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Maedi-visna (MV) is a complex lentiviral disease syndrome characterised by long immunological and clinical latencies and chronic progressive inflammatory pathology. Incurable at the individual level, it is widespread in most sheep-keeping countries, and is a cause of lost production and poor animal welfare. Culling seropositive animals is the main means of control, but it might be possible to manage virus transmission effectively if its epidemiology was better quantified. We derive a mathematical epidemiological model of the temporal distributions of seroconversion probabilities and estimate susceptibility, transmission rate and latencies in three serological datasets. We demonstrate the existence of epidemiological latency, which has not explicitly been recognised in the SRLV literaure. This time delay between infection and infectiousness apparently exceeds the delay between infection and seroconversion. Poor body condition was associated with more rapid seroconversion, but not with a higher probability of infection. We estimate transmission rates amongst housed sheep to be at about 1,000 times faster than when sheep were at grass, when transmission was negligible. Maternal transmission has only a small role in transmission, because lambs from infected ewes have a low probability of being infected directly by them, and only a small proportion of lambs need be retained to maintain flock size. Our results show that MV is overwhelmingly a disease of housing, where sheep are kept in close proximity. Prevalence of MV is likely to double each year from an initial low incidence in housed flocks penned in typically-sized groups of sheep (c. 50) for even a few days per year. Ewes kept entirely at grass are unlikely to experience transmission frequently enough for MV to persist, and pre-existing infection should die out as older ewes are replaced, thereby essentially curing the flock.

Circadian rhythms enable organisms to synchronise the processes underpinning survival and reproduction to anticipate daily changes in the external environment. Recent work shows that daily (circadian) rhythms also enable parasites to maximise fitness in the context of ecological interactions with their hosts. Because parasite rhythms matter for their fitness, understanding how they are regulated could lead to innovative ways to reduce the severity and spread of diseases. Here, we examine how host circadian rhythms influence rhythms in the asexual replication of malaria parasites. Asexual replication is responsible for the severity of malaria and fuels transmission of the disease, yet, how parasite rhythms are driven remains a mystery. We perturbed feeding rhythms of hosts by 12 hours (i.e. diurnal feeding in nocturnal mice) to desynchronise the host’s peripheral oscillators from the central, light-entrained oscillator in the brain and their rhythmic outputs. We demonstrate that the rhythms of rodent malaria parasites in day-fed hosts become inverted relative to the rhythms of parasites in night-fed hosts. Our results reveal that the host’s peripheral rhythms (associated with the timing of feeding and metabolism), but not rhythms driven by the central, light-entrained circadian oscillator in the brain, determine the timing (phase) of parasite rhythms. Further investigation reveals that parasite rhythms correlate closely with blood glucose rhythms. In addition, we show that parasite rhythms resynchronise to the altered host feeding rhythms when food availability is shifted, which is not mediated through rhythms in the host immune system. Our observations suggest that parasites actively control their developmental rhythms. Finally, counter to expectation, the severity of disease symptoms expressed by hosts was not affected by desynchronisation of their central and peripheral rhythms. Our study at the intersection of disease ecology and chronobiology opens up a new arena for studying host-parasite-vector coevolution and has broad implications for applied bioscience., Author summary How cycles of asexual replication by malaria parasites are coordinated to occur in synchrony with the circadian rhythms of the host is a long-standing mystery. We reveal that rhythms associated with the time-of-day that hosts feed are responsible for the timing of rhythms in parasite development. Specifically, we altered host feeding time to phase-shift peripheral rhythms, whilst leaving rhythms driven by the central circadian oscillator in the brain unchanged. We found that parasite developmental rhythms remained synchronous but changed their phase, by 12 hours, to follow the timing of host feeding. Furthermore, our results suggest that parasites themselves schedule rhythms in their replication to coordinate with rhythms in glucose in the host’s blood, rather than have rhythms imposed upon them by, for example, host immune responses. Our findings reveal a novel relationship between hosts and parasites that if disrupted, could reduce both the severity and transmission of malaria infection.

On average, more than two new species of human virus are reported every year. We constructed the cumulative species discovery curve for human viruses going back to 1901. We fitted a statistical model to these data; the shape of the curve strongly suggests that the process of virus discovery is far from complete. We generated a 95% credible interval for the pool of as yet undiscovered virus species of 38–562. We extrapolated the curve and generated an estimate of 10–40 new species to be discovered by 2020. Although we cannot predict the level of health threat that these new viruses will present, we conclude that novel virus species must be anticipated in public health planning. More systematic virus discovery programmes, covering both humans and potential animal reservoirs of human viruses, should be considered.

