we considered the effect of pathogen resistance against conventional treatment. We show that, for low coverage of tolerance-based treatment, chronic infections can cause even more deaths than without treatment. Overall, we found that conventional treatment always outperforms tolerance-based treatment, even when we allow the emergence of pathogen resistance. Our results cast doubt on the potential benefit of tolerance-based over conventional treatment. Any clinical application of tolerance-based treatment of infectious diseases has to consider the associated detrimental epidemiological feedback.

Hematopoietic stem cells in mammals are known to reside mostly in the bone marrow, but also transitively passage in small numbers in the blood. Experimental findings have suggested that they exist in a dynamic equilibrium, continuously migrating between these two compartments. Here we construct an individual-based mathematical model of this process, which is parametrised using existing empirical findings from mice. This approach allows us to quantify the amount of migration between the bone marrow niches and the peripheral blood. We use this model to investigate clonal hematopoiesis, which is a significant risk factor for hematologic cancers. We also analyse the engraftment of donor stem cells into non-conditioned and conditioned hosts, quantifying the impact of different treatment scenarios. The simplicity of the model permits a thorough mathematical analysis, providing deeper insights into the dynamics of both the model and of the real-world system. We predict the time taken for mutant clones to expand within a host, as well as chimerism levels that can be expected following transplantation therapy, and the probability that a preconditioned host is reconstituted by donor cells.

Intense use of antibiotics for the treatment of diseases such as tuberculosis, malaria, Staphylococcus aureus or gonorrhea has led to rapidly increasing population levels of drug resistance. This has generally necessitated a switch to new drugs and the discontinuation of older ones, after which resistance often only declines slowly or even persists indefinitely. These long-term effects are usually ascribed to low fitness costs of resistance in absence of the drug. Here we show that structure in the host population, in particular heterogeneity in number of contacts, also plays an important role in the reversion dynamics. Host contact structure acts both during the phase of intense treatment, leading to non-random distributions of the resistant strain among the infected population, and after the discontinuation of the drug, by affecting the competition dynamics resulting in a mitigation of fitness advantages. As a consequence, we observe both a lower rate of reversion and a lower probability that reversion to sensitivity on the population level occurs after treatment is stopped. Our simulations show that the impact of heterogeneity in the host structure is maximal in the biologically most plausible parameter range, namely when fitness costs of resistance are small.

Rhythmical activity patterns are ubiquitous in nature. We study an oscillatory biological system: collective activity cycles in ant colonies. Ant colonies have become model systems for research on biological networks because the interactions between the component parts are visible to the naked eye, and because the time-ordered contact network formed by these interactions serves as the substrate for the distribution of information and other resources throughout the colony. To understand how the collective activity cycles influence the contact network transport properties, we used an automated tracking system to record the movement of all the individuals within nine different ant colonies. From these trajectories we extracted over two million ant-to-ant interactions. Time-series analysis of the temporal fluctuations of the overall colony interaction and movement rates revealed that both the period and amplitude of the activity cycles exhibit a diurnal cycle, in which daytime cycles are faster and of greater amplitude than night cycles. Using epidemiology-derived models of transmission over networks, we compared the transmission properties of the observed periodic contact networks with those of synthetic aperiodic networks. These simulations revealed that contrary to some predictions, regularly-oscillating contact networks should impede information transmission. Further, we provide a mechanistic explanation for this effect, and present evidence in support of it.

Multiple treatment strategies are available for empiric antibiotic therapy in hospitals, but neither clinical studies nor theoretical investigations have yielded a clear picture when which strategy is optimal and why. Extending earlier work of others and us, we present a mathematical model capturing treatment strategies using two drugs, i.e the multi-drug therapies referred to as cycling, mixing, and combination therapy, as well as monotherapy with either drug. We randomly sample a large parameter space to determine the conditions determining success or failure of these strategies. We find that combination therapy tends to outperform the other treatment strategies. By using linear discriminant analysis and particle swarm optimization, we find that the most important parameters determining success or failure of combination therapy relative to the other treatment strategies are the de novo rate of emergence of double resistance in patients infected with sensitive bacteria and the fitness costs associated with double resistance. The rate at which double resistance is imported into the hospital via patients admitted from the outside community has little influence, as all treatment strategies are affected equally. The parameter sets for which combination therapy fails tend to fall into areas with low biological plausibility as they are characterised by very high rates of de novo emergence of resistance to both drugs compared to a single drug, and the cost of double resistance is considerably smaller than the sum of the costs of single resistance.

