Avian influenza A(H5N1) poses a public health risk due to its pandemic potential should the virus mutate to become human-to-human transmissible. To date, reported influenza A(H5N1) human cases have typically occurred in the lower respiratory tract with a high case fatality rate. There is prior evidence of some influenza A(H5N1) strains being a small number of amino acid mutations away from achieving droplet transmissibility, possibly allowing them to be spread between humans. We present a mechanistic within-host influenza A(H5N1) infection model, novel for its explicit consideration of the biological differences between the upper and lower respiratory tracts. We then estimate a distribution of viral lifespans and effective replication rates in human H5N1 influenza cases. By combining our within-host model with a viral mutation model, we determine the probability of an infected individual generating a droplet transmissible strain of influenza A(H5N1) through mutation. For three mutations, we found a peak probability of approximately [Formula: see text] that a human case of H5N1 influenza produces at least one virion during the infectious period. Our findings provide insights into the risk of differing infectious pathways of influenza A(H5N1) (namely avian-human versus avian-mammal-human routes), demonstrating the three-mutation pathway being a cause of concern in human cases.

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.

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.

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.

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.

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.

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.

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.

In this thesis, I present a series of mathematical models for describing the infection dynamics of two lethal intracellular pathogens, namely Francisella tularensis and Ebola virus. Through the construction of both stochastic and deterministic models, a multi-disciplinary approach is used to account for the key processes that dictate disease progression. Each model describes the dynamics of a population of host cells, with the analysis of interactions between individual cells and single bacteria or virus particles allowing for greater detail to be included. Throughout this thesis, the theory of birth-and-death processes, matrix analytic methods and numerical simulation algorithms are used to study the stochastic processes. In addition to these techniques, a Bayesian approach to statistical inference is applied in order to parametrise each of the models with relevant infection data.

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.