Rachel Norman

EPIFIL: the development of an age-structured model for describing the transmission dynamics and control of lymphatic filariasis.

Mathematical models of transmission dynamics of infectious diseases provide a useful tool for investigating the impact of community based control measures. Previously, we used a dynamic (constant force-of-infection) model for lymphatic filariasis to describe observed patterns of infection and disease in endemic communities. In this paper, we expand the model to examine the effects of control options against filariasis by incorporating the impact of age structure of the human community and by addressing explicitly the dynamics of parasite transmission from and to the vector population. This model is tested using data for Wuchereria bancrofti transmitted by Culex quinquefasciatus in Pondicherry, South India. The results show that chemotherapy has a larger short-term impact than vector control but that the effects of vector control can last beyond the treatment period. In addition we compare rates of recrudescence for drugs with different macrofilaricidal effects.

Pathogen Interactions, Population Cycles, and Phase Shifts

Interspecific pathogen interactions can profoundly affect pathogen population dynamics and the efficacy of control strategies. However, many pathogens exhibit cyclic abundance patterns (e.g., seasonality), and temporal asynchrony between interacting pathogens could reduce the impact of those interactions. Here we use an extension of our previously published model to investigate the effects of cycles on pathogen interaction. We demonstrate that host immune memory can maintain the impact of an interaction, even when the effector pathogen abundance is low or the pathogen is absent. Paradoxically, immune memory can result in pathogens interacting more strongly when temporally out of phase. We find that interactions between species can result in changes to the temporal pattern of the affected species. We further demonstrate that this may be observed in a natural host‐pathogen system. Given the continuing debate regarding the relevance of pathogen interactions in natural systems and increasing concern about treatment strategies for coinfections, both the discovery of a shift in cycle in empirical data and the mechanism by which we identified it are important. Finally, because the model structure used here is analogous to models of a simple predator‐prey system, we also consider the consequences of these findings in the context of that system.

Developing the use of process algebra in the derivation and analysis of mathematical models of infectious disease

We introduce a series of descriptions of disease spread using the process algebra WSCCS and compare the derived mean field equations with the traditional ordinary differential equation model. Even the preliminary work presented here brings to light interesting theoretical questions about the “best” way to defined the model.

Evaluating the Efficacy of Entomopathogenic Nematodes for the Biological Control of Crop Pests: A Nonequilibrium Approach

The efficacy of entomopathogenic nematodes for biological control is assessed using deterministic models. Typically, the examination of such models involves stability analyses to determine the long‐term persistence of control. However, in agricultural systems, control is often needed within a single season. Hence, the transient dynamics of the systems were assessed under specific, short‐term control scenarios using stage‐structured models. Analyses suggest that preemptive application may be the optimum strategy if nematode mortality rates are low; applying before pest invasion can result in greater control than applying afterward. In addition, repeated applications will suppress a pest, providing the application rate exceeds a threshold. However, the period between applications affects control success, so the economic injury level of the crop and the life history of the pest should be evaluated before deciding the strategy. In all scenarios, the most important parameter influencing control is the transmission rate. These findings are applicable to more traditional biological control agents (e.g., microparasites and parasitoids), and we recommend the approach adopted here when considering their practical use. It is concluded that it is essential to consider the specific crop and pest characteristics and the definition of control success before selecting the appropriate control strategy.

Breaking beta: deconstructing the parasite transmission function

Transmission is a fundamental step in the life cycle of every parasite but it is also one of the most challenging processes to model and quantify. In most host–parasite models, the transmission process is encapsulated by a single parameter β. Many different biological processes and interactions, acting on both hosts and infectious organisms, are subsumed in this single term. There are, however, at least two undesirable consequences of this high level of abstraction. First, nonlinearities and heterogeneities that can be critical to the dynamic behaviour of infections are poorly represented; second, estimating the transmission coefficient β from field data is often very difficult. In this paper, we present a conceptual model, which breaks the transmission process into its component parts. This deconstruction enables us to identify circumstances that generate nonlinearities in transmission, with potential implications for emergent transmission behaviour at individual and population scales. Such behaviour cannot be explained by the traditional linear transmission frameworks. The deconstruction also provides a clearer link to the empirical estimation of key components of transmission and enables the construction of flexible models that produce a unified understanding of the spread of both micro- and macro-parasite infectious disease agents. This article is part of the themed issue ‘Opening the black box: re-examining the ecology and evolution of parasite transmission’.