Most of the mathematical models that were developed to study the UK 2001 foot-and-mouth disease epidemic assumed that the infectiousness of infected premises was constant over their infectious periods. However, there is some controversy over whether this assumption is appropriate. Uncertainty about which farm infected which in 2001 means that the only method to determine if there were trends in farm infectiousness is the fitting of mechanistic mathematical models to the epidemic data. The parameter values that are estimated using this technique, however, may be influenced by missing and inaccurate data. In particular to the UK 2001 epidemic, this includes unreported infectives, inaccurate farm infection dates and unknown farm latent periods. Here, we show that such data degradation prevents successful determination of trends in farm infectiousness.

Previous studies suggest that protective immunity against Schistosoma haematobium is primarily stimulated by antigens from dying worms. Praziquantel treatment kills adult worms, boosting antigen exposure and protective antibody levels. Current schistosomiasis control efforts use repeated mass drug administration (MDA) of praziquantel to reduce morbidity, and may also reduce transmission. The long-term impact of MDA upon protective immunity, and subsequent effects on infection dynamics, are not known. A stochastic individual-based model describing levels of S. haematobium worm burden, egg output and protective parasite-specific antibody, which has previously been fitted to cross-sectional and short-term post-treatment egg count and antibody patterns, was used to predict dynamics of measured egg output and antibody during and after a 5-year MDA campaign. Different treatment schedules based on current World Health Organisation recommendations as well as different assumptions about reductions in transmission were investigated. We found that antibody levels were initially boosted by MDA, but declined below pre-intervention levels during or after MDA if protective immunity was short-lived. Following cessation of MDA, our models predicted that measured egg counts could sometimes overshoot pre-intervention levels, even if MDA had had no effect on transmission. With no reduction in transmission, this overshoot occurred if protective immunity was short-lived. This implies that disease burden may temporarily increase following discontinuation of treatment, even in the absence of any reduction in the overall transmission rate. If MDA was additionally assumed to reduce transmission, a larger overshoot was seen across a wide range of parameter combinations, including those with longer-lived protective immunity. MDA may reduce population levels of immunity to urogenital schistosomiasis in the long-term (3–10 years), particularly if transmission is reduced. If MDA is stopped while S. haematobium is still being transmitted, large rebounds (up to a doubling) in egg counts could occur., Author Summary Urogenital schistosomiasis, caused by schistosome blood flukes, infects more than 100 million people in sub-Saharan Africa. Current control efforts involve regularly treating all school-aged children with the drug praziquantel, which kills schistosome worms. Earlier work by our group suggests that protective immunity against schistosomes is mainly stimulated by dying worms, and that in the short term, praziquantel treatment boosts immunity through killing worms. The longer-term impact upon the development of protective immunity is unknown. In this paper, we used a mathematical model which was able to replicate short-term patterns of infection and antibody to predict the long-term changes in antibody and infection levels that would occur during and after a 5-year treatment programme. We found that the longevity of protective immunity was particularly influential. Short-lived protective immunity was associated with levels of protective antibody declining below pre-treatment levels in the long term, and also with an increase in measured infection levels (eggs in urine) to peak above pre-treatment levels after the treatment programme finished. Antibody declines and infection peaks post-treatment were also predicted if treatment programmes reduced schistosome transmission. These results highlight the possible negative consequences of ceasing mass treatment programmes once they have commenced.

We test models for the evolution of helical regions of RNA sequences, where the base pairing constraint leads to correlated compensatory substitutions occurring on either side of the pair. These models are of three types: 6-state models include only the four Watson-Crick pairs plus GU and UG; 7-state models include a single mismatch state that combines all of the 10 possible mismatches; 16-state models treat all mismatch states separately. We analyzed a set of eubacterial ribosomal RNA sequences with a well-established phylogenetic tree structure. For each model, the maximum-likelihood values of the parameters were obtained. The models were compared using the Akaike information criterion, the likelihood-ratio test, and Cox’s test. With a high significance level, models that permit a nonzero rate of double substitutions performed better than those that assume zero double substitution rate. Some models assume symmetry between GC and CG, between AU and UA, and between GU and UG. Models that relaxed this symmetry assumption performed slightly better, but the tests did not all agree on the significance level. The most general time-reversible model significantly outperformed any of the simplifications. We consider the relative merits of all these models for molecular phylogenetics.

