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Pathogens that consist of multiple antigenic variants are a serious public health concern. These infections, which include dengue virus, influenza and malaria, generate substantial morbidity and mortality. However, there are considerable theoretical challenges involved in modelling such infections. As well as describing the interaction between strains that occurs as a result cross-immunity and evolution, models must balance biological realism with mathematical and computational tractability. Here we review different modelling approaches, and suggest a number of biological problems that are potential candidates for study with these methods. We provide a comprehensive outline of the benefits and disadvantages of available frameworks, and describe what biological information is preserved and lost under different modelling assumptions. We also consider the emergence of new disease strains, and discuss how models of pathogens with multiple strains could be developed further in future. This includes extending the flexibility and biological realism of current approaches, as well as interface with data.

Existing mathematical models of drift typically assume that influenza A is free to change its antigenic properties without any fitness cost in other respects. This paper asks what might be the impact of antigenic mutations being bound to fitness cost. The effect on drift is explored via a mathematical model. This paper also offers some novel features for multi-strain modeling. In contrast to the unconstrained drift models, this system can exhibit both drift-like patterns and single strain dynamics. These can occur for the same parameter values: a bistable system where it is possible to switch between these behaviours. This raises some important prospects for vaccination strategies, particularly pausing influenza drift.

Campylobacter jejuni is one of the most common causes of acute enteritis in the developed world. The consumption of contaminated poultry, where C. jejuni is believed to be a commensal organism, is a major risk factor. However, the dynamics of this colonization process in commercially reared chickens is still poorly understood. Quantification of these dynamics of infection at an individual level is vital to understand transmission within populations and formulate new control strategies. There are multiple potential routes of introduction of C. jejuni into a commercial flock. Introduction is followed by a rapid increase in environmental levels of C. jejuni and the level of colonization of individual broilers. Recent experimental and epidemiological evidence suggest that the celerity of this process could be masking a complex pattern of colonization and extinction of bacterial strains within individual hosts. Despite the rapidity of colonization, experimental transmission studies exhibit a highly variable and unexplained delay time in the initial stages of the process. We review past models of transmission of C. jejuni in broilers and consider simple modifications, motivated by the plausible biological mechanisms of clearance and latency, which could account for this delay. We show how simple mathematical models can be used to guide the focus of experimental studies by providing testable predictions based on our hypotheses. We conclude by suggesting that competition experiments could be used to further understand the dynamics and mechanisms underlying the colonization process. The population models for such competition processes have been extensively studied in other ecological and evolutionary contexts. However, C. jejuni can potentially adapt phenotypically through phase variation in gene expression, leading to unification of ecological and evolutionary time-scales. For a theoretician, the colonization dynamics of C. jejuni offer an experimental system to explore these 'phylodynamics', the synthesis of population dynamics and evolutionary biology.

Strain structure is of fundamental importance in the underlying dynamics of a number of pathogens. However, previous models have been too complex to accommodate many strains. This paper offers a solution to this problem, in the form of a simple model that is capable of capturing the dynamics of a large number of antigenic types that interact via host cross-immunity. We derive the structure of the model, which can manage the complexity of many strains by using a status-based formulation, assuming polarized immunity and cross-immunity act to reduced transmission probability. We then apply the model to address basic questions in strain dynamics, focusing particularly on the interpandemic dynamics of influenza. This model shows that strains have a tendency to "cluster." For a long infectious period, relative to host lifetime, clusters may coexist. By contrast, a short infectious period leads to a single dominant cluster at any given time. We show how the speed of cluster replacement depends on the specificity of cross-immunity and on the underlying pathogen mutation rate.