Since its emergence in 1968, influenza A H3N2 has caused yearly epidemics in temperate regions. While infection confers immunity against antigenically similar strains, new antigenically distinct strains that evade existing immunity regularly emerge ('antigenic drift'). Immunity at the individual level is complex, depending on an individual's lifetime infection history. An individual's first infection with influenza typically elicits the greatest response with subsequent infections eliciting progressively reduced responses ('antigenic seniority'). The combined effect of individual-level immune responses and antigenic drift on the epidemiological dynamics of influenza are not well understood. Here we develop an integrated modelling framework of influenza transmission, immunity, and antigenic drift to show how individual-level exposure, and the build-up of population level immunity, shape the long-term epidemiological dynamics of H3N2. Including antigenic seniority in the model, we observe that following an initial decline after the pandemic year, the average annual attack rate increases over the next 80 years, before reaching an equilibrium, with greater increases in older age-groups. Our analyses suggest that the average attack rate of H3N2 is still in a growth phase. Further increases, particularly in the elderly, may be expected in coming decades, driving an increase in healthcare demand due to H3N2 infections.

Contact tracing is an important public health measure used to reduce transmission of infectious diseases. Contact tracers typically conduct telephone interviews with cases to identify contacts and direct them to quarantine, with the aim of preventing onward transmission. However, in situations where caseloads exceed the capacity of the public health system, timely interviews may not be feasible for all cases. Here we present a modelling framework for assessing the impact of different case interview prioritisation strategies on disease transmission. Our model is based on Australian contact tracing procedures and informed by contact tracing data on COVID-19 cases notified in Australia from 2020 to 2021. Our results demonstrate that last-in-first-out strategies (where cases with the most recent swab or notification dates are interviewed first) are more effective at reducing transmission than first-in-first-out strategies (where cases with the oldest swab or notification dates are interviewed first) or strategies with no explicit prioritisation. To maximise the public health benefit from a given case interview capacity, public health practitioners may consider our findings when designing case interview prioritisation protocols for outbreak response.

Plasmodium vivax is one of the most geographically widespread malaria parasites in the world, primarily found across South-East Asia, Latin America, and parts of Africa. One of the significant characteristics of the P. vivax parasite is its ability to remain dormant in the human liver as hypnozoites and subsequently reactivate after the initial infection (i.e. relapse infections). Mathematical modelling approaches have been widely applied to understand P. vivax dynamics and predict the impact of intervention outcomes. Models that capture P. vivax dynamics differ from those that capture P. falciparum dynamics, as they must account for relapses caused by the activation of hypnozoites. In this article, we provide a scoping review of mathematical models that capture P. vivax transmission dynamics published between January 1988 and May 2023. The primary objective of this work is to provide a comprehensive summary of the mathematical models and techniques used to model P. vivax dynamics. In doing so, we aim to assist researchers working on mathematical epidemiology, disease transmission, and other aspects of P. vivax malaria by highlighting best practices in currently published models and highlighting where further model development is required. We categorise P. vivax models according to whether a deterministic or agent-based approach was used. We provide an overview of the different strategies used to incorporate the parasite's biology, use of multiple scales (within-host and population-level), superinfection, immunity, and treatment interventions. In most of the published literature, the rationale for different modelling approaches was driven by the research question at hand. Some models focus on the parasites' complicated biology, while others incorporate simplified assumptions to avoid model complexity. Overall, the existing literature on mathematical models for P. vivax encompasses various aspects of the parasite's dynamics. We recommend that future research should focus on refining how key aspects of P. vivax dynamics are modelled, including spatial heterogeneity in exposure risk and heterogeneity in susceptibility to infection, the accumulation of hypnozoite variation, the interaction between P. falciparum and P. vivax, acquisition of immunity, and recovery under superinfection.