Controlling tick-borne diseases through domestic animal management: a theoretical approach

Vector-borne diseases are of global importance to human and animal health. Empirical trials of effective methods to control vectors and their pathogens can be difficult for practical, financial and ethical reasons. Here, therefore, we use a mathematical model to predict the effectiveness of a vector-borne disease control method. As a case study, we use the tick-louping ill virus system, where sheep are treated with acaricide in an attempt to control ticks and disease in red grouse , an economically important game bird. We ran the model under different scenarios of sheep flock sizes, alternative host (deer) densities, acaricide efficacies and tick burdens. The model predicted that, with very low deer densities, using sheep as tick mops can reduce the tick population and virus prevalence. However, treatment is ineffective above a certain threshold deer density, dependent on the comparative tick burden on sheep and deer. The model also predicted that high efficacy levels of acaricide must be maintained for effective tick control. This study suggests that benignly managing one host species to protect another host species from a vector and pathogen can be effective under certain conditions. It also highlights the importance of understanding the ecological complexity of a system, in order to target control methods only under certain circumstances for maximum effectiveness.

Process Algebra Models of Population Dynamics

It is well understood that populations cannot grow without bound and that it is competition between individuals for resources which restricts growth. Despite centuries of interest, the question of how best to model density dependent population growth still has no definitive answer. We address this question here through a number of individual based models of populations expressed using the process algebra WSCCS. The advantage of these models is that they can be explicitly based on observations of individual interactions. From our probabilistic models we derive equations expressing overall population dynamics, using a formal and rigorous rewriting based method. These equations are easily compared with the traditionally used deterministic Ordinary Differential Equation models and allow evaluation of those ODE models, challenging their assumptions about system dynamics. Further, the approach is applied to epidemiology, combining population growth with disease spread.

From individuals to populations: A mean field semantics for process algebra

A new semantics in terms of mean field equations is presented for WSCCS (Weighted Synchronous Calculus of Communicating Systems). The semantics captures the average behaviour of the system over time, but without computing the entire state space, therefore avoiding the state space explosion problem. This allows easy investigation of models with large numbers of components. The new semantics is shown to be equivalent to the standard Discrete Time Markov Chain semantics of WSCCS as the number of processes tends to infinity. The method of deriving the semantics is illustrated with examples drawn from biology and from computing.

Improved Continuous Approximation of PEPA Models through Epidemiological Examples

We present two individual based models of disease systems using PEPA (Performance Evaluation Process Algebra). The models explore contrasting mechanisms of disease transmission: direct transmission (e.g. measles) and indirect transmission (e.g. malaria, via mosquitos). We extract ordinary differential equations (ODEs) as a continuous approximation to the PEPA models using the Hillston method and compare these with the traditionally used ODE disease models and with the results of stochastic simulation. Improvements to the Hillston method of ODE extraction for this context are proposed, and the new results compare favourably with stochastic simulation results and to ODEs derived for equivalent models in WSCCS (Weighted Synchronous Calculus of Communicating Systems).

The role of lambs in louping-ill virus amplification

In some areas of Scotland, the prevalence of louping-ill virus has not decreased despite the vaccination of replacement ewes for over 30 years. The role of unvaccinated lambs in viral persistence was examined through a combination of an empirical study of infection rates of lambs and mathematical modelling. Serological sampling revealed that most lambs were protected by colostral immunity at turnout in May/June but were fully susceptible by the end of September. Between 8 and 83% of lambs were infected over the first season, with seroconversion rates greater in late rather than early summer. The proportion of lambs that could have amplified the louping-ill virus was low, however, because high initial titres of colostral antibody on farms with a high force of infection gave protection for several months. A simple mathematical model suggested that the relationship between the force of infection and the percentage of lambs that became viraemic was not linear and that the maximum percentage of viraemic lambs occurred at moderately high infection rates. Examination of the conditions required for louping-ill persistence suggested that the virus could theoretically persist in a sheep flock with over 370 lambs, if the grazing season was longer than 130 days. In practice, however, lamb viraemia is not a general explanation for louping-ill virus persistence as these conditions are not met in most management systems and because the widespread use of acaracides in most tick-affected hill farming systems reduces the number of ticks feeding successfully.