One model to rule them all? Modelling approaches across OneHealth for human, animal and plant epidemics

One hundred years after the 1918 influenza outbreak, are we ready for the next pandemic? This paper addresses the need to identify and develop collaborative, interdisciplinary and cross-sectoral approaches to modelling of infectious diseases including the fields of not only human and veterinary medicine, but also plant epidemiology. Firstly, the paper explains the concepts on which the most common epidemiological modelling approaches are based, namely the division of a host population into susceptible, infected and removed (SIR) classes and the proportionality of the infection rate to the size of the susceptible and infected populations. It then demonstrates how these simple concepts have been developed into a vast and successful modelling framework that has been used in predicting and controlling disease outbreaks for over 100 years. Secondly, it considers the compartmental models based on the SIR paradigm within the broader concept of a ‘disease tetrahedron’ (comprising host, pathogen, environment and man) and uses it to review the similarities and differences among the fields comprising the ‘OneHealth’ approach. Finally, the paper advocates interactions between all fields and explores the future challenges facing modellers

Cost-benefit Analysis of Epidemics Spreading on Clustered Random Networks

We study, control of infectious disease epidemics spreading on random networks with different levels of clustering. We use Gleeson’s et al., Phys. Rev. E80, 036107 (2009) algorithm to create clustered networks in which a proportion of individuals is located in fully-connected cliques of certain size. A SIR model is extended to include delayed and imperfect detection of infectious individuals. We also include a combination of responsive (palliative) and preventive (vaccination) treatments and design cost-effective disease control strategies. Cost-benefit analysis is used in combination with epidemiological simulations to identify an optimal radius for a treatment centred upon the symptomatic individual. Three general control strategies occur depending on the relative cost of treatment and prevention. Network topology and, in particular, clustering also affects the applicability of the control strategy. The average path length appears to be more important; the range for the control strategy is wider with the length, but the optimal radius of control also extends. As the proportion of individuals in cliques and therefore the coefficient of clustering is higher, the range of the costs for which control scenario is optimal is greater. This results have important consequences for designing disease control strategies that also satisfy economic optimality criteria

Estimation of force of infection based on different epidemiological proxies: 2009/2010 Influenza epidemic in Malta

Information about infectious disease outbreaks is often gathered indirectly, from doctor's reports and health board records. It also typically underestimates the actual number of cases, but the relationship between the observed proxies and the numbers that drive the diseases is complicated, nonlinear and potentially time- and state-dependent. We use a combination of data collection from the 2009-2010 H1N1 outbreak in Malta, compartmental modelling and Bayesian inference to explore the effect of using various sources of information (consultations, doctor's diagnose, swabbing and molecular testing) on estimation of the effective basic reproduction ratio, Rt. Different proxies and different sampling rates (daily and weekly) lead to similar behaviour of Rt as the epidemic unfolds, although individual parameters (force of infection, length of latent and infectious period) vary. We also demonstrate that the relationship between different proxies varies as epidemic progresses, with the first period characterised by high ratio of consultations and influenza diagnoses to actual confirmed cases of H1N1. This has important consequences for modelling that is based on reconstructing influenza cases from doctor's reports

Efficient Control of Epidemics Spreading on Networks: Balance between Treatment and Recovery

We analyse two models describing disease transmission and control on regular and small-world networks. We use simulations to find a control strategy that minimizes the total cost of an outbreak, thus balancing the costs of disease against that of the preventive treatment. The models are similar in their epidemiological part, but differ in how the removed/recovered individuals are treated. The differences in models affect choice of the strategy only for very cheap treatment and slow spreading disease. However for the combinations of parameters that are important from the epidemiological perspective (high infectiousness and expensive treatment) the models give similar results. Moreover, even where the choice of the strategy is different, the total cost spent on controlling the epidemic is very similar for both models

Payment for multiple forest benefits alters the effect of tree disease on optimal forest rotation length

Forests deliver multiple benefits both to their owners and to wider society. However, a wave of forest pests and pathogens is threatening this worldwide. In this paper we examine the effect of disease on the optimal rotation length of a single-aged, single rotation forest when a payment for non-timber benefits, which is offered to private forest owners to partly internalise the social values of forest management, is included. Using a generalisable bioeconomic framework we show how this payment counteracts the negative economic effect of disease by increasing the optimal rotation length, and under some restrictive conditions, even makes it optimal to never harvest the forest. The analysis shows a range of complex interactions between factors including the rate of spread of infection and the impact of disease on the value of harvested timber and non-timber benefits. A key result is that the effect of disease on the optimal rotation length is dependent on whether the disease affects the timber benefit only compared to when it affects both timber and non-timber benefits. Our framework can be extended to incorporate multiple ecosystem services delivered by forests and details of how disease can affect their production, thus facilitating a wide range of applications

Pesticides and bees: ecological-economic modelling of bee populations on farmland

Production of insect-pollinated crops typically relies on both pesticide use and pollination, leading to a potential conflict between these two inputs. In this paper we combine ecological modelling with economic analysis to investigate the effects of pesticide use on wild and commercial bees, whilst allowing farmers to partly offset the negative effects of pesticides on bee populations by creating more on-farm bee habitat. Farmers have incentives to invest in creating wild bee habitat to increase pollination inputs. However, the optimal allocation of on-farm habitat strongly depends on the negative effects of pesticides, with a threshold-like behaviour at a critical level of the impairment. When this threshold is crossed, the population of wild bees becomes locally extinct and their availability to pollinate breaks down. We also show that availability of commercial bees masks the decrease in pollination services which would otherwise incentivise farmers to conserve the wild pollinator population, therefore indirectly leading to local wild bee extinction. The paper demonstrat es the importance of combining ecological modelling with economics to study sustainability in the provision of ecosystem services in agro-ecosystems

The effects of disease on optimal forest rotation: a generalisable analytical framework

The arrival of novel pathogens and pests can have a devastating effect on the market values of forests. Calibrating management strategies/decisions to consider the effect of disease may help to reduce disease impacts on forests. Here, we use a novel generalisable, bioeconomic model framework, which combines an epidemiological compartmental model with a Faustmann optimal rotation length model, to explore the management decision of when to harvest a single rotation, even-aged, plantation forest under varying disease conditions. Sensitivity analysis of the rate of spread of infection and the effect of disease on the timber value reveals a key trade-off between waiting for the timber to grow and the infection spreading further. We show that the optimal rotation length, which maximises the net present value of the forest, is reduced when timber from infected trees has no value; but when the infection spreads quickly, and the value of timber from infected trees is non-zero, it can be optimal to wait until the disease-free optimal rotation length to harvest. Our original approach provides an exemplar framework showing how a bioeconomic model can be used to examine the effect of tree diseases on management strategies/decisions

Modelling plant health for policy

Plant health is relatively poorly funded compared with animal and human health issues. However, we contend it is at least as complex and likely more so given the number of pests and hosts and that outbreaks occur in poorly monitored open systems. Modelling is often suggested as a method to better consider the threats to plant health to aid resource and time poor decision makers in their prioritisation of responses. However, like other areas of science, the modelling community has not always provided accessible and relevant solutions. We describe some potential solutions to developing plant health models in conjunction with decision makers based upon a recent example and illustrate how an increased emphasis on plant health is slowly expanding the potential role of modelling in decision making. We place the research in the Credibility, Relevance and Legitimacy (CRELE) framework and discuss the implications for future developments in co-construction of policy-linked models