Background Marek's disease virus (MDV) is an economically important oncogenic herpesvirus of poultry. Since the 1960s, increasingly virulent strains have caused continued poultry industry production losses worldwide. To understand the mechanisms of this virulence evolution and to evaluate the epidemiological consequences of putative control strategies, it is imperative to understand how virulence is defined and how this correlates with host mortality and infectiousness during MDV infection. We present a mathematical approach to quantify key epidemiological parameters. Host lifespan, virus latent periods and host viral shedding rates were estimated for unvaccinated and vaccinated birds, infected with one of three MDV strains. The strains had previously been pathotyped to assign virulence scores according to pathogenicity of strains in hosts. Results Our analyses show that strains of higher virulence have a higher viral shedding rate, and more rapidly kill hosts. Vaccination enhances host life expectancy but does not significantly reduce the shedding rate of the virus. While the primary latent period of the virus does not vary with challenge strain nor vaccine treatment of host, the time until the maximum viral shedding rate is increased with vaccination. Conclusions Our approach provides the tools necessary for a formal analysis of the evolution of virulence in MDV, and potentially simpler and cheaper approaches to comparing the virulence of MDV strains.

Urogenital schistosomiasis is a tropical disease infecting more than 100 million people in sub-Saharan Africa. Individuals in endemic areas endure repeated infections with long-lived schistosome worms, and also encounter larval and egg stages of the life cycle. Protective immunity against infection develops slowly with age. Distinctive age-related patterns of infection and specific antibody responses are seen in endemic areas, including an infection ‘peak shift’ and a switch in the antibody types produced. Deterministic models describing changing levels of infection and antibody with age in homogeneously exposed populations were developed to identify the key mechanisms underlying the antibody switch, and to test two theories for the slow development of protective immunity: that (i) exposure to dying (long-lived) worms, or (ii) experience of a threshold level of antigen, is necessary to stimulate protective antibody. Different model structures were explored, including alternative stages of the life cycle as the main antigenic source and the principal target of protective antibody, different worm survival distributions, antigen thresholds and immune cross-regulation. Models were identified which could reproduce patterns of infection and antibody consistent with field data. Models with dying worms as the main source of protective antigen could reproduce all of these patterns, but so could some models with other continually-encountered life stages acting as the principal antigen source. An antigen threshold enhanced the ability of the model to replicate these patterns, but was not essential for it to do so. Models including either non-exponential worm survival or cross-regulation were more likely to be able to reproduce field patterns, but neither of these was absolutely required. The combination of life cycle stage stimulating, and targeted by, antibody was found to be critical in determining whether models could successfully reproduce patterns in the data, and a number of combinations were excluded as being inconsistent with field data., Author Summary Urogenital schistosomiasis is a tropical infectious disease caused by schistosome blood flukes, infecting more than 100 million people in sub-Saharan Africa. Protective immunity develops against schistosomes, but takes many years to do so, with children acquiring multiple infections with long-lived parasites. It is important to understand how this protection develops, both to aid vaccine development, and to understand the long-term implications of other control strategies which may reduce or alter natural exposure to the parasite. We used mathematical models to investigate possible explanations for this slow development of protection, including the possibility that when worms die (after surviving in the host for 3–10 years) they release large quantities of the molecules needed to stimulate a protective immune response, or the idea that an individual's infection burden needs to exceed a threshold number of parasites before they mount a protective immune response. We found that these mechanisms were consistent with patterns of levels of infection and antibody measured in populations with schistosome infection, but that neither was essential to explain these patterns. We found that the combination of the stage of the parasite life cycle which stimulated protective immunity, and the life cycle stage targeted by this immunity, was critical.