Treatment failure after therapy of pulmonary tuberculosis (TB) infections is an important challenge, especially when it coincides with de novo emergence of multi-drug-resistant TB (MDR-TB). We seek to explore possible causes why MDR-TB has been found to occur much more often in patients with a history of previous treatment. We develop a mathematical model of the replication of Mycobacterium tuberculosis within a patient reflecting the compartments of macrophages, granulomas, and open cavities as well as parameterizing the effects of drugs on the pathogen dynamics in these compartments. We use this model to study the influence of patient adherence to therapy and of common retreatment regimens on treatment outcome. As expected, the simulations show that treatment success increases with increasing adherence. However, treatment occasionally fails even under perfect adherence due to interpatient variability in pharmacological parameters. The risk of generating MDR de novo is highest between 40% and 80% adherence. Importantly, our simulations highlight the double-edged effect of retreatment: On the one hand, the recommended retreatment regimen increases the overall success rate compared to re-treating with the initial regimen. On the other hand, it increases the probability to accumulate more resistant genotypes. We conclude that treatment adherence is a key factor for a positive outcome, and that screening for resistant strains is advisable after treatment failure or relapse.

Acquired resistance is one of the major barriers to successful cancer therapy. The development of resistance is commonly attributed to genetic heterogeneity. However, heterogeneity of drug penetration of the tumor microenvironment both on the microscopic level within solid tumors as well as on the macroscopic level across metastases may also contribute to acquired drug resistance. Here we use mathematical models to investigate the effect of drug heterogeneity on the probability of escape from treatment and the time to resistance. Specifically we address scenarios with sufficiently potent therapies that suppress growth of all preexisting genetic variants in the compartment with the highest possible drug concentration. To study the joint effect of drug heterogeneity, growth rate, and evolution of resistance, we analyze a multi-type stochastic branching process describing growth of cancer cells in multiple compartments with different drug concentrations and limited migration between compartments. We show that resistance is likely to arise first in the sanctuary compartment with poor drug penetrations and from there populate non-sanctuary compartments with high drug concentrations. Moreover, we show that only below a threshold rate of cell migration does spatial heterogeneity accelerate resistance evolution, otherwise deterring drug resistance with excessively high migration rates. Our results provide new insights into understanding why cancers tend to quickly become resistant, and that cell migration and the presence of sanctuary sites with little drug exposure are essential to this end.

ISSN:1553-734X

Quantifying epidemiological dynamics is crucial for understanding and forecasting the spread of an epidemic. The coalescent and the birth-death model are used interchangeably to infer epidemiological parameters from the genealogical relationships of the pathogen population under study, which in turn are inferred from the pathogen genetic sequencing data. To compare the performance of these widely applied models, we performed a simulation study. We simulated phylogenetic trees under the constant rate birth-death model and the coalescent model with a deterministic exponentially growing infected population. For each tree, we re-estimated the epidemiological parameters using both a birth-death and a coalescent based method, implemented as an MCMC procedure in BEAST v2.0. In our analyses that estimate the growth rate of an epidemic based on simulated birth-death trees, the point estimates such as the maximum a posteriori/maximum likelihood estimates are not very different. However, the estimates of uncertainty are very different. The birth-death model had a higher coverage than the coalescent model, i.e. contained the true value in the highest posterior density (HPD) interval more often (2-13% vs. 31-75% error). The coverage of the coalescent decreases with decreasing basic reproductive ratio and increasing sampling probability of infecteds. We hypothesize that the biases in the coalescent are due to the assumption of deterministic rather than stochastic population size changes. Both methods performed reasonably well when analyzing trees simulated under the coalescent. The methods can also identify other key epidemiological parameters as long as one of the parameters is fixed to its true value. In summary, when using genetic data to estimate epidemic dynamics, our results suggest that the birth-death method will be less sensitive to population fluctuations of early outbreaks than the coalescent method that assumes a deterministic exponentially growing infected population.

