Modeling the Impact of a Highly Potent Plasmodium falciparum Transmission-Blocking Monoclonal Antibody in Areas of Seasonal Malaria Transmission.

Transmission-blocking interventions can play an important role in combating malaria worldwide. Recently, a highly potent Plasmodium falciparum transmission-blocking monoclonal antibody (TB31F) was demonstrated to be safe and efficacious in malaria-naive volunteers. Here we predict the potential public health impact of large-scale implementation of TB31F alongside existing interventions. We developed a pharmaco-epidemiological model, tailored to 2 settings of differing transmission intensity with already established insecticide-treated nets and seasonal malaria chemoprevention interventions. Community-wide annual administration (at 80% coverage) of TB31F over a 3-year period was predicted to reduce clinical incidence by 54% (381 cases averted per 1000 people per year) in a high-transmission seasonal setting, and 74% (157 cases averted per 1000 people per year) in a low-transmission seasonal setting. Targeting school-aged children gave the largest reduction in terms of cases averted per dose. An annual administration of the transmission-blocking monoclonal antibody TB31F may be an effective intervention against malaria in seasonal malaria settings.

Modelling upper respiratory viral load dynamics of SARS-CoV-2.

Relationships between viral load, severity of illness, and transmissibility of virus are fundamental to understanding pathogenesis and devising better therapeutic and prevention strategies for COVID-19. Here we present within-host modelling of viral load dynamics observed in the upper respiratory tract (URT), drawing upon 2172 serial measurements from 605 subjects, collected from 17 different studies. We developed a mechanistic model to describe viral load dynamics and host response and contrast this with simpler mixed-effects regression analysis of peak viral load and its subsequent decline. We observed wide variation in URT viral load between individuals, over 5 orders of magnitude, at any given point in time since symptom onset. This variation was not explained by age, sex, or severity of illness, and these variables were not associated with the modelled early or late phases of immune-mediated control of viral load. We explored the application of the mechanistic model to identify measured immune responses associated with the control of the viral load. Neutralising antibodies correlated strongly with modelled immune-mediated control of viral load amongst subjects who produced neutralising antibodies. Our models can be used to identify host and viral factors which control URT viral load dynamics, informing future treatment and transmission blocking interventions.

Comparative efficacy of two pyrethroid-piperonyl butoxide nets (Olyset Plus and PermaNet 3.0) against pyrethroid resistant malaria vectors: a non-inferiority assessment.

BACKGROUND: Pyrethroid-PBO nets were conditionally recommended for control of malaria transmitted by mosquitoes with oxidase-based pyrethroid-resistance based on epidemiological evidence of additional protective effect with Olyset Plus compared to a pyrethroid-only net (Olyset Net). Entomological studies can be used to assess the comparative performance of other brands of pyrethroid-PBO ITNs to Olyset Plus. METHODS: An experimental hut trial was performed in Cové, Benin to compare PermaNet 3.0 (deltamethrin plus PBO on roof panel only) to Olyset Plus (permethrin plus PBO on all panels) against wild pyrethroid-resistant Anopheles gambiae sensu lato (s.l.) following World Health Organization (WHO) guidelines. Both nets were tested unwashed and after 20 standardized washes compared to Olyset Net. Laboratory bioassays were also performed to help explain findings in the experimental huts. RESULTS: With unwashed nets, mosquito mortality was higher in huts with PermaNet 3.0 compared to Olyset Plus (41% vs. 28%, P < 0.001). After 20 washes, mortality declined significantly with PermaNet 3.0 (41% unwashed vs. 17% after washing P < 0.001), but not with Olyset Plus (28% unwashed vs. 24% after washing P = 0.433); Olyset Plus induced significantly higher mortality than PermaNet 3.0 and Olyset Net after 20 washes. PermaNet 3.0 showed a higher wash retention of PBO compared to Olyset Plus. A non-inferiority analysis performed with data from unwashed and washed nets together using a margin recommended by the WHO, showed that PermaNet 3.0 was non-inferior to Olyset Plus in terms of mosquito mortality (25% with Olyset Plus vs. 27% with PermaNet 3.0, OR = 1.528, 95%CI = 1.02-2.29) but not in reducing mosquito feeding (25% with Olyset Plus vs. 30% with PermaNet 3.0, OR = 1.192, 95%CI = 0.77-1.84). Both pyrethroid-PBO nets were superior to Olyset Net. CONCLUSION: Olyset Plus outperformed PermaNet 3.0 in terms of its ability to cause greater margins of improved mosquito mortality compared to a standard pyrethroid net, after multiple standardized washes. However, using a margin of non-inferiority defined by the WHO, PermaNet 3.0 was non-inferior to Olyset Plus in inducing mosquito mortality. Considering the low levels of mortality observed and increasing pyrethroid-resistance in West Africa, it is unclear whether either of these nets would demonstrate the same epidemiological impact observed in community trials in East Africa.

