Synthesizing environmental, epidemiological and vector and parasite genetic data to assist decision making for disease elimination.

We present a framework for identifying when conditions are favourable for transmission of vector-borne diseases between communities by incorporating predicted disease prevalence mapping with landscape analysis of sociological, environmental and host/parasite genetic data. We explored the relationship between environmental features and gene flow of a filarial parasite of humans, Onchocerca volvulus, and its vector, blackflies in the genus Simulium. We generated a baseline microfilarial prevalence map from point estimates from 47 locations in the ecological transition separating the savannah and forest in Ghana, where transmission of O. volvulus persists despite onchocerciasis control efforts. We generated movement suitability maps based on environmental correlates with mitochondrial population structure of 164 parasites from 15 communities and 93 vectors from only four sampling sites, and compared these to the baseline prevalence map. Parasite genetic distance between sampling locations was significantly associated with elevation (r = .793, p = .005) and soil moisture (r = .507, p = .002), while vector genetic distance was associated with soil moisture (r = .788, p = .0417) and precipitation (r = .835, p = .0417). The correlation between baseline prevalence and parasite resistance surface maps was stronger than that between prevalence and vector resistance surface maps. The centre of the study area had high prevalence and suitability for parasite and vector gene flow, potentially contributing to persistent transmission and suggesting the importance of re-evaluating transmission zone boundaries. With suitably dense sampling, this framework can help delineate transmission zones for onchocerciasis and would be translatable to other vector-borne diseases.

Ethical dilemma arises from optimizing interventions for epidemics in heterogeneous populations.

Interventions to mitigate the spread of infectious diseases, while succeeding in their goal, have economic and social costs associated with them. These limit the duration and intensity of the interventions. We study a class of interventions which reduce the reproduction number and find the optimal strength of the intervention which minimizes the final epidemic size for an immunity inducing infection. The intervention works by eliminating the overshoot part of an epidemic, and avoids a second wave of infections. We extend the framework by considering a heterogeneous population and find that the optimal intervention can pose an ethical dilemma for decision and policymakers. This ethical dilemma is shown to be analogous to the trolley problem. We apply this optimization strategy to real-world contact data and case fatality rates from three pandemics to underline the importance of this ethical dilemma in real-world scenarios.

Heterogeneity in network structure switches the dominant transmission mode of infectious diseases.

Several recent emerging diseases have exhibited both sexual and nonsexual transmission modes (Ebola, Zika, and mpox). In the recent mpox outbreaks, transmission through sexual contacts appears to be the dominant mode of transmission. Motivated by this, we use an SIR-like model to argue that an initially dominant sexual transmission mode can be overtaken by casual transmission at later stages, even if the basic casual reproduction number is less than one. Our results highlight the risk of intervention designs which are informed only by the early dynamics of the disease.

Modelling mass drug administration strategies for reducing scabies burden in Monrovia, Liberia.

Scabies is a parasitic infestation with high global burden. Mass drug administrations (MDAs) are recommended for communities with a scabies prevalence of >10%. Quantitative analyses are needed to demonstrate the likely effectiveness of MDA recommendations. In this study, we developed an agent-based model of scabies transmission calibrated to demographic and epidemiological data from Monrovia. We used this model to compare the effectiveness of MDA scenarios for achieving scabies elimination and reducing scabies burden, as measured by time until recrudescence following delivery of an MDA and disability-adjusted-life-years (DALYs) averted. Our model showed that three rounds of MDA delivered at six-month intervals and reaching 80% of the population could reduce prevalence below 2% for three years following the final round, before recrudescence. When MDAs were followed by increased treatment uptake, prevalence was maintained below 2% indefinitely. Increasing the number of and coverage of MDA rounds increased the probability of achieving elimination and the number of DALYs averted. Our results suggest that acute reduction of scabies prevalence by MDA can support a transition to improved treatment access. This study demonstrates how modelling can be used to estimate the expected impact of MDAs by projecting future epidemiological dynamics and health gains under alternative scenarios.

Evaluating the role of asymptomatic throat carriage of Streptococcus pyogenes in impetigo transmission in remote Aboriginal communities in Northern Territory, Australia: a retrospective genomic analysis.