The role of direct cell-to-cell spread in viral infections-where virions spread between host and susceptible cells without needing to be secreted into the extracellular environment-has come to be understood as essential to the dynamics of medically significant viruses like hepatitis C and influenza. Recent work in both the experimental and mathematical modelling literature has attempted to quantify the prevalence of cell-to-cell infection compared to the conventional free virus route using a variety of methods and experimental data. However, estimates are subject to significant uncertainty and moreover rely on data collected by inhibiting one mode of infection by either chemical or physical factors, which may influence the other mode of infection to an extent which is difficult to quantify. In this work, we conduct a simulation-estimation study to probe the practical identifiability of the proportion of cell-to-cell infection, using two standard mathematical models and synthetic data that would likely be realistic to obtain in the laboratory. We show that this quantity cannot be estimated using non-spatial data alone, and that the collection of data which describes the spatial structure of the infection is necessary to infer the proportion of cell-to-cell infection. Our results provide guidance for the design of relevant experiments and mathematical tools for accurately inferring the prevalence of cell-to-cell infection in in vitro and in vivo contexts.

The influenza pandemic of 1918-19 was the most devastating pandemic of the 20th century. It killed an estimated 50-100 million people worldwide. In late 1918, when the severity of the disease was apparent, the Australian Quarantine Service was established. Vessels returning from overseas and inter-state were intercepted, and people were examined for signs of illness and quarantined. Some of these vessels carried the infection throughout their voyage and cases were prevalent by the time the ship arrived at a Quarantine Station. We study four outbreaks that took place on board the Medic, Boonah, Devon, and Manuka in late 1918. These ships had returned from overseas and some of them were carrying troops that served in the First World War. By analysing these outbreaks under a stochastic Bayesian hierarchical modeling framework, we estimate the transmission rates among crew and passengers aboard these ships. Furthermore, we ask whether the removal of infectious, convalescent, and healthy individuals after arriving at a Quarantine Station in Australia was an effective public health response.

Epidemiological and clinical evidence indicates that humans infected with the 1918 pandemic H1N1 influenza virus and highly pathogenic avian H5N1 influenza viruses often displayed severe lung pathology. High viral load and extensive infiltration of macrophages are the hallmarks of highly pathogenic (HP) influenza viral infections. However, it remains unclear what biological mechanisms primarily determine the observed difference in the kinetics of viral load and macrophages between HP and low pathogenic (LP) viral infections, and how the mechanistic differences are associated with viral pathogenicity. In this study, we develop a mathematical model of viral dynamics that includes the dynamics of different macrophage populations and interferon. We fit the model to in vivo kinetic data of viral load and macrophage level from BALB/c mice infected with an HP or LP strain of H1N1/H5N1 virus to estimate model parameters using Bayesian inference. Our primary finding is that HP viruses have a higher viral infection rate, a lower interferon production rate and a lower macrophage recruitment rate compared to LP viruses, which are strongly associated with more severe tissue damage (quantified by a higher percentage of epithelial cell loss). We also quantify the relative contribution of macrophages to viral clearance and find that macrophages do not play a dominant role in the direct clearance of free viruses although their role in mediating immune responses such as interferon production is crucial. Our work provides new insight into the mechanisms that convey the observed difference in viral and macrophage kinetics between HP and LP infections and establishes an improved model-fitting framework to enhance the analysis of new data on viral pathogenicity.

Prevalence of impetigo (skin sores) remains high in remote Australian Aboriginal communities, Fiji, and other areas of socio-economic disadvantage. Skin sore infections, driven primarily in these settings by Group A Streptococcus (GAS) contribute substantially to the disease burden in these areas. Despite this, estimates for the force of infection, infectious period and basic reproductive ratio-all necessary for the construction of dynamic transmission models-have not been obtained. By utilising three datasets each containing longitudinal infection information on individuals, we estimate each of these epidemiologically important parameters. With an eye to future study design, we also quantify the optimal sampling intervals for obtaining information about these parameters. We verify the estimation method through a simulation estimation study, and test each dataset to ensure suitability to the estimation method. We find that the force of infection differs by population prevalence, and the infectious period is estimated to be between 12 and 20 days. We also find that optimal sampling interval depends on setting, with an optimal sampling interval between 9 and 11 days in a high prevalence setting, and 21 and 27 days for a lower prevalence setting. These estimates unlock future model-based investigations on the transmission dynamics of skin sores.