The impact of delayed treatment of uncomplicated P. falciparum malaria on progression to severe malaria: A systematic review and a pooled multicentre individual-patient meta-analysis.

BACKGROUND: Delay in receiving treatment for uncomplicated malaria (UM) is often reported to increase the risk of developing severe malaria (SM), but access to treatment remains low in most high-burden areas. Understanding the contribution of treatment delay on progression to severe disease is critical to determine how quickly patients need to receive treatment and to quantify the impact of widely implemented treatment interventions, such as 'test-and-treat' policies administered by community health workers (CHWs). We conducted a pooled individual-participant meta-analysis to estimate the association between treatment delay and presenting with SM. METHODS AND FINDINGS: A search using Ovid MEDLINE and Embase was initially conducted to identify studies on severe Plasmodium falciparum malaria that included information on treatment delay, such as fever duration (inception to 22nd September 2017). Studies identified included 5 case-control and 8 other observational clinical studies of SM and UM cases. Risk of bias was assessed using the Newcastle-Ottawa scale, and all studies were ranked as 'Good', scoring ≥7/10. Individual-patient data (IPD) were pooled from 13 studies of 3,989 (94.1% aged <15 years) SM patients and 5,780 (79.6% aged <15 years) UM cases in Benin, Malaysia, Mozambique, Tanzania, The Gambia, Uganda, Yemen, and Zambia. Definitions of SM were standardised across studies to compare treatment delay in patients with UM and different SM phenotypes using age-adjusted mixed-effects regression. The odds of any SM phenotype were significantly higher in children with longer delays between initial symptoms and arrival at the health facility (odds ratio [OR] = 1.33, 95% CI: 1.07-1.64 for a delay of >24 hours versus ≤24 hours; p = 0.009). Reported illness duration was a strong predictor of presenting with severe malarial anaemia (SMA) in children, with an OR of 2.79 (95% CI:1.92-4.06; p < 0.001) for a delay of 2-3 days and 5.46 (95% CI: 3.49-8.53; p < 0.001) for a delay of >7 days, compared with receiving treatment within 24 hours from symptom onset. We estimate that 42.8% of childhood SMA cases and 48.5% of adult SMA cases in the study areas would have been averted if all individuals were able to access treatment within the first day of symptom onset, if the association is fully causal. In studies specifically recording onset of nonsevere symptoms, long treatment delay was moderately associated with other SM phenotypes (OR [95% CI] >3 to ≤4 days versus ≤24 hours: cerebral malaria [CM] = 2.42 [1.24-4.72], p = 0.01; respiratory distress syndrome [RDS] = 4.09 [1.70-9.82], p = 0.002). In addition to unmeasured confounding, which is commonly present in observational studies, a key limitation is that many severe cases and deaths occur outside healthcare facilities in endemic countries, where the effect of delayed or no treatment is difficult to quantify. CONCLUSIONS: Our results quantify the relationship between rapid access to treatment and reduced risk of severe disease, which was particularly strong for SMA. There was some evidence to suggest that progression to other severe phenotypes may also be prevented by prompt treatment, though the association was not as strong, which may be explained by potential selection bias, sample size issues, or a difference in underlying pathology. These findings may help assess the impact of interventions that improve access to treatment.