BACKGROUND: Streptococcus pyogenes, or group A Streptococcus (GAS), infections contribute to a high burden of disease in Aboriginal Australians, causing skin infections and immune sequelae such as rheumatic heart disease. Controlling skin infections in these populations has proven difficult, with transmission dynamics being poorly understood. We aimed to identify the relative contributions of impetigo and asymptomatic throat carriage to GAS transmission. METHODS: In this genomic analysis, we retrospectively applied whole genome sequencing to GAS isolates that were collected as part of an impetigo surveillance longitudinal household survey conducted in three remote Aboriginal communities in the Northern Territory of Australia between Aug 6, 2003, and June 22, 2005. We included GAS isolates from all throats and impetigo lesions of people living in two of the previously studied communities. We classified isolates into genomic lineages based on pairwise shared core genomes of more than 99% with five or fewer single nucleotide polymorphisms. We used a household network analysis of epidemiologically and genomically linked lineages to quantify the transmission of GAS within and between households. FINDINGS: We included 320 GAS isolates in our analysis: 203 (63%) from asymptomatic throat swabs and 117 (37%) from impetigo lesions. Among 64 genomic lineages (encompassing 39 emm types) we identified 264 transmission links (involving 93% of isolates), for which the probable source was asymptomatic throat carriage in 166 (63%) and impetigo lesions in 98 (37%). Links originating from impetigo cases were more frequent between households than within households. Households were infected with GAS for a mean of 57 days (SD 39 days), and once cleared, reinfected 62 days (SD 40 days) later. Increased household size and community presence of GAS and scabies were associated with slower clearance of GAS. INTERPRETATION: In communities with high prevalence of endemic GAS-associated skin infection, asymptomatic throat carriage is a GAS reservoir. Public health interventions such as vaccination or community infection control programmes aimed at interrupting transmission of GAS might need to include consideration of asymptomatic throat carriage. FUNDING: Australian National Health and Medical Research Council.

Capturing Household Structure and Mobility within and between Remote Aboriginal Communities in Northern Australia Using Longitudinal Data: A Pilot Study.

Cultural practices and development level can influence a population's household structures and mixing patterns. Within some populations, households can be organized across multiple dwellings. This likely affects the spread of infectious disease through these communities; however, current demographic data collection tools do not record these data. METHODS: Between June and October 2018, the Contact And Mobility Patterns in remote Aboriginal Australian communities (CAMP-remote) pilot study recruited Aboriginal mothers with infants in a remote northern Australian community to complete a monthly iPad-based contact survey. RESULTS: Thirteen mother-infant pairs (participants) completed 69 study visits between recruitment and the end of May 2019. Participants reported they and their other children slept in 28 dwellings during the study. The median dwelling occupancy, defined as people sleeping in the same dwelling on the previous night, was ten (range: 3.5-25). Participants who completed at least three responses (n = 8) slept in a median of three dwellings (range: 2-9). Each month, a median of 28% (range: 0-63%) of the participants travelled out of the community. Including these data in disease transmission models amplified estimates of infectious disease spread in the study community, compared to models parameterized using census data. CONCLUSIONS: The lack of data on mixing patterns in populations where households can be organized across dwellings may impact the accuracy of infectious disease models for these communities and the efficacy of public health actions they inform.

Modelling the effect of within-host dynamics on the diversity of a multi-strain pathogen.

Multi-strain pathogens such as Group A Streptococcus, Streptococcus pneumoniae, and Staphylococcus aureus cause millions of infections each year with a substantial health burden. Control of multi-strain pathogens can be complicated by the high strain diversity often observed in endemic settings. It is not well understood how high strain diversity is maintained in populations, given that they compete with each other both directly (within an individual host) and indirectly (via host immunity). Previous modelling studies have investigated how indirect competition affects the prevalence and diversity of strains. However, these studies often make simplifying assumptions about the direct competition that occurs within hosts. Currently, little data is available to validate these assumptions, hence there is a need to clarify how sensitive model outputs are to these assumptions. In this study, we compare the dynamics of multi-strain pathogens under different assumptions about direct competition between strains using an agent-based model. We find that the assumptions made about direct competition can affect the epidemiological dynamics, particularly when there is no long-term immunity following infections and a low rate of importation of non-circulating strains. Our results suggest that while direct and indirect competition can each decrease strain diversity when they act in isolation, they may increase strain diversity when they act together. This finding highlights the importance of examining sensitivity to assumptions about strain competition. In particular, omitting consideration of direct competition can lead to inaccurate estimates of the likely effectiveness of control strategies as changes in strain diversity shift the level of direct strain competition.

