The reproduction number and its probability distribution for stochastic viral dynamics.

We consider stochastic models of individual infected cells. The reproduction number, R, is understood as a random variable representing the number of new cells infected by one initial infected cell in an otherwise susceptible (target cell) population. Variability in R results partly from heterogeneity in the viral burst size (the number of viral progeny generated from an infected cell during its lifetime), which depends on the distribution of cellular lifetimes and on the mechanism of virion release. We analyse viral dynamics models with an eclipse phase: the period of time after a cell is infected but before it is capable of releasing virions. The duration of the eclipse, or the subsequent infectious, phase is non-exponential, but composed of stages. We derive the probability distribution of the reproduction number for these viral dynamics models, and show it is a negative binomial distribution in the case of constant viral release from infectious cells, and under the assumption of an excess of target cells. In a deterministic model, the ultimate in-host establishment or extinction of the viral infection depends entirely on whether the mean reproduction number is greater than, or less than, one, respectively. Here, the probability of extinction is determined by the probability distribution of R, not simply its mean value. In particular, we show that in some cases the probability of infection is not an increasing function of the mean reproduction number.

Using mixture density networks to emulate a stochastic within-host model of Francisella tularensis infection.

For stochastic models with large numbers of states, analytical techniques are often impractical, and simulations time-consuming and computationally demanding. This limitation can hinder the practical implementation of such models. In this study, we demonstrate how neural networks can be used to develop emulators for two outputs of a stochastic within-host model of Francisella tularensis infection: the dose-dependent probability of illness and the incubation period. Once the emulators are constructed, we employ Markov Chain Monte Carlo sampling methods to parameterize the within-host model using records of human infection. This inference is only possible through the use of a mixture density network to emulate the incubation period, providing accurate approximations of the corresponding probability distribution. Notably, these estimates improve upon previous approaches that relied on bacterial counts from the lungs of macaques. Our findings reveal a 50% infectious dose of approximately 10 colony-forming units and we estimate that the incubation period can last for up to 11 days following low dose exposure.

Simplified within-host and Dose-response Models of SARS-CoV-2.

Understanding the mechanistic dynamics of transmission is key to designing more targeted and effective interventions to limit the spread of infectious diseases. A well-described within-host model allows explicit simulation of how infectiousness changes over time at an individual level. This can then be coupled with dose-response models to investigate the impact of timing on transmission. We collected and compared a range of within-host models used in previous studies and identified a minimally-complex model that provides suitable within-host dynamics while keeping a reduced number of parameters to allow inference and limit unidentifiability issues. Furthermore, non-dimensionalised models were developed to further overcome the uncertainty in estimates of the size of the susceptible cell population, a common problem in many of these approaches. We will discuss these models, and their fit to data from the human challenge study (see Killingley et al. (2022)) for SARS-CoV-2 and the model selection results, which has been performed using ABC-SMC. The parameter posteriors have then used to simulate viral-load based infectiousness profiles via a range of dose-response models, which illustrate the large variability of the periods of infection window observed for COVID-19.

A Stochastic Intracellular Model of Anthrax Infection With Spore Germination Heterogeneity.

We present a stochastic mathematical model of the intracellular infection dynamics of Bacillus anthracis in macrophages. Following inhalation of B. anthracis spores, these are ingested by alveolar phagocytes. Ingested spores then begin to germinate and divide intracellularly. This can lead to the eventual death of the host cell and the extracellular release of bacterial progeny. Some macrophages successfully eliminate the intracellular bacteria and will recover. Here, a stochastic birth-and-death process with catastrophe is proposed, which includes the mechanism of spore germination and maturation of B. anthracis. The resulting model is used to explore the potential for heterogeneity in the spore germination rate, with the consideration of two extreme cases for the rate distribution: continuous Gaussian and discrete Bernoulli. We make use of approximate Bayesian computation to calibrate our model using experimental measurements from in vitro infection of murine peritoneal macrophages with spores of the Sterne 34F2 strain of B. anthracis. The calibrated stochastic model allows us to compute the probability of rupture, mean time to rupture, and rupture size distribution, of a macrophage that has been infected with one spore. We also obtain the mean spore and bacterial loads over time for a population of cells, each assumed to be initially infected with a single spore. Our results support the existence of significant heterogeneity in the germination rate, with a subset of spores expected to germinate much later than the majority. Furthermore, in agreement with experimental evidence, our results suggest that most of the spores taken up by macrophages are likely to be eliminated by the host cell, but a few germinated spores may survive phagocytosis and lead to the death of the infected cell. Finally, we discuss how this stochastic modelling approach, together with dose-response data, allows us to quantify and predict individual infection risk following exposure.