Asymptomatic recrudescence after artemether-lumefantrine treatment for uncomplicated falciparum malaria: a systematic review and meta-analysis.

BACKGROUND: In clinical trials of therapy for uncomplicated Plasmodium falciparum, there are usually some patients who fail treatment even in the absence of drug resistance. Treatment failures, which can be due to recrudescence or re-infection, are categorized as 'clinical' or 'parasitological' failures, the former indicating that symptoms have returned. Asymptomatic recrudescence has public health implications for continued malaria transmission and may be important for the spread of drug-resistant malaria. As the number of recrudescences in an individual trial is often low, it is difficult to assess how commonplace asymptomatic recrudescence is, and with what factors it is associated. METHODS: A systematic literature review was carried out on clinical trials of artemether-lumefantrine (AL) in patients seeking treatment for symptomatic uncomplicated falciparum malaria, and information on symptoms during treatment failure was recorded. Only treatment failures examined by polymerase chain reaction (PCR) were included, so as to exclude re-infections. A multivariable Bayesian regression model was used to explore factors potentially explaining the proportion of recrudescent infections which are symptomatic across the trials included in the study. RESULTS: Across 60 published trials, including 9137 malaria patients, 37.8% [95% CIs (26.6-49.4%)] of recrudescences were symptomatic. A positive association was found between transmission intensity and the observed proportion of recrudescences that were asymptomatic. Symptoms were more likely to return in trials that only enrolled children aged < 72 months [odds ratio = 1.62, 95% CIs (1.01, 2.59)]. However, 84 studies had to be excluded from this analysis, as recrudescences were not specified as symptomatic or asymptomatic. CONCLUSIONS: AL, the most widely used treatment for uncomplicated P. falciparum in Africa, remains a highly efficacious drug in most endemic countries. However in the small proportion of patients where AL does not clear parasitaemia, the majority of patients do not develop symptoms again and thus would be unlikely to seek another course of treatment. This continued asymptomatic parasite carriage in patients who have been treated may have implications for drug-resistant parasites being introduced into high-transmissions settings.

Anopheles aquatic development kinetic and adults' longevity through different seasons in laboratory and semi-field conditions in Burkina Faso.

ABSTRACT: BACKGROUND: Anopheles mosquitoes are ectothermic and involved in numerous pathogen transmissions. Their life history traits are influenced by several environmental factors such as temperature, relative humidity and photoperiodicity. Despite extensive investigations of these environmental conditions on vector population ecology, their impact on the different life stages of Anopheles at different seasons in the year remains poorly explored. This study reports the potential impact of these abiotic factors on the immature and adult stages of Anopheles gambiae sensu lato during different seasons. METHODS: Environmental conditions were simulated in the laboratory using incubators to mimic the environmental conditions of two important periods of the year in Burkina Faso: the peak of rainy season (August) and the onset of dry season (December). Eggs from wild An. coluzzii and An. gambiae s.l. were reared separately under each environmental condition. For Anopheles coluzzii or An. gambiae s.l., eggs were equally divided into two groups assigned to the two experimental conditions. Four replicates were carried out for this experiment. Then, egg hatching rate, pupation rate, larval development time, larva-to-pupae development time, adult emergence dynamics and longevity of Anopheles were evaluated. Also, pupae-to-adult development time from wild L3 and L4 Anopheles larvae was estimated under semi-field conditions in December. RESULTS: A better egg hatching rate was recorded overall with conditions mimicking the onset of the dry season compared to the peak of the rainy season. Larval development time and longevity of An. gambiae s.l. female were significantly longer at the onset of the dry season compared than at the peak of the rainy season. Adult emergence was spread over 48 and 96 h at the peak of the rainy season and onset of dry season conditions respectively. This 96h duration in the controlled conditions of December was also observed in the semi-field conditions in December. CONCLUSIONS: The impact of temperature and relative humidity on immature stages and longevity of An. gambiae s.l. adult females differed under both conditions. These findings contribute to a better understanding of vector population dynamics throughout different seasons of the year and may facilitate tailoring of control strategies.