The efficacy of sampling strategies for estimating scabies prevalence.

BACKGROUND: Estimating community level scabies prevalence is crucial for targeting interventions to areas of greatest need. The World Health Organisation recommends sampling at the unit of households or schools, but there is presently no standardised approach to scabies prevalence assessment. Consequently, a wide range of sampling sizes and methods have been used. As both prevalence and drivers of transmission vary across populations, there is a need to understand how sampling strategies for estimating scabies prevalence interact with local epidemiology to affect the accuracy of prevalence estimates. METHODS: We used a simulation-based approach to compare the efficacy of different scabies sampling strategies. First, we generated synthetic populations broadly representative of remote Australian Indigenous communities and assigned a scabies status to individuals to achieve a specified prevalence using different assumptions about scabies epidemiology. Second, we calculated an observed prevalence for different sampling methods and sizes. RESULTS: The distribution of prevalence in subpopulation groups can vary substantially when the underlying scabies assignment method changes. Across all of the scabies assignment methods combined, the simple random sampling method produces the narrowest 95% confidence interval for all sample sizes. The household sampling method introduces higher variance compared to simple random sampling when the assignment of scabies includes a household-specific component. The school sampling method overestimates community prevalence when the assignment of scabies includes an age-specific component. DISCUSSION: Our results indicate that there are interactions between transmission assumptions and surveillance strategies, emphasizing the need for understanding scabies transmission dynamics. We suggest using the simple random sampling method for estimating scabies prevalence. Our approach can be adapted to various populations and diseases.

Modelling testing and response strategies for COVID-19 outbreaks in remote Australian Aboriginal communities.

BACKGROUND: Remote Australian Aboriginal and Torres Strait Islander communities have potential to be severely impacted by COVID-19, with multiple factors predisposing to increased transmission and disease severity. Our modelling aims to inform optimal public health responses. METHODS: An individual-based simulation model represented SARS-CoV2 transmission in communities ranging from 100 to 3500 people, comprised of large, interconnected households. A range of strategies for case finding, quarantining of contacts, testing, and lockdown were examined, following the silent introduction of a case. RESULTS: Multiple secondary infections are likely present by the time the first case is identified. Quarantine of close contacts, defined by extended household membership, can reduce peak infection prevalence from 60 to 70% to around 10%, but subsequent waves may occur when community mixing resumes. Exit testing significantly reduces ongoing transmission. Concurrent lockdown of non-quarantined households for 14 days is highly effective for epidemic control and reduces overall testing requirements; peak prevalence of the initial outbreak can be constrained to less than 5%, and the final community attack rate to less than 10% in modelled scenarios. Lockdown also mitigates the effect of a delay in the initial response. Compliance with lockdown must be at least 80-90%, however, or epidemic control will be lost. CONCLUSIONS: A SARS-CoV-2 outbreak will spread rapidly in remote communities. Prompt case detection with quarantining of extended-household contacts and a 14 day lockdown for all other residents, combined with exit testing for all, is the most effective strategy for rapid containment. Compliance is crucial, underscoring the need for community supported, culturally sensitive responses.

A model of population dynamics with complex household structure and mobility: implications for transmission and control of communicable diseases.

Households are known to be high-risk locations for the transmission of communicable diseases. Numerous modelling studies have demonstrated the important role of households in sustaining both communicable diseases outbreaks and endemic transmission, and as the focus for control efforts. However, these studies typically assume that households are associated with a single dwelling and have static membership. This assumption does not appropriately reflect households in some populations, such as those in remote Australian Aboriginal and Torres Strait Islander communities, which can be distributed across more than one physical dwelling, leading to the occupancy of individual dwellings changing rapidly over time. In this study, we developed an individual-based model of an infectious disease outbreak in communities with demographic and household structure reflective of a remote Australian Aboriginal community. We used the model to compare the dynamics of unmitigated outbreaks, and outbreaks constrained by a household-focused prophylaxis intervention, in communities exhibiting fluid vs. stable dwelling occupancy. We found that fluid dwelling occupancy can lead to larger and faster outbreaks in modelled scenarios, and may interfere with the effectiveness of household-focused interventions. Our findings suggest that while short-term restrictions on movement between dwellings may be beneficial during outbreaks, in the longer-term, strategies focused on reducing household crowding may be a more effective way to reduce the risk of severe outbreaks occurring in populations with fluid dwelling occupancy.