Background Key to the control of pandemic influenza are surveillance systems that raise alarms rapidly and sensitively. In addition, they must minimise false alarms during a normal influenza season. We develop a method that uses historical syndromic influenza data from the existing surveillance system 'SERVIS' (Scottish Enhanced Respiratory Virus Infection Surveillance) for influenza-like illness (ILI) in Scotland. Methods We develop an algorithm based on the weekly case ratio (WCR) of reported ILI cases to generate an alarm for pandemic influenza. From the seasonal influenza data from 13 Scottish health boards, we estimate the joint probability distribution of the country-level WCR and the number of health boards showing synchronous increases in reported influenza cases over the previous week. Pandemic cases are sampled with various case reporting rates from simulated pandemic influenza infections and overlaid with seasonal SERVIS data from 2001 to 2007. Using this combined time series we test our method for speed of detection, sensitivity and specificity. Also, the 2008-09 SERVIS ILI cases are used for testing detection performances of the three methods with a real pandemic data. Results We compare our method, based on our simulation study, to the moving-average Cumulative Sums (Mov-Avg Cusum) and ILI rate threshold methods and find it to be more sensitive and rapid. For 1% case reporting and detection specificity of 95%, our method is 100% sensitive and has median detection time (MDT) of 4 weeks while the Mov-Avg Cusum and ILI rate threshold methods are, respectively, 97% and 100% sensitive with MDT of 5 weeks. At 99% specificity, our method remains 100% sensitive with MDT of 5 weeks. Although the threshold method maintains its sensitivity of 100% with MDT of 5 weeks, sensitivity of Mov-Avg Cusum declines to 92% with increased MDT of 6 weeks. For a two-fold decrease in the case reporting rate (0.5%) and 99% specificity, the WCR and threshold methods, respectively, have MDT of 5 and 6 weeks with both having sensitivity close to 100% while the Mov-Avg Cusum method can only manage sensitivity of 77% with MDT of 6 weeks. However, the WCR and Mov-Avg Cusum methods outperform the ILI threshold method by 1 week in retrospective detection of the 2009 pandemic in Scotland. Conclusions While computationally and statistically simple to implement, the WCR algorithm is capable of raising alarms, rapidly and sensitively, for influenza pandemics against a background of seasonal influenza. Although the algorithm was developed using the SERVIS data, it has the capacity to be used at other geographic scales and for different disease systems where buying some early extra time is critical.

Malarial infection is associated with complex immune and erythropoietic responses in the host. A quantitative understanding of these processes is essential to help inform malaria therapy and for the design of effective vaccines. In this study, we use a statistical model-fitting approach to investigate the immune and erythropoietic responses in Plasmodium chabaudi infections of mice. Three mouse phenotypes (wildtype, T-cell-deficient nude mice, and nude mice reconstituted with T-cells taken from wildtype mice) were infected with one of two parasite clones (AS or AJ). Under a Bayesian framework, we use an adaptive population-based Markov chain Monte Carlo method and fit a set of dynamical models to observed data on parasite and red blood cell (RBC) densities. Model fits are compared using Bayes' factors and parameter estimates obtained. We consider three independent immune mechanisms: clearance of parasitised RBCs (pRBC), clearance of unparasitised RBCs (uRBC), and clearance of parasites that burst from RBCs (merozoites). Our results suggest that the immune response of wildtype mice is associated with less destruction of uRBCs, compared to the immune response of nude mice. There is a greater degree of synchronisation between pRBC and uRBC clearance than between either mechanism and merozoite clearance. In all three mouse phenotypes, control of the peak of parasite density is associated with pRBC clearance. In wildtype mice and AS-infected nude mice, control of the peak is also associated with uRBC clearance. Our results suggest that uRBC clearance, rather than RBC infection, is the major determinant of RBC dynamics from approximately day 12 post-innoculation. During the first 2–3 weeks of blood-stage infection, immune-mediated clearance of pRBCs and uRBCs appears to have a much stronger effect than immune-mediated merozoite clearance. Upregulation of erythropoiesis is dependent on mouse phenotype and is greater in wildtype and reconstitited mice. Our study highlights the informative power of statistically rigorous model-fitting techniques in elucidating biological systems., Author Summary Malaria is a disease caused by a protozoan parasite of the genus Plasmodium. Every year there are around 250 million human cases of malaria, resulting in around a million deaths. Most of the severe cases and deaths are due to Plasmodium falciparum, which is endemic in much of sub-Saharan Africa and other tropical areas. The pathology of malaria is related to the asexual stage of the parasite. Understanding the infection dynamics during this stage is therefore essential to inform malaria treatment and vaccine design. Experimental infections of rodents represent an important first step towards understanding the more complicated human infections. We developed a series of models representing different hypotheses about the main processes regulating the infection dynamics during the asexual stage. Models were fit to data on Plasmodium chabaudi infections of mice, using a Bayesian statistical framework. The accuracy of different models in explaining the RBC and parasite densities was quantified. We identify the role of different types of immune-mediated mechanism, and show that RBC production (erythropoiesis) increases during infection. Differences between mouse phenotypes are explained. Our study highlights the informative power of model-fitting techniques in explaining biological systems.