Assessing the variability in experimental hut trials evaluating insecticide-treated nets against malaria vectors.

Experimental hut trials (EHTs) are used to evaluate indoor vector control interventions against malaria vectors in a controlled setting. The level of variability present in the assay will influence whether a given study is well powered to answer the research question being considered. We utilised disaggregated data from 15 previous EHTs to gain insight into the behaviour typically observed. Using simulations from generalised linear mixed models to obtain power estimates for EHTs, we show how factors such as the number of mosquitoes entering the huts each night and the magnitude of included random effects can influence study power. A wide variation in behaviour is observed in both the mean number of mosquitoes collected per hut per night (ranging from 1.6 to 32.5) and overdispersion in mosquito mortality. This variability in mortality is substantially greater than would be expected by chance and should be included in all statistical analyses to prevent false precision of results. We utilise both superiority and non-inferiority trials to illustrate our methodology, using mosquito mortality as the outcome of interest. The framework allows the measurement error of the assay to be reliably assessed and enables the identification of outlier results which could warrant further investigation. EHTs are increasingly playing an important role in the evaluation and regulation of indoor vector control interventions so it is important to ensure that these studies are adequately powered.

Projected health impact of post-discharge malaria chemoprevention among children with severe malarial anaemia in Africa.

Children recovering from severe malarial anaemia (SMA) remain at high risk of readmission and death after discharge from hospital. However, a recent trial found that post-discharge malaria chemoprevention (PDMC) with dihydroartemisinin-piperaquine reduces this risk. We developed a mathematical model describing the daily incidence of uncomplicated and severe malaria requiring readmission among 0-5-year old children after hospitalised SMA. We fitted the model to a multicentre clinical PDMC trial using Bayesian methods and modelled the potential impact of PDMC across malaria-endemic African countries. In the 20 highest-burden countries, we estimate that only 2-5 children need to be given PDMC to prevent one hospitalised malaria episode, and less than 100 to prevent one death. If all hospitalised SMA cases access PDMC in moderate-to-high transmission areas, 38,600 (range 16,900-88,400) malaria-associated readmissions could be prevented annually, depending on access to hospital care. We estimate that recurrent SMA post-discharge constitutes 19% of all SMA episodes in moderate-to-high transmission settings.

Delftia tsuruhatensis TC1 symbiont suppresses malaria transmission by anopheline mosquitoes.

Malaria control demands the development of a wide range of complementary strategies. We describe the properties of a naturally occurring, non-genetically modified symbiotic bacterium, Delftia tsuruhatensis TC1, which was isolated from mosquitoes incapable of sustaining the development of Plasmodium falciparum parasites. D. tsuruhatensis TC1 inhibits early stages of Plasmodium development and subsequent transmission by the Anopheles mosquito through secretion of a small-molecule inhibitor. We have identified this inhibitor to be the hydrophobic molecule harmane. We also found that, on mosquito contact, harmane penetrates the cuticle, inhibiting Plasmodium development. D. tsuruhatensis TC1 stably populates the mosquito gut, does not impose a fitness cost on the mosquito, and inhibits Plasmodium development for the mosquito's life. Contained field studies in Burkina Faso and modeling showed that D. tsuruhatensis TC1 has the potential to complement mosquito-targeted malaria transmission control.

Analysis of blood and nasal epithelial transcriptomes to identify mechanisms associated with control of SARS-CoV-2 viral load in the upper respiratory tract.

