"There are many diseases in our environment. Generally, if you can't understand a computer model of a disease, then it's probably not worth understanding."
"Biology is complicated enough. The reason for using Maths in Biology is to make things simpler and clearer... not simply to be clear of anything that's remotely understandable."
"Black box algorithms [ie. hidden mathematical formulae] are 'black box' because no one can tell how they work - models that are 'black box' should be locked up and the key should be thrown away. Administrators are forced to trust these mathematical menaces, and they will continue to do so, until we find something better. Biomodels represent something better."
Epidemiologists know that there are problems with mathematical models and the above quotes reflect some of the current issues facing the industry [1]. One of the issues that appears to be most damaging in terms of public confidence in mathematical modelling (or in computer models of disease) is that the models continue to fail in their predictions. Mathematicians would argue that by making mistakes, the outlook is brighter for the next disease epidemic. Sceptics would argue by making continual mistakes, the outlook for the future is considerably worse [2], and relying upon inaccurate models is either foolish, or even possibly negligent. There are however, new advances that provide significant strides in improving the accuracy of computer models, and these involve looking more closely at the biology of the disease, rather than just the maths [3]. To appreciate the latest approach, there's probably good merit in briefly looking at the older models, for comparison.
Originally when computer models were constructed, a random factor was added to make the models more realistic. This randomness duly created a range of possible outcomes for the disease spread and simulated where disease would spread to, but the range wasn't a problem. The problem centred around a large amount of guessing that was required to convert the biology into maths ie. incubation periods (usually measured in days) had to be guessed or sometimes averaged because incubation periods were seldom a single, stable or set value. By the time the rest of the biology was also guessed or averaged, the resulting models were more often than not, dangerously inaccurate and were seldom usefully accurate [4]. Examples of the additional and variable biology that was guessed, included the infectious periods, the effects of age and herd management on disease transmission rates, the effects of pregnancy and lactation on immunity, etc., [14]. These were first generation maths models.
It's important to note that getting the first generation models to mirror past epidemics wasn't difficult [examples:
], simply because the internal workings of a model can be changed ie. if you put a Spitfire engine into a Ford Fiesta, you can make it accelerate like a racing car. However, whether such a super-charged Ford Fiesta will actually stay on a racing track is another matter. Similarly, first generation disease computer models were seldom on track in terms of predicting what would happen in the future. When first generation models are used to investigate the likely success of different disease control programmes, their problem with the predictive accuracy resurfaces - if the model isn't accurate in predicting the course of a diease, then how can its simulation of disease control programmes be trusted? The simple answer is that without predictive accuracy, first generation models aren't useful in simulating the likely success of disease contingency plans. Hence, the usefulness of these first generation models is generally now limited to either demonstrations or teaching purposes.
Second generation computer models however, turn their attention back towards the biology of a disease to predict the future course of a disease epidemic, and the duration of an epidemic. This becomes possible because many diseases have a subclinical form that doesn't show clinical signs, and is therefore undetected as it spreads. A large number of individuals can become infected long before the disease is diagnosed, so effectively, the disease is seeded and spread throughout a group or region before it is recognised. This seeding of subclinical disease (SCD) determines the prevalence of an outbreak (at the local level) or an epidemic (at the regional level) ie. the seeding determines the total number of individuals that will become infected. The seeding also determines the duration of an epidemic [12]. Knowing how long an epidemic will last allows administrators to decide whether control measures such as vaccination will be effective (for humans) or cost effective (for animals).
Moreover, a useful aspect of second generation models is that they can provide insights into how and when various control measures should be used against a disease. Not all individuals and groups will become infected by subclinical disease, but conversely they will show acute clinical signs that are easily recognized. Individuals and groups with acute signs of a disease can be treated quickly (ie. for humans and animals) or culled quickly (ie. for animals) - hence, the future spread of disease can be controlled [9].
The disease ratio (DR) between individuals showing mild clinical signs (which follow on from subclinical disease) and acute clinical signs, is optimally 1:1. When a disease ratio is 1:1, the predictive capabilities of a biomodel is optimally balanced with the disease control capabilities of the biomodel. Hence a biomodel holding a DR value of 1, permits optimal predictions to be made about the spread of a disease, whilst at the same time the disease demonstrates epidemiological characteristics that permit a speedy control of the disease spread.
Biomodels are reliant upon a careful examination of historical data, but they are not reliant upon any mathematical guesswork with respect to the biology or the epidemiology of a disease; they are equally applicable to both human and animal diseases. Biomodels are therefore representative of a second generation of mathematically-based disease models [13].