Quantification of Ebola virus replication kinetics in vitro.

Mathematical modelling has successfully been used to provide quantitative descriptions of many viral infections, but for the Ebola virus, which requires biosafety level 4 facilities for experimentation, modelling can play a crucial role. Ebola virus modelling efforts have primarily focused on in vivo virus kinetics, e.g., in animal models, to aid the development of antivirals and vaccines. But, thus far, these studies have not yielded a detailed specification of the infection cycle, which could provide a foundational description of the virus kinetics and thus a deeper understanding of their clinical manifestation. Here, we obtain a diverse experimental data set of the Ebola virus infection in vitro, and then make use of Bayesian inference methods to fully identify parameters in a mathematical model of the infection. Our results provide insights into the distribution of time an infected cell spends in the eclipse phase (the period between infection and the start of virus production), as well as the rate at which infectious virions lose infectivity. We suggest how these results can be used in future models to describe co-infection with defective interfering particles, which are an emerging alternative therapeutic.

Stochastic dynamics of Francisella tularensis infection and replication.

We study the pathogenesis of Francisella tularensis infection with an experimental mouse model, agent-based computation and mathematical analysis. Following inhalational exposure to Francisella tularensis SCHU S4, a small initial number of bacteria enter lung host cells and proliferate inside them, eventually destroying the host cell and releasing numerous copies that infect other cells. Our analysis of disease progression is based on a stochastic model of a population of infectious agents inside one host cell, extending the birth-and-death process by the occurrence of catastrophes: cell rupture events that affect all bacteria in a cell simultaneously. Closed expressions are obtained for the survival function of an infected cell, the number of bacteria released as a function of time after infection, and the total bacterial load. We compare our mathematical analysis with the results of agent-based computation and, making use of approximate Bayesian statistical inference, with experimental measurements carried out after murine aerosol infection with the virulent SCHU S4 strain of the bacterium Francisella tularensis, that infects alveolar macrophages. The posterior distribution of the rate of replication of intracellular bacteria is consistent with the estimate that the time between rounds of bacterial division is less than 6 hours in vivo.

An Investigation of the Effect of Transfected Defective, Ebola Virus Genomes on Ebola Replication.

As the ongoing outbreak in the Democratic Republic of Congo illustrates, Ebola virus disease continues to pose a significant risk to humankind and this necessitates the continued development of therapeutic options. One option that warrants evaluation is that of defective genomes; these can potentially parasitize resources from the wild-type virus and may even be packaged for repeated co-infection cycles. Deletion and copy-back defective genomes have been identified and reported in the literature. As a crude, mixed preparation these were found to have limiting effects on cytopathology. Here we have used synthetic virology to clone and manufacture two deletion defective genomes. These genomes were tested with Ebola virus using in vitro cell culture and shown to inhibit viral replication; however, and against expectations, the defective genomes were not released in biologically significant numbers. We propose that EBOV might have yet unknown mechanisms to prevent parasitisation by defective interfering particles beyond the known mechanism that prevents sequential infection of the same cell. Understanding this mechanism would be necessary in any development of a defective interfering particle-based therapy.

A Novel Stochastic Multi-Scale Model of Francisella tularensis Infection to Predict Risk of Infection in a Laboratory.

We present a multi-scale model of the within-phagocyte, within-host and population-level infection dynamics of Francisella tularensis, which extends the mechanistic one proposed by Wood et al. (2014). Our multi-scale model incorporates key aspects of the interaction between host phagocytes and extracellular bacteria, accounts for inter-phagocyte variability in the number of bacteria released upon phagocyte rupture, and allows one to compute the probability of response, and mean time until response, of an infected individual as a function of the initial infection dose. A Bayesian approach is applied to parameterize both the within-phagocyte and within-host models using infection data. Finally, we show how dose response probabilities at the individual level can be used to estimate the airborne propagation of Francisella tularensis in indoor settings (such as a microbiology laboratory) at the population level, by means of a deterministic zonal ventilation model.