OBJECTIVES: The amount of SARS-CoV-2 detected in the upper respiratory tract (URT viral load) is a key driver of transmission of infection. Current evidence suggests that mechanisms constraining URT viral load are different from those controlling lower respiratory tract viral load and disease severity. Understanding such mechanisms may help to develop treatments and vaccine strategies to reduce transmission. Combining mathematical modelling of URT viral load dynamics with transcriptome analyses we aimed to identify mechanisms controlling URT viral load. METHODS: COVID-19 patients were recruited in Spain during the first wave of the pandemic. RNA sequencing of peripheral blood and targeted NanoString nCounter transcriptome analysis of nasal epithelium were performed and gene expression analysed in relation to paired URT viral load samples collected within 15 days of symptom onset. Proportions of major immune cells in blood were estimated from transcriptional data using computational differential estimation. Weighted correlation network analysis (adjusted for cell proportions) and fixed transcriptional repertoire analysis were used to identify associations with URT viral load, quantified as standard deviations (z-scores) from an expected trajectory over time. RESULTS: Eighty-two subjects (50% female, median age 54 years (range 3-73)) with COVID-19 were recruited. Paired URT viral load samples were available for 16 blood transcriptome samples, and 17 respiratory epithelial transcriptome samples. Natural Killer (NK) cells were the only blood cell type significantly correlated with URT viral load z-scores (r = -0.62, P = 0.010). Twenty-four blood gene expression modules were significantly correlated with URT viral load z-score, the most significant being a module of genes connected around IFNA14 (Interferon Alpha-14) expression (r = -0.60, P = 1e-10). In fixed repertoire analysis, prostanoid-related gene expression was significantly associated with higher viral load. In nasal epithelium, only GNLY (granulysin) gene expression showed significant negative correlation with viral load. CONCLUSIONS: Correlations between the transcriptional host response and inter-individual variations in SARS-CoV-2 URT viral load, revealed many molecular mechanisms plausibly favouring or constraining viral replication. Existing evidence corroborates many of these mechanisms, including likely roles for NK cells, granulysin, prostanoids and interferon alpha-14. Inhibition of prostanoid production and administration of interferon alpha-14 may be attractive transmission-blocking interventions.

Predicting the public health impact of a malaria transmission-blocking vaccine.

Transmission-blocking vaccines that interrupt malaria transmission from humans to mosquitoes are being tested in early clinical trials. The activity of such a vaccine is commonly evaluated using membrane-feeding assays. Understanding the field efficacy of such a vaccine requires knowledge of how heavily infected wild, naturally blood-fed mosquitoes are, as this indicates how difficult it will be to block transmission. Here we use data on naturally infected mosquitoes collected in Burkina Faso to translate the laboratory-estimated activity into an estimated activity in the field. A transmission dynamics model is then utilised to predict a transmission-blocking vaccine's public health impact alongside existing interventions. The model suggests that school-aged children are an attractive population to target for vaccination. Benefits of vaccination are distributed across the population, averting the greatest number of cases in younger children. Utilising a transmission-blocking vaccine alongside existing interventions could have a substantial impact against malaria.

Monoclonal antibodies block transmission of genetically diverse Plasmodium falciparum strains to mosquitoes.

Malaria parasite transmission to mosquitoes relies on the uptake of sexual stage parasites during a blood meal and subsequent formation of oocysts on the mosquito midgut wall. Transmission-blocking vaccines (TBVs) and monoclonal antibodies (mAbs) target sexual stage antigens to interrupt human-to-mosquito transmission and may form important tools for malaria elimination. Although most epitopes of these antigens are considered highly conserved, little is known about the impact of natural genetic diversity on the functional activity of transmission-blocking antibodies. Here we measured the efficacy of three mAbs against leading TBV candidates (Pfs48/45, Pfs25 and Pfs230) in transmission assays with parasites from naturally infected donors compared to their efficacy against the strain they were raised against (NF54). Transmission-reducing activity (TRA) was measured as reduction in mean oocyst intensity. mAb 45.1 (α-Pfs48/45) and mAb 4B7 (α-Pfs25) reduced transmission of field parasites from almost all donors with IC80 values similar to NF54. Sequencing of oocysts that survived high mAb concentrations did not suggest enrichment of escape genotypes. mAb 2A2 (α-Pfs230) only reduced transmission of parasites from a minority of the donors, suggesting that it targets a non-conserved epitope. Using six laboratory-adapted strains, we revealed that mutations in one Pfs230 domain correlate with mAb gamete surface binding and functional TRA. Our findings demonstrate that, despite the conserved nature of sexual stage antigens, minor sequence variation can significantly impact the efficacy of transmission-blocking mAbs. Since mAb 45.1 shows high potency against genetically diverse strains, our findings support its further clinical development and may inform Pfs48/45 vaccine design.

