Abstract
Epidemiological modelling has a vital role to play in policy planning and prediction for the control of vectors, and hence the subsequent control of vector-borne diseases. To decide between competing policies requires models that can generate accurate predictions, which in turn requires accurate knowledge of vector natural histories. Here we highlight the importance of the distribution of times between life-history events, using short-lived midge species as an example. In particular we focus on the distribution of the extrinsic incubation period (EIP) which determines the time between infection and becoming infectious, and the distribution of the length of the gonotrophic cycle which determines the time between successful bites. We show how different assumptions for these periods can radically change the basic reproductive ratio (R0) of an infection and additionally the impact of vector control on the infection. These findings highlight the need for detailed entomological data, based on laboratory experiments and field data, to correctly construct the next-generation of policy-informing models.
Highlights
The language of probabilities and chance entered mathematical epidemiology, dubbed pathometry, almost from its foundations [1]
Using bluetongue virus spread by biting midges as an exemplar we demonstrate that biologically plausible alterations to the classical assumptions can significantly change the modeller’s prediction of R0 with both serious over-estimation and under-estimation being possible
We are in a position to consider the numerical values associated with the quantities formulated above, and consider how they are influenced by the assumed distributions for the length of the gonotrophic cycle and the extinsic incubation period
Summary
The language of probabilities and chance entered mathematical epidemiology, dubbed pathometry, almost from its foundations [1]. The common use, and huge success, of deterministic models for disease dynamics (ODEs) have made certain probabilistic assumptions very popular in the literature; for example the implicit assumption that the time between various epidemiologically important events is exponentially distributed, which follows from assuming constant per capita rates of change. Variation between vector life histories can be modelled as probabilistic; the difference in outcomes between vectors are modelled as being due to identically distributed chance factors rather than intrinsic variation in vector fitness. This requires estimation of the underlying random distributions governing vector life histories. The popularity in the modelling literature of implicitly assuming that relevant distributions are either exponential or fixed length is often due to the popularity of ODE models and mathematical convenience rather than biological motivation
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