Epidemiological consequences of enduring strain-specific immunity requiring repeated episodes of infection.

Group A Streptococcus (GAS) skin infections are caused by a diverse array of strain types and are highly prevalent in disadvantaged populations. The role of strain-specific immunity in preventing GAS infections is poorly understood, representing a critical knowledge gap in vaccine development. A recent GAS murine challenge study showed evidence that sterilising strain-specific and enduring immunity required two skin infections by the same GAS strain within three weeks. This mechanism of developing enduring immunity may be a significant impediment to the accumulation of immunity in populations. We used an agent-based mathematical model of GAS transmission to investigate the epidemiological consequences of enduring strain-specific immunity developing only after two infections with the same strain within a specified interval. Accounting for uncertainty when correlating murine timeframes to humans, we varied this maximum inter-infection interval from 3 to 420 weeks to assess its impact on prevalence and strain diversity, and considered additional scenarios where no maximum inter-infection interval was specified. Model outputs were compared with longitudinal GAS surveillance observations from northern Australia, a region with endemic infection. We also assessed the likely impact of a targeted strain-specific multivalent vaccine in this context. Our model produced patterns of transmission consistent with observations when the maximum inter-infection interval for developing enduring immunity was 19 weeks. Our vaccine analysis suggests that the leading multivalent GAS vaccine may have limited impact on the prevalence of GAS in populations in northern Australia if strain-specific immunity requires repeated episodes of infection. Our results suggest that observed GAS epidemiology from disease endemic settings is consistent with enduring strain-specific immunity being dependent on repeated infections with the same strain, and provide additional motivation for relevant human studies to confirm the human immune response to GAS skin infection.

The Role of Pleiotropy in the Evolutionary Maintenance of Positive Niche Construction.

Organisms often modify their environments to their advantage through a process of niche construction. Environments that are improved through positive niche construction can be viewed as a public good. If free riders appear that do not contribute to the shared resource and therefore do not incur any associated costs, the constructed niche may become degraded, resulting in a tragedy of the commons and the extinction of niche constructors. Niche construction can persist if free riders are excluded, for example, if niche constructors monopolize the resource they produce to a sufficient degree. We suggest, however, that the problem of free riders remains because it is possible that nonniche constructors with an enhanced ability to access the resource appear and invade a population of constructors. Using mathematical models we show that positive niche construction can be maintained if it is inextricably linked to a mechanism that makes free riding costly, such as a trait that confers a benefit to only niche constructors. We discuss this finding in terms of genetic interactions and illustrate the principle with a two-locus model. We conclude that positive niche construction can both evolve and be maintained when it has other beneficial effects via pleiotropy. This situation may apply generally to the evolutionary maintenance of cooperation.

Implications of asymptomatic carriers for infectious disease transmission and control.

For infectious pathogens such as Staphylococcus aureus and Streptococcus pneumoniae, some hosts may carry the pathogen and transmit it to others, yet display no symptoms themselves. These asymptomatic carriers contribute to the spread of disease but go largely undetected and can therefore undermine efforts to control transmission. Understanding the natural history of carriage and its relationship to disease is important for the design of effective interventions to control transmission. Mathematical models of infectious diseases are frequently used to inform decisions about control and should therefore accurately capture the role played by asymptomatic carriers. In practice, incorporating asymptomatic carriers into models is challenging due to the sparsity of direct evidence. This absence of data leads to uncertainty in estimates of model parameters and, more fundamentally, in the selection of an appropriate model structure. To assess the implications of this uncertainty, we systematically reviewed published models of carriage and propose a new model of disease transmission with asymptomatic carriage. Analysis of our model shows how different assumptions about the role of asymptomatic carriers can lead to different conclusions about the transmission and control of disease. Critically, selecting an inappropriate model structure, even when parameters are correctly estimated, may lead to over- or under-estimates of intervention effectiveness. Our results provide a more complete understanding of the role of asymptomatic carriers in transmission and highlight the importance of accurately incorporating carriers into models used to make decisions about disease control.