The potential public health consequences of COVID-19 on malaria in Africa.

The burden of malaria is heavily concentrated in sub-Saharan Africa (SSA) where cases and deaths associated with COVID-19 are rising1. In response, countries are implementing societal measures aimed at curtailing transmission of SARS-CoV-22,3. Despite these measures, the COVID-19 epidemic could still result in millions of deaths as local health facilities become overwhelmed4. Advances in malaria control this century have been largely due to distribution of long-lasting insecticidal nets (LLINs)5, with many SSA countries having planned campaigns for 2020. In the present study, we use COVID-19 and malaria transmission models to estimate the impact of disruption of malaria prevention activities and other core health services under four different COVID-19 epidemic scenarios. If activities are halted, the malaria burden in 2020 could be more than double that of 2019. In Nigeria alone, reducing case management for 6 months and delaying LLIN campaigns could result in 81,000 (44,000-119,000) additional deaths. Mitigating these negative impacts is achievable, and LLIN distributions in particular should be prioritized alongside access to antimalarial treatments to prevent substantial malaria epidemics.

How delayed and non-adherent treatment contribute to onward transmission of malaria: a modelling study.

INTRODUCTION: Artemether-lumefantrine (AL) is the most widely-recommended treatment for uncomplicated Plasmodium falciparum malaria. Its efficacy has been extensively assessed in clinical trials. In routine healthcare settings, however, its effectiveness can be diminished by delayed access to treatment and poor adherence. As well as affecting clinical outcomes, these factors can lead to increased transmission, which is the focus of this study. METHODS: We extend a within-host model of P. falciparum to include gametocytes, the parasite forms responsible for onward transmission. The model includes a pharmacokinetic-pharmacodynamic model of AL, calibrated against both immature and mature gametocytes using individual-level patient data, to estimate the impact that delayed access and imperfect adherence to treatment can have on onward transmission of the parasite to mosquitoes. RESULTS: Using survey data from seven African countries to determine the time taken to acquire antimalarials following fever increased our estimates of mean total infectivity of a malaria episode by up to 1.5-fold, compared with patients treated after 24 hours. Realistic adherence behaviour, based on data from a monitored cohort in Tanzania, increased the contribution to transmission by 2.2 to 2.4-fold, compared with a perfectly-adherent cohort. This was driven largely by increased rates of treatment failure leading to chronic infection, rather than prolonged gametocytaemia in patients who have slower, but still successful, clearance of parasites after imperfect adherence to treatment. Our model estimated that the mean infectivity of untreated infections was 29-51 times higher than that of treated infections (assuming perfect drug adherence), underlining the importance of improving treatment coverage. CONCLUSION: Using mathematical modelling, we quantify how delayed treatment and non-adherent treatment can increase transmission compared with prompt effective treatment. We also highlight that transmission from the large proportion of infections which never receive treatment is substantially higher than those treated.

Assessing the impact of imperfect adherence to artemether-lumefantrine on malaria treatment outcomes using within-host modelling.

Artemether-lumefantrine (AL) is the most widely-recommended treatment for uncomplicated Plasmodium falciparum malaria worldwide. Its safety and efficacy have been extensively demonstrated in clinical trials; however, its performance in routine health care settings, where adherence to drug treatment is unsupervised and therefore may be suboptimal, is less well characterised. Here we develop a within-host modelling framework for estimating the effects of sub-optimal adherence to AL treatment on clinical outcomes in malaria patients. Our model incorporates the data on the human immune response to the parasite, and AL's pharmacokinetic and pharmacodynamic properties. Utilising individual-level data of adherence to AL in 482 Tanzanian patients as input for our model predicted higher rates of treatment failure than were obtained when adherence was optimal (9% compared to 4%). Our model estimates that the impact of imperfect adherence was worst in children, highlighting the importance of advice to caregivers.

