Metal stresses affect the population dynamics of disease transmission
in aquaculture species
Chung-Min Liao
a,⁎
,1, Chao-Fang Chang
a,1, Ching-Hung Yeh
a,1, Szu-Chieh Chen
a,
Kuo-Chin Chiang
a, Chia-Pin Chio
a, Berry Yun-Hua Chou
a, Li-John Jou
a,b,
Guang-Wen Lien
c, Chieh-Ming Lin
a, Huan-Hsiang Shen
a, Guan-De Wu
daEcotoxicological Modeling Center, Department of Bioenvironmental Systems Engineering, National Taiwan University,
Taipei, Taiwan 10617 ROC
bDepartment of Biomechatronic Engineering, National Ilan University, Ilan, Taiwan 260 ROC cInstitute of Environmental Health, National Taiwan University, Taipei, Taiwan 10617 ROC dInstitute of Environmental Engineering, National Taiwan University, Taipei, Taiwan 10617 ROC
Received 14 December 2005; received in revised form 7 February 2006; accepted 28 February 2006
Abstract
The purpose of this study is to develop a mechanistic-based population dynamics of disease model to predict the effect of heavy-metal stresses on the susceptibility of the aquaculture species to pollution-associated infectious diseases. We link an ecologically based nonlinear epidemiological dynamics of host–parasite interactions with a deterministic susceptibility-infectious-mortality (SIM) model to evaluate the host susceptibility to the waterborne metal stressors. We test the proposed pollution-associated population dynamics of disease model against published data regarding the effect of metal cations (Cd2+, Cu2+, and Hg2+) on the susceptibility of hard clam (Meretrix lusoria) to birnavirus. We estimate stressor-specific transmission rate and basic reproductive number (R0), defined as the average number of secondary cases generated by one primary infected
case, by fitting SIM model to published cumulative mortality data. The median pollution-associated R0 estimates range from
0.99 to 1.03. Here we show that the interplay of environmental chemical stressors and disease transmission explains the host– pathogen interactions presenting in the immunomodulating chemicals contaminated aquacultural systems, suggesting that predicting schemes will require the consideration of both environmental stressor variability and host size in aquaculture species populations. We suggest that in the future potential management actions the pathogen manipulation is better to be integrated to improve the on-line environmental stressors monitoring in aquacultural systems.
© 2006 Elsevier B.V. All rights reserved.
Keywords: Aquaculture; Density dependence; Disease; Ecotoxicology; Host–pathogen interactions; Epidemiology; Metal stress; Population dynamics
1. Introduction
Aquacultural practices frequently result in high population densities and other environmental stressors such as immunomodulating chemicals and numerous ⁎ Corresponding author. Tel.: +886 2 2363 4512; fax: +886 2 2362
6433.
E-mail address:cmliao@ntu.edu.tw(C.-M. Liao).
1The authors contributed equally to this paper that was initiated at
the Fall 2005 Class“Simulation and Computation of Biosystems.” 0044-