11 Discussion of the Modelling, Impacts and Management of Epidemics
11.3 Differences Between and within Epidemics
This result greatly simplifies modelling, since we can dispense with models of the local structure and dynamics of the fish population.
11.2.6 Mortality
The proportion of mortality, as opposed to recovery, of infected individuals does not impact on the epidemic's behaviour in terms of the speed and local persistence of the mortality. It is of great significance for its longer-term impact (see 11.4). The model produces very high levels of infection and so the epidemic's long-term impact is largely controlled by the fraction of those infected individuals that die. We do not have a good handle on this value. The average value in Western Australia varied from 15% in 1995 to 60% in 1999 and showed very large local variation. In 1995 in South Australia mortality was 60% of the population. This figure is the fraction of the population killed, but with infection levels of over 90% the fraction of the population killed is not very different from the fraction of infected fish killed.
There are also problems with assuming a constant east-flowing current. The epidemic wave speed, if driven by advection, would respond linearly to changes in current speed.
The very limited variation from the linear regression of the epidemic's progress in Western Australia shows that there were no such distortions. Propagation rate was unaffected by several storms (Fletcher et al. 1997), surely these events would lead to variation in advection rate. The rapid northward development of the epidemic along the eastern coast of Australia appears to be directly against the prevailing current (Griffin et al. 1997). In 1999 rapid expansion of the epidemic occurred simultaneously north to Newcastle and south to Hobart, which presents obvious problems for this theory.
The speed of the advection would have to have halved between 1995 and 1998/9. This process would only lead to the differences in the speeds of the two wings of the
epidemic. It can not explain the difference in the total rate of spread between the two epidemics.
11.3.2 Viral Evolution
Two parameters, viral transmission rate and the latent period of the infection, may be changed resulting in changes in the wave speed. The epidemic wave speed is very sensitive to these parameters, particularly to the latent period's length. Evolution of viruses can occur over a few generations if selective pressures are strong (Ebert 1998).
Evolution in the virus's properties almost certainly did occur between the two epidemics. Viral lesions were much less abundant in the 1998/9 epidemic than they were in 1995 (AAHL 1999). Therefore the production of viruses, and hence probably β, seems to have dropped.
It would seem strange for the virus to evolve such that one wing of a single epidemic travelled at twice the speed of the other, while these epidemic wings were internally highly consistent in speed. There would have to be some environmental difference to drive such evolution. In any case the major difference in the appearance of lesions between the two epidemics would suggest major differences would be apparent in pathology.
Such viral evolution is very likely to be a cause of differences between the speed of the two epidemics, but it is questionable that it explains the large differences within the epidemics.
Changes in the viral transmission rate cannot alone account for the variation in the wave speed. This is because the slower wave speed is only consistent with low diffusion coefficients, while faster wave speeds are not consistent with such low diffusion
coefficients, for a given latent period. The initial behaviour of both epidemics seems to be consistent with a longer four or more days latent period length. Extreme changes in latent period length do not appear appropriate, but the wave speed is very sensitive this parameter, so small changes may have significant effects. The transmission rate and latent period could evolve in parallel.
11.3.3 Differences in Diffusion due to changes in Fish or Vector Behaviour All epidemic models considered produce epidemic wave speeds that respond to the square root of diffusion. A change in this parameter by a factor of four leads to a change in speed by a factor of two.
The final option is thus that there is some difference between fish (or vector) behaviour east and west. This would result in changes in the diffusion coefficient, which would have to be some four times greater towards the east. This explanation would be consistent between the epidemics. However, the cause of any such difference must be explained.
The evidence suggests that pilchard movement, not that of vectors, is responsible for the epidemic's spread. Diffusion coefficients are within the values that can easily be
generated by pilchards – large diffusion coefficients are not consistent with the tightly focus mortality wave observed. Mortality only occasionally affects juvenile pilchards, which suggests fish to fish mixing rather than vectors at least some of which would be likely to feed on adults or juveniles with less discrimination.
Pilchard movement on the east coast of Australia may be less inhibited by boundaries than on the west coast. Indeed the evidence appears to show a very rapid progression between the Bass Strait and east coast populations. Towards the west, Cape Leeuwin forms a strong boundary to the mixing of pilchard populations.