Persistent infections in immunocompromised hosts are rarely sources of new pathogen variants.

Many viruses, including human norovirus and influenza, cause self-limiting diseases of short duration. However, infection by the same viruses in an immunocompromised host can result in prolonged illness in the absence of effective treatment. Such persistent infections are often characterized by increased genetic diversity with potentially elevated rates of evolution compared to acute infections, leading to suggestions that immunocompromised hosts represent an important reservoir for the emergence of novel viral variants. Here, we develop a mathematical model that combines epidemiological dynamics with within-host evolution to quantify the relative contribution of immunocompromised hosts to the overall rate of pathogen evolution. Using human norovirus as a case study we show that the majority of evolutionary substitutions are expected to occur in acute infections of immunocompetent hosts. Hence, despite their potential to generate a high level of diversity, infections of immunocompromised hosts likely contribute less to the evolution and emergence of new genetic variants at the epidemiological scale because such hosts are rare and tend to be isolated. This result is robust to variation in key parameters, including the proportion of the population immunocompromised, and provides a means to understand the adaptive significance of mutations that arise during chronic infections in immunocompromised hosts.

Tracking the evolution of cancer cell populations through the mathematical lens of phenotype-structured equations.

BACKGROUND: A thorough understanding of the ecological and evolutionary mechanisms that drive the phenotypic evolution of neoplastic cells is a timely and key challenge for the cancer research community. In this respect, mathematical modelling can complement experimental cancer research by offering alternative means of understanding the results of in vitro and in vivo experiments, and by allowing for a quick and easy exploration of a variety of biological scenarios through in silico studies. RESULTS: To elucidate the roles of phenotypic plasticity and selection pressures in tumour relapse, we present here a phenotype-structured model of evolutionary dynamics in a cancer cell population which is exposed to the action of a cytotoxic drug. The analytical tractability of our model allows us to investigate how the phenotype distribution, the level of phenotypic heterogeneity, and the size of the cell population are shaped by the strength of natural selection, the rate of random epimutations, the intensity of the competition for limited resources between cells, and the drug dose in use. CONCLUSIONS: Our analytical results clarify the conditions for the successful adaptation of cancer cells faced with environmental changes. Furthermore, the results of our analyses demonstrate that the same cell population exposed to different concentrations of the same cytotoxic drug can take different evolutionary trajectories, which culminate in the selection of phenotypic variants characterised by different levels of drug tolerance. This suggests that the response of cancer cells to cytotoxic agents is more complex than a simple binary outcome, i.e., extinction of sensitive cells and selection of highly resistant cells. Also, our mathematical results formalise the idea that the use of cytotoxic agents at high doses can act as a double-edged sword by promoting the outgrowth of drug resistant cellular clones. Overall, our theoretical work offers a formal basis for the development of anti-cancer therapeutic protocols that go beyond the 'maximum-tolerated-dose paradigm', as they may be more effective than traditional protocols at keeping the size of cancer cell populations under control while avoiding the expansion of drug tolerant clones. REVIEWERS: This article was reviewed by Angela Pisco, Sébastien Benzekry and Heiko Enderling.

Controlled fire use in early humans might have triggered the evolutionary emergence of tuberculosis.

Tuberculosis (TB) is caused by the Mycobacterium tuberculosis complex (MTBC), a wildly successful group of organisms and the leading cause of death resulting from a single bacterial pathogen worldwide. It is generally accepted that MTBC established itself in human populations in Africa and that animal-infecting strains diverged from human strains. However, the precise causal factors of TB emergence remain unknown. Here, we propose that the advent of controlled fire use in early humans created the ideal conditions for the emergence of TB as a transmissible disease. This hypothesis is supported by mathematical modeling together with a synthesis of evidence from epidemiology, evolutionary genetics, and paleoanthropology.

Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation.