Rapid detection of infectious disease outbreaks is often crucial for their effective control. One example is highly pathogenic avian influenza (HPAI) such as H5N1 in commercial poultry flocks. There are no quantitative data, however, on how quickly the effects of HPAI infection in poultry flocks can be detected. Here, we study, using an individual-based mathematical model, time to detection in chicken flocks. Detection is triggered when mortality, food or water intake or egg production in layers pass recommended thresholds suggested from the experience of past HPAI outbreaks. We suggest a new threshold for caged flocks—the cage mortality detection threshold—as a more sensitive threshold than current ones. Time to detection is shown to depend nonlinearly on R 0 and is particularly sensitive for R 0 R 0 HPAI strain such as H7N7 over a wide range of flock sizes. Time to detection of the effects of a low R 0 HPAI strain such as H5N1 can be significantly improved, particularly for large flocks, by lowering detection thresholds, and this can be accomplished without causing excessive false alarms in uninfected flocks. The results are discussed in terms of optimizing the design of disease surveillance programmes in general.

Background Models of Foot and Mouth Disease (FMD) transmission have assumed a homogeneous landscape across which Euclidean distance is a suitable measure of the spatial dependency of transmission. This paper investigated features of the landscape and their impact on transmission during the period of predominantly local spread which followed the implementation of the national movement ban during the 2001 UK FMD epidemic. In this study 113 farms diagnosed with FMD which had a known source of infection within 3 km (cases) were matched to 188 control farms which were either uninfected or infected at a later timepoint. Cases were matched to controls by Euclidean distance to the source of infection and farm size. Intervening geographical features and connectivity between the source of infection and case and controls were compared. Results Road distance between holdings, access to holdings, presence of forest, elevation change between holdings and the presence of intervening roads had no impact on the risk of local FMD transmission (p > 0.2). However the presence of linear features in the form of rivers and railways acted as barriers to FMD transmission (odds ratio = 0.507, 95% CIs = 0.297,0.887, p = 0.018). Conclusion This paper demonstrated that although FMD spread can generally be modelled using Euclidean distance and numbers of animals on susceptible holdings, the presence of rivers and railways has an additional protective effect reducing the probability of transmission between holdings.

Since 2001 models of the spread of foot-and-mouth disease, supported by the data from the UK epidemic, have been expounded as some of the best examples of problem-driven epidemic models. These claims are generally based on a comparison between model results and epidemic data at fairly coarse spatio-temporal resolution. Here, we focus on a comparison between model and data at the individual farm level, assessing the potential of the model to predict the infectious status of farms in both the short and long terms. Although the accuracy with which the model predicts farms reporting infection is between 5 and 15%, these low levels are attributable to the expected level of variation between epidemics, and are comparable to the agreement between two independent model simulations. By contrast, while the accuracy of predicting culls is higher (20–30%), this is lower than expected from the comparison between model epidemics. These results generally support the contention that the type of the model used in 2001 was a reliable representation of the epidemic process, but highlight the difficulties of predicting the complex human response, in terms of control strategies to the perceived epidemic risk.

Livestock movement is thought to be a risk factor for the transmission of infectious diseases of farm animals. Simple mathematical models were constructed for the transmission of Escherichia coli serogroup O157 between Scottish cattle farms, and the models were used in a preliminary exploration of factors contributing to the levels of infection reported in the field. The results suggest that cattle movement can make a significant contribution to the observed prevalence of E. coli O157-positive farms, but is not by itself sufficient for the persistence of E. coli O157. The results also suggest that cattle movements involving infected farms with cattle shedding an exceptional amount of E. coli O157, ‘super-shedders’, also make a substantial contribution to the prevalence of infected farms. Simulations indicate that E. coli O157 could have reached the currently observed prevalence levels in less than a decade. Implications and findings from our models are discussed in relation to possible control of E. coli O157 in Scottish cattle.

Background A key challenge for modelling infectious disease dynamics is to understand the spatial spread of infection in real landscapes. This ideally requires a parallel record of spatial epidemic spread and a detailed map of susceptible host density along with relevant transport links and geographical features. Results Here we analyse the most detailed such data to date arising from the UK 2001 foot and mouth epidemic. We show that Euclidean distance between infectious and susceptible premises is a better predictor of transmission risk than shortest and quickest routes via road, except where major geographical features intervene. Conclusion Thus, a simple spatial transmission kernel based on Euclidean distance suffices in most regions, probably reflecting the multiplicity of transmission routes during the epidemic.