Suppressing escape events in maps of the unit interval with demographic noise.

We explore the properties of discrete-time stochastic processes with a bounded state space, whose deterministic limit is given by a map of the unit interval. We find that, in the mesoscopic description of the system, the large jumps between successive iterates of the process can result in probability leaking out of the unit interval, despite the fact that the noise is multiplicative and vanishes at the boundaries. By including higher-order terms in the mesoscopic expansion, we are able to capture the non-Gaussian nature of the noise distribution near the boundaries, but this does not preclude the possibility of a trajectory leaving the interval. We propose a number of prescriptions for treating these escape events, and we compare the results with those obtained for the metastable behavior of the microscopic model, where escape events are not possible. We find that, rather than truncating the noise distribution, censoring this distribution to prevent escape events leads to results which are more consistent with the microscopic model. The addition of higher moments to the noise distribution does not increase the accuracy of the final results, and it can be replaced by the simpler Gaussian noise.

Turing-like instabilities from a limit cycle.

The Turing instability is a paradigmatic route to pattern formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become unstable when subject to external perturbation. As a consequence, the system evolves towards a stationary, nonhomogeneous attractor. Stable patterns can be also obtained via oscillation quenching of an initially synchronous state of diffusively coupled oscillators. In the literature this is known as the oscillation death phenomenon. Here, we show that oscillation death is nothing but a Turing instability for the first return map of the system in its synchronous periodic state. In particular, we obtain a set of approximated closed conditions for identifying the domain in the parameter space that yields the instability. This is a natural generalization of the original Turing relations, to the case where the homogeneous solution of the examined system is a periodic function of time. The obtained framework applies to systems embedded in continuum space, as well as those defined on a networklike support. The predictive ability of the theory is tested numerically, using different reaction schemes.

Intrinsic noise and two-dimensional maps: quasicycles, quasiperiodicity, and chaos.

We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit of large system sizes is shown to be very well-approximated by a Fokker-Planck-like equation, or equivalently by a set of stochastic difference equations. This formalism is applied to the specific case of two species: one predator species and its prey species. Quasicycles, stochastic cycles sustained and amplified by the demographic noise, previously found in continuous-time predator-prey models are shown to exist, and their behavior predicted from a linear noise analysis is shown to be in very good agreement with simulations. The effects of the noise on other attractors in the corresponding deterministic map, such as periodic cycles, quasiperiodicity, and chaos, are also investigated.

The theory of pattern formation on directed networks.

Dynamical processes on networks have generated widespread interest in recent years. The theory of pattern formation in reaction-diffusion systems defined on symmetric networks has often been investigated, due to its applications in a wide range of disciplines. Here we extend the theory to the case of directed networks, which are found in a number of different fields, such as neuroscience, computer networks and traffic systems. Owing to the structure of the network Laplacian, the dispersion relation has both real and imaginary parts, at variance with the case for a symmetric, undirected network. The homogeneous fixed point can become unstable due to the topology of the network, resulting in a new class of instabilities, which cannot be induced on undirected graphs. Results from a linear stability analysis allow the instability region to be analytically traced. Numerical simulations show travelling waves, or quasi-stationary patterns, depending on the characteristics of the underlying graph.

Synchronization of stochastic oscillators in biochemical systems.

We investigate the synchronization of stochastic oscillations in biochemical models by calculating the complex coherence function within the linear noise approximation. The method is illustrated on a simple example and then applied to study the synchronization of chemical concentrations in social amoeba. The degree to which variation of rate constants in different cells and the volume of the cells affects synchronization of the oscillations is explored and the phase lag calculated. In all cases the analytical results are shown to be in good agreement with those obtained through numerical simulations.