BACKGROUND: Drug-induced drug resistance in cancer has been attributed to diverse biological mechanisms at the individual cell or cell population scale, relying on stochastically or epigenetically varying expression of phenotypes at the single cell level, and on the adaptability of tumours at the cell population level. SCOPE OF REVIEW: We focus on intra-tumour heterogeneity, namely between-cell variability within cancer cell populations, to account for drug resistance. To shed light on such heterogeneity, we review evolutionary mechanisms that encompass the great evolution that has designed multicellular organisms, as well as smaller windows of evolution on the time scale of human disease. We also present mathematical models used to predict drug resistance in cancer and optimal control methods that can circumvent it in combined therapeutic strategies. MAJOR CONCLUSIONS: Plasticity in cancer cells, i.e., partial reversal to a stem-like status in individual cells and resulting adaptability of cancer cell populations, may be viewed as backward evolution making cancer cell populations resistant to drug insult. This reversible plasticity is captured by mathematical models that incorporate between-cell heterogeneity through continuous phenotypic variables. Such models have the benefit of being compatible with optimal control methods for the design of optimised therapeutic protocols involving combinations of cytotoxic and cytostatic treatments with epigenetic drugs and immunotherapies. GENERAL SIGNIFICANCE: Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics. This article is part of a Special Issue entitled "System Genetics" Guest Editor: Dr. Yudong Cai and Dr. Tao Huang.

The emergence of latent infection in the early evolution of Mycobacterium tuberculosis.

Mycobacterium tuberculosis has an unusual natural history in that the vast majority of its human hosts enter a latent state that is both non-infectious and devoid of any symptoms of disease. From the pathogen perspective, it seems counterproductive to relinquish reproductive opportunities to achieve a détente with the host immune response. However, a small fraction of latent infections reactivate to the disease state. Thus, latency has been argued to provide a safe harbour for future infections which optimizes the persistence of M. tuberculosis in human populations. Yet, if a pathogen begins interactions with humans as an active disease without latency, how could it begin to evolve latency properties without incurring an immediate reproductive disadvantage? We address this question with a mathematical model. Results suggest that the emergence of tuberculosis latency may have been enabled by a mechanism akin to cryptic genetic variation in that detrimental latency properties were hidden from natural selection until their expression became evolutionarily favoured.

Dissecting the dynamics of epigenetic changes in phenotype-structured populations exposed to fluctuating environments.

An enduring puzzle in evolutionary biology is to understand how individuals and populations adapt to fluctuating environments. Here we present an integro-differential model of adaptive dynamics in a phenotype-structured population whose fitness landscape evolves in time due to periodic environmental oscillations. The analytical tractability of our model allows for a systematic investigation of the relative contributions of heritable variations in gene expression, environmental changes and natural selection as drivers of phenotypic adaptation. We show that environmental fluctuations can induce the population to enter an unstable and fluctuation-driven epigenetic state. We demonstrate that this can trigger the emergence of oscillations in the size of the population, and we establish a full characterisation of such oscillations. Moreover, the results of our analyses provide a formal basis for the claim that higher rates of epimutations can bring about higher levels of intrapopulation heterogeneity, whilst intense selection pressures can deplete variation in the phenotypic pool of asexual populations. Finally, our work illustrates how the dynamics of the population size is led by a strong synergism between the rate of phenotypic variation and the frequency of environmental oscillations, and identifies possible ecological conditions that promote the maximisation of the population size in fluctuating environments.

Mathematical model reveals how regulating the three phases of T-cell response could counteract immune evasion.

T cells are key players in immune action against the invasion of target cells expressing non-self antigens. During an immune response, antigen-specific T cells dynamically sculpt the antigenic distribution of target cells, and target cells concurrently shape the host's repertoire of antigen-specific T cells. The succession of these reciprocal selective sweeps can result in 'chase-and-escape' dynamics and lead to immune evasion. It has been proposed that immune evasion can be countered by immunotherapy strategies aimed at regulating the three phases of the immune response orchestrated by antigen-specific T cells: expansion, contraction and memory. Here, we test this hypothesis with a mathematical model that considers the immune response as a selection contest between T cells and target cells. The outcomes of our model suggest that shortening the duration of the contraction phase and stabilizing as many T cells as possible inside the long-lived memory reservoir, using dual immunotherapies based on the cytokines interleukin-7 and/or interleukin-15 in combination with molecular factors that can keep the immunomodulatory action of these interleukins under control, should be an important focus of future immunotherapy research.