Most organisms live in ever-changing environments, and have to cope with a range of different conditions. Often, the set of biological traits that are needed to grow, reproduce, and survive varies between conditions. As a consequence, organisms have evolved sensory systems to detect environmental signals, and to modify the expression of biological traits in response. However, there are limits to the ability of such plastic responses to cope with changing environments. Sometimes, environmental shifts might occur suddenly, and without preceding signals, so that organisms might not have time to react. Other times, signals might be unreliable, causing organisms to prepare themselves for changes that then do not occur. Here, we focus on such unreliable signals that indicate the onset of adverse conditions. We use analytical and individual-based models to investigate the evolution of simple rules that organisms use to decide whether or not to switch to a protective state. We find evolutionary transitions towards organisms that use a combination of random switching and switching in response to the signal. We also observe that, in spatially heterogeneous environments, selection on the switching strategy depends on the composition of the population, and on population size. These results are in line with recent experiments that showed that many unicellular organisms can attain different phenotypic states in a probabilistic manner, and lead to testable predictions about how this could help organisms cope with unreliable signals.

Contact structure is believed to have a large impact on epidemic spreading and consequently using networks to model such contact structure continues to gain interest in epidemiology. However, detailed knowledge of the exact contact structure underlying real epidemics is limited. Here we address the question whether the structure of the contact network leaves a detectable genetic fingerprint in the pathogen population. To this end we compare phylogenies generated by disease outbreaks in simulated populations with different types of contact networks. We find that the shape of these phylogenies strongly depends on contact structure. In particular, measures of tree imbalance allow us to quantify to what extent the contact structure underlying an epidemic deviates from a null model contact network and illustrate this in the case of random mixing. Using a phylogeny from the Swiss HIV epidemic, we show that this epidemic has a significantly more unbalanced tree than would be expected from random mixing.

Human immunodeficiency virus (HIV-1) is, like most pathogens, under selective pressure to escape the immune system of its host. In particular, HIV-1 can avoid recognition by cytotoxic T lymphocytes (CTLs) by altering the binding affinity of viral peptides to human leukocyte antigen (HLA) molecules, the role of which is to present those peptides to the immune system. It is generally assumed that HLA escape mutations carry a replicative fitness cost, but these costs have not been quantified. In this study, we assess the replicative cost of mutations which are likely to escape presentation by HLA molecules in the region of HIV-1 protease and reverse transcriptase. Specifically, we combine computational approaches for prediction of in vitro replicative fitness and peptide binding affinity to HLA molecules. We find that mutations which impair binding to HLA-A molecules tend to have lower in vitro replicative fitness than mutations which do not impair binding to HLA-A molecules, suggesting that HLA-A escape mutations carry higher fitness costs than non-escape mutations. We argue that the association between fitness and HLA-A binding impairment is probably due to an intrinsic cost of escape from HLA-A molecules, and these costs are particularly strong for HLA-A alleles associated with efficient virus control. Counter-intuitively, we do not observe a significant effect in the case of HLA-B, but, as discussed, this does not argue against the relevance of HLA-B in virus control. Overall, this article points to the intriguing possibility that HLA-A molecules preferentially target more conserved regions of HIV-1, emphasizing the importance of HLA-A genes in the evolution of HIV-1 and RNA viruses in general.