Pilchards off South America exhibit substantial differences in their patterns of movement between El Niño years and other years (Torres et al. 1984). It is therefore quite possible that the behaviour of pilchards could be different in different
environments in the west and east. Long migrations exhibited by South American (Torres et al. 1984) and southern African (Newman 1970) pilchards appear quite different from the behaviour of Western Australia where populations and sub- population (Cochrane 1999) appear to be restricted to well defined localities. The eastern Australian population is divided into two populations (Bass Strait and east coast) but it is quite possible that they are more mobile. Yardin et al. (1998) noted a high degree of mixing in south eastern Australian pilchard stocks. Their distribution varies with time (Hobday 1992, Neira et al. 1999), so these populations are mobile.
Mortality patterns also indicate a mobile population, on both occasions mortality
occurred at similar locations in Western Australia while in the east mortality occurred in quite different areas, such as northern Tasmania in 1995 but not 1999, and south-east Tasmania in 1999 but not 1995. It is therefore possible that eastern Australia's pilchards could behave quite differently to those in the west.
Inter-annually, 1995 was at the end of an El Niño year and this was associated with low rainfall leading to low nutrient inputs and hence low production in coastal waters such as Port Phillip Bay (Neira et al. 1999). This could have lead to fish searching for food over larger distances, hence leading to higher diffusion rates.
Small diffusion coefficients maintain the sharply focused wave of mortality in the advancing front. It is possible that in 1998 the diffusion in the eastbound wave is too
large relative to lower production in the second epidemic, causing the wave to become dispersed and thus only rarely detectable once it was mature.
The epidemic advanced up the east coast less regularly than the western advance. In 1998/9 the epidemic was only apparent irregularly. This could be evidence that diffusion was larger and involved larger scale movements of the fish, leading to
dispersal of peaks and random advective components to the movement; this advection is due to the motion of fish not the water. Dispersion of peaks by strong diffusion could lead to low continuous rates of mortality that might be undetectable if scavengers removed the small numbers of dead fish.
11.3.4 Conclusions
There are two explanations for the differences between epidemics waves to the east and west. Under one model, there is a 10 km advection in 1995 and 5 km advection in 1998/9. The alternative explanation is that diffusion coefficients in the east are inherently four times larger than those in the west. The properties of the epidemic are unlikely to be very different within a single outbreak. The population density has only a minimal effect on the epidemic's speed.
Which cause is more likely? If advection drove the differences in wave speed then this would respond linearly to changes in advection, it seems unlikely that advection would be constant for months and yet change in speed by a factor of two in different years.
The very high degree of constancy of the westbound propagation rate would show any fluctuations in current speed if advection were important. On the east coast the currents run against the epidemic in spite of rapid advance along that coast (Griffin et al. 1997).
The diffusion explanation relies on fundamentally different behaviour in pilchard populations. This is certainly possible. Pilchard population in Western Australia appears to consist of specific populations and sub populations which, while mixing, live in restricted areas. On the other hand, South American and southern African pilchards migrate over 100s or even 1000s of kms on a regular basis. Therefore other pilchard populations behave quite differently and it is perfectly possible that the eastern
pilchards are more mobile than those in the west are. The wave speed only responds to the square root of diffusion, so small changes would have little effect on the wave's speed. This would allow the highly constant advance of the westbound wave.
Interannual variation is due either a drop in the diffusion coefficient by a factor of four, or a large increase in β combined with an increase in the latent period. Advection cannot affect the speed in both directions in the same way; increase in one direction must lead to decrease in the other. The large change in the abundance of lesions in infected fish between 1995 and 1998 indicates that transmission efficiency has changed, so this is at least part of the explanation for the interannual change in the epidemic.
Changes in the nature of the infection could be combined with changes in diffusion.
Since 1995 was the end of a severe El Niño it is possible that low nutrients, leading to increased movement of pilchards as they searched for more isolated food sources.
In conclusion, we attribute difference between the eastern and western behaviours of the epidemic are due to differences in diffusion owing to different fish behaviours in
different populations. Interannual variation is due to changes in viral properties, probably with further changes in diffusion coefficient.