Laboratory models are often used to understand the interaction of related pathogens via host immunity. For example, recent experiments where ferrets were exposed to two influenza strains within a short period of time have shown how the effects of cross-immunity vary with the time between exposures and the specific strains used. On the other hand, studies of the workings of different arms of the immune response, and their relative importance, typically use experiments involving a single infection. However, inferring the relative importance of different immune components from this type of data is challenging. Using simulations and mathematical modelling, here we investigate whether the sequential infection experiment design can be used not only to determine immune components contributing to cross-protection, but also to gain insight into the immune response during a single infection. We show that virological data from sequential infection experiments can be used to accurately extract the timing and extent of cross-protection. Moreover, the broad immune components responsible for such cross-protection can be determined. Such data can also be used to infer the timing and strength of some immune components in controlling a primary infection, even in the absence of serological data. By contrast, single infection data cannot be used to reliably recover this information. Hence, sequential infection data enhances our understanding of the mechanisms underlying the control and resolution of infection, and generates new insight into how previous exposure influences the time course of a subsequent infection.

Influenza is an infectious disease that primarily attacks the respiratory system. Innate immunity provides both a very early defense to influenza virus invasion and an effective control of viral growth. Previous modelling studies of virus-innate immune response interactions have focused on infection with a single virus and, while improving our understanding of viral and immune dynamics, have been unable to effectively evaluate the relative feasibility of different hypothesised mechanisms of antiviral immunity. In recent experiments, we have applied consecutive exposures to different virus strains in a ferret model, and demonstrated that viruses differed in their ability to induce a state of temporary immunity or viral interference capable of modifying the infection kinetics of the subsequent exposure. These results imply that virus-induced early immune responses may be responsible for the observed viral hierarchy. Here we introduce and analyse a family of within-host models of re-infection viral kinetics which allow for different viruses to stimulate the innate immune response to different degrees. The proposed models differ in their hypothesised mechanisms of action of the non-specific innate immune response. We compare these alternative models in terms of their abilities to reproduce the re-exposure data. Our results show that 1) a model with viral control mediated solely by a virus-resistant state, as commonly considered in the literature, is not able to reproduce the observed viral hierarchy; 2) the synchronised and desynchronised behaviour of consecutive virus infections is highly dependent upon the interval between primary virus and challenge virus exposures and is consistent with virus-dependent stimulation of the innate immune response. Our study provides the first mechanistic explanation for the recently observed influenza viral hierarchies and demonstrates the importance of understanding the host response to multi-strain viral infections. Re-exposure experiments provide a new paradigm in which to study the immune response to influenza and its role in viral control.

We present a method to measure the relative transmissibility ("transmission fitness") of one strain of a pathogen compared to another. The model is applied to data from "competitive mixtures" experiments in which animals are co-infected with a mixture of two strains. We observe the mixture in each animal over time and over multiple generations of transmission. We use data from influenza experiments in ferrets to demonstrate the approach. Assessment of the relative transmissibility between two strains of influenza is important in at least three contexts: 1) Within the human population antigenically novel strains of influenza arise and compete for susceptible hosts. 2) During a pandemic event, a novel sub-type of influenza competes with the existing seasonal strain(s). The unfolding epidemiological dynamics are dependent upon both the population's susceptibility profile and the inherent transmissibility of the novel strain compared to the existing strain(s). 3) Neuraminidase inhibitors (NAIs), while providing significant potential to reduce transmission of influenza, exert selective pressure on the virus and so promote the emergence of drug-resistant strains. Any adverse outcome due to selection and subsequent spread of an NAI-resistant strain is exquisitely dependent upon the transmission fitness of that strain. Measurement of the transmission fitness of two competing strains of influenza is thus of critical importance in determining the likely time-course and epidemiology of an influenza outbreak, or the potential impact of an intervention measure such as NAI distribution. The mathematical framework introduced here also provides an estimate for the size of the transmitted inoculum. We demonstrate the framework's behaviour using data from ferret transmission studies, and through simulation suggest how to optimise experimental design for assessment of transmissibility. The method introduced here for assessment of mixed transmission events has applicability beyond influenza, to other viral and bacterial pathogens.