Antibiotic resistant nosocomial infections are an important cause of mortality and morbidity in hospitals. Antibiotic cycling has been proposed to contain this spread by a coordinated use of different antibiotics. Theoretical work, however, suggests that often the random deployment of drugs ("mixing") might be the better strategy. We use an epidemiological model for a single hospital ward in order to assess the performance of cycling strategies which take into account the frequency of antibiotic resistance in the hospital ward. We assume that information on resistance frequencies stems from microbiological tests, which are performed in order to optimize individual therapy. Thus the strategy proposed here represents an optimization at population-level, which comes as a free byproduct of optimizing treatment at the individual level. We find that in most cases such an informed switching strategy outperforms both periodic cycling and mixing, despite the fact that information on the frequency of resistance is derived only from a small sub-population of patients. Furthermore we show that the success of this strategy is essentially a stochastic phenomenon taking advantage of the small population sizes in hospital wards. We find that the performance of an informed switching strategy can be improved substantially if information on resistance tests is integrated over a period of one to two weeks. Finally we argue that our findings are robust against a (moderate) preexistence of doubly resistant strains and against transmission via environmental reservoirs. Overall, our results suggest that switching between different antibiotics might be a valuable strategy in small patient populations, if the switching strategies take the frequencies of resistance alleles into account.

Antagonistic coevolution between hosts and parasites can involve rapid fluctuations of genotype frequencies that are known as Red Queen dynamics. Under such dynamics, recombination in the hosts may be advantageous because genetic shuffling can quickly produce disproportionately fit offspring (the Red Queen hypothesis). Previous models investigating these dynamics have assumed rather simple models of genetic interactions between hosts and parasites. Here, we assess the robustness of earlier theoretical predictions about the Red Queen with respect to the underlying host-parasite interactions. To this end, we created large numbers of random interaction matrices, analysed the resulting dynamics through simulation, and ascertained whether recombination was favoured or disfavoured. We observed Red Queen dynamics in many of our simulations provided the interaction matrices exhibited sufficient 'antagonicity'. In agreement with previous studies, strong selection on either hosts or parasites favours selection for increased recombination. However, fast changes in the sign of linkage disequilibrium or epistasis were only infrequently observed and do not appear to be a necessary condition for the Red Queen hypothesis to work. Indeed, recombination was often favoured even though the linkage disequilibrium remained of constant sign throughout the simulations. We conclude that Red Queen-type dynamics involving persistent fluctuations in host and parasite genotype frequencies appear to not be an artefact of specific assumptions about host-parasite fitness interactions, but emerge readily with the general interactions studied here. Our results also indicate that although recombination is often favoured, some of the factors previously thought to be important in this process such as linkage disequilibrium fluctuations need to be reassessed when fitness interactions between hosts and parasites are complex.

Most population genetic theories on the evolution of sex or recombination are based on fairly restrictive assumptions about the nature of the underlying fitness landscapes. Here we use computer simulations to study the evolution of sex on fitness landscapes with different degrees of complexity and epistasis. We evaluate predictors of the evolution of sex, which are derived from the conditions established in the population genetic literature for the evolution of sex on simpler fitness landscapes. These predictors are based on quantities such as the variance of Hamming distance, mean fitness, additive genetic variance, and epistasis. We show that for complex fitness landscapes all the predictors generally perform poorly. Interestingly, while the simplest predictor, Delta Var(HD), also suffers from a lack of accuracy, it turns out to be the most robust across different types of fitness landscapes. Delta Var(HD) is based on the change in Hamming distance variance induced by recombination and thus does not require individual fitness measurements. The presence of loci that are not under selection can, however, severely diminish predictor accuracy. Our study thus highlights the difficulty of establishing reliable criteria for the evolution of sex on complex fitness landscapes and illustrates the challenge for both theoretical and experimental research on the origin and maintenance of sexual reproduction.

Both theoretical predictions and experimental findings suggest that T cell populations can compete with each other. There is some debate on whether T cells compete for aspecific stimuli, such as access to the surface on antigen-presenting cells (APCs) or for specific stimuli, such as their cognate epitope ligand. We have developed an individual-based computer simulation model to study T cell competition. Our model shows that the expression level of foreign epitopes per APC determines whether T cell competition is mainly for specific or aspecific stimuli. Under low epitope expression, competition is mainly for the specific epitope stimuli, and, hence, different epitope-specific T cell populations coexist readily. However, if epitope expression levels are high, aspecific competition becomes more important. Such between-specificity competition can lead to competitive exclusion between different epitope-specific T cell populations. Our model allows us to delineate the circumstances that facilitate coexistence of T cells of different epitope specificity. Understanding mechanisms of T cell coexistence has important practical implications for immune therapies that require a broad immune response.