Oilseed rape (Brassica napus) as a resource for farmland insect pollinators: quantifying floral traits in conventional varieties and breeding systems.

Oilseed rape (OSR; Brassica napus L.) is a major crop in temperate regions and provides an important source of nutrition to many of the yield-enhancing insect flower visitors that consume floral nectar. The manipulation of mechanisms that control various crop plant traits for the benefit of pollinators has been suggested in the bid to increase food security, but little is known about inherent floral trait expression in contemporary OSR varieties or the breeding systems used in OSR breeding programmes. We studied a range of floral traits in glasshouse-grown, certified conventional varieties of winter OSR to test for variation among and within breeding systems. We measured 24-h nectar secretion rate, amount, concentration and ratio of nectar sugars per flower, and sizes and number of flowers produced per plant from 24 varieties of OSR representing open-pollinated (OP), genic male sterility (GMS) hybrid and cytoplasmic male sterility (CMS) hybrid breeding systems. Sugar concentration was consistent among and within the breeding systems; however, GMS hybrids produced more nectar and more sugar per flower than CMS hybrid or OP varieties. With the exception of ratio of fructose/glucose in OP varieties, we found that nectar traits were consistent within all the breeding systems. When scaled, GMS hybrids produced 1.73 times more nectar resource per plant than OP varieties. Nectar production and amount of nectar sugar in OSR plants were independent of number and size of flowers. Our data show that floral traits of glasshouse-grown OSR differed among breeding systems, suggesting that manipulation and enhancement of nectar rewards for insect flower visitors, including pollinators, could be included in future OSR breeding programmes.

Nest inheritance is the missing source of direct fitness in a primitively eusocial insect.

Animals that cooperate with nonrelatives represent a challenge to inclusive fitness theory, unless cooperative behavior is shown to provide direct fitness benefits. Inheritance of breeding resources could provide such benefits, but this route to cooperation has been little investigated in the social insects. We show that nest inheritance can explain the presence of unrelated helpers in a classic social insect model, the primitively eusocial wasp Polistes dominulus. We found that subordinate helpers produced more direct offspring than lone breeders, some while still subordinate but most after inheriting the dominant position. Thus, while indirect fitness obtained through helping relatives has been the dominant paradigm for understanding eusociality in insects, direct fitness is vital to explain cooperation in P. dominulus.

Unrelated helpers in a primitively eusocial wasp: is helping tailored towards direct fitness?

The paper wasp Polistes dominulus is unique among the social insects in that nearly one-third of co-foundresses are completely unrelated to the dominant individual whose offspring they help to rear and yet reproductive skew is high. These unrelated subordinates stand to gain direct fitness through nest inheritance, raising the question of whether their behaviour is adaptively tailored towards maximizing inheritance prospects. Unusually, in this species, a wealth of theory and empirical data allows us to predict how unrelated subordinates should behave. Based on these predictions, here we compare helping in subordinates that are unrelated or related to the dominant wasp across an extensive range of field-based behavioural contexts. We find no differences in foraging effort, defense behaviour, aggression or inheritance rank between unrelated helpers and their related counterparts. Our study provides no evidence, across a number of behavioural scenarios, that the behaviour of unrelated subordinates is adaptively modified to promote direct fitness interests.

Host specific social parasites (Psithyrus) indicate chemical recognition system in bumblebees.

Semiochemicals influence many aspects of insect behavior, including interactions between parasites and their hosts. We studied the chemical recognition system of bumblebees (Bombus) by examining the cuticular hydrocarbon cues of 14 species, including five species of social parasites, known as cuckoo bees (subgenus Psithyrus). We found that bumblebees possess species-specific alkene positional isomer profiles that are stable over large geographical regions and are mimicked by three host-specific cuckoo parasites. In three host-cuckoo associations where mimicry is poor, possibly due to recent host shifts, these cuckoos produce dodecyl acetate a known chemical repellent that allows the cuckoos to invade their host colonies. Our findings indicate cuckoos use two chemical mechanisms, mimicry and repellents, to invade their hosts, and this may reflect different stages of an ongoing dynamic arms race.