Porcine reproductive and respiratory syndrome (PRRS) is one of the most economically significant viral diseases facing the global swine industry. Viremia profiles of PRRS virus challenged pigs reflect the severity and progression of infection within the host and provide crucial information for subsequent control measures. In this study we analyse the largest longitudinal PRRS viremia dataset from an in-vivo experiment. The primary objective was to provide a suitable mathematical description of all viremia profiles with biologically meaningful parameters for quantitative analysis of profile characteristics. The Wood's function, a gamma-type function, and a biphasic extended Wood's function were fit to the individual profiles using Bayesian inference with a likelihood framework. Using maximum likelihood inference and numerous fit criteria, we established that the broad spectrum of viremia trends could be adequately represented by either uni- or biphasic Wood's functions. Three viremic categories emerged: cleared (uni-modal and below detection within 42 days post infection(dpi)), persistent (transient experimental persistence over 42 dpi) and rebound (biphasic within 42 dpi). The convenient biological interpretation of the model parameters estimates, allowed us not only to quantify inter-host variation, but also to establish common viremia curve characteristics and their predictability. Statistical analysis of the profile characteristics revealed that persistent profiles were distinguishable already within the first 21 dpi, whereas it is not possible to predict the onset of viremia rebound. Analysis of the neutralizing antibody(nAb) data indicated that there was a ubiquitous strong response to the homologous PRRSV challenge, but high variability in the range of cross-protection of the nAbs. Persistent pigs were found to have a significantly higher nAb cross-protectivity than pigs that either cleared viremia or experienced rebound within 42 dpi. Our study provides novel insights into the nature and degree of variation of hosts' responses to infection as well as new informative traits for subsequent genomic and modelling studies.

In a discrete-generation, individual-oriented model of predator-prey interactions that exhibits oscillations, we show that the self-structuring of the populations into spiral waves induces a selection pressure for ever-increasing dispersal distances in both populations. As the dispersal distances increase, the sizes of the spatial patterns increase, until they are too large to fit into the limited space. The patterns are then lost and the predators go extinct. This scenario, is, however, not the only outcome. A second selection pressure induced by the spatial boundary can cause reduction of the dispersal distances. Depending on the relative strengths of the two selection pressures, the predators and prey may speciate to give coexistence between short-dispersing boundary quasi-species and far-dispersing spiral quasi-species. Now, when pattern loss occurs, the predators switch to predating on the boundary prey quasi-species and do not go extinct. Also, if the populations reproduce sexually, local gene flow can inhibit the evolution of increasing dispersal distances, and hence the spatial patterns are not lost. Speciation and coexistence can also occur in the sexually reproducing species.

Background and Methodology: Various approaches have been used to investigate how properties of farm contact networks impact on the transmission of infectious diseases. The potential for transmission of an infection through a contact network can be evaluated in terms of the basic reproduction number, R-0. The magnitude of R-0 is related to the mean contact rate of a host, in this case a farm, and is further influenced by heterogeneities in contact rates of individual hosts. The latter can be evaluated as the second order moments of the contact matrix (variances in contact rates, and co-variance between contacts to and from individual hosts). Here we calculate these quantities for the farms in a country-wide livestock network: >15,000 Scottish sheep farms in each of 4 years from July 2003 to June 2007. The analysis is relevant to endemic and chronic infections with prolonged periods of infectivity of affected animals, and uses different weightings of contacts to address disease scenarios of low, intermediate and high animal-level prevalence.Principal Findings and Conclusions: Analysis of networks of Scottish farms via sheep movements from July 2003 to June 2007 suggests that heterogeneities in movement patterns (variances and covariances of rates of movement on and off the farms) make a substantial contribution to the potential for the transmission of infectious diseases, quantified as R-0, within the farm population. A small percentage of farms (80%) and these farms could be efficiently targeted by interventions aimed at reducing spread of diseases via animal movement.

Mathematical modelling has proven an important tool in elucidating and quantifying mechanisms that govern the age structure and population dynamics of red blood cells (RBCs). Here we synthesise ideas from previous experimental data and the mathematical modelling literature with new data in order to test hypotheses and generate new predictions about these mechanisms. The result is a set of competing hypotheses about three intrinsic mechanisms: the feedback from circulating RBC concentration to production rate of immature RBCs (reticulocytes) in bone marrow, the release of reticulocytes from bone marrow into the circulation, and their subsequent ageing and clearance. In addition we examine two mechanisms specific to our experimental system: the effect of phenylhydrazine (PHZ) and blood sampling on RBC dynamics. We performed a set of experiments to quantify the dynamics of reticulocyte proportion, RBC concentration, and erythropoietin concentration in PHZ-induced anaemic mice. By quantifying experimental error we are able to fit and assess each hypothesis against our data and recover parameter estimates using Markov chain Monte Carlo based Bayesian inference. We find that, under normal conditions, about 3% of reticulocytes are released early from bone marrow and upon maturation all cells are released immediately. In the circulation, RBCs undergo random clearance but have a maximum lifespan of about 50 days. Under anaemic conditions reticulocyte production rate is linearly correlated with the difference between normal and anaemic RBC concentrations, and their release rate is exponentially correlated with the same. PHZ appears to age rather than kill RBCs, and younger RBCs are affected more than older RBCs. Blood sampling caused short aperiodic spikes in the proportion of reticulocytes which appear to have a different developmental pathway than normal reticulocytes. We also provide evidence of large diurnal oscillations in serum erythropoietin levels during anaemia., Author Summary Red blood cells are made in the bone marrow and released into the blood stream. Their population is kept at equilibrium by complex negative feedback mechanisms. Genetic diseases, pathogens such as malaria, and extreme environmental changes can alter this equilibrium, either directly by prematurely killing red blood cells or indirectly through disrupting these feedback mechanisms. In this paper we test competing hypotheses about the nature of some of these mechanisms by fitting mathematical models to experimental data. Our results give us a better understanding of the mechanisms that govern the red blood cell population and will improve models of diseases that affect red blood cells.

Malarial infections are often genetically diverse, leading to competitive interactions between parasites. A quantitative understanding of the competition between strains is essential to understand a wide range of issues, including the evolution of virulence and drug resistance. In this study, we use dynamical-model based Bayesian inference to investigate the cause of competitive suppression of an avirulent clone of Plasmodium chabaudi (AS) by a virulent clone (AJ) in immuno-deficient and competent mice. We test whether competitive suppression is caused by clone-specific differences in one or more of the following processes: adaptive immune clearance of merozoites and parasitised red blood cells (RBCs), background loss of merozoites and parasitised RBCs, RBC age preference, RBC infection rate, burst size, and within-RBC interference. These processes were parameterised in dynamical mathematical models and fitted to experimental data. We found that just one parameter , the ratio of background loss rate of merozoites to invasion rate of mature RBCs, needed to be clone-specific to predict the data. Interestingly, was found to be the same for both clones in single-clone infections, but different between the clones in mixed infections. The size of this difference was largest in immuno-competent mice and smallest in immuno-deficient mice. This explains why competitive suppression was alleviated in immuno-deficient mice. We found that competitive suppression acts early in infection, even before the day of peak parasitaemia. These results lead us to argue that the innate immune response clearing merozoites is the most likely, but not necessarily the only, mediator of competitive interactions between virulent and avirulent clones. Moreover, in mixed infections we predict there to be an interaction between the clones and the innate immune response which induces changes in the strength of its clearance of merozoites. What this interaction is unknown, but future refinement of the model, challenged with other datasets, may lead to its discovery., Author Summary Malaria infections often consist of more than one strain of the same parasitic species. Understanding the within-host competition between these various strains is essential to understanding the evolution and epidemiology of drug resistance in malarial infections. The infection process and the competition between strains involve complicated biological processes that are explained by various hypotheses. Mathematical models tested against experimental data provide quantitative measures to compare these hypotheses and enable us to discern the actual biological processes that contribute to the observed dynamics. We use a group of models against experimental data on rodent malaria to test various hypotheses. Such quantitative measures, in understanding rodent malaria, can be considered as a step towards understanding within-host parasite dynamics. Our work presented here demonstrates how confronting mathematical models with data allows the discovery of subtle and novel interactions between hosts and parasites that would be impractical to do in an experiment and allows the rejection of hypotheses that are incorrect. It is our contention that understanding the forces controlling within-host parasite dynamics in well-defined experimental model is a necessary step towards understanding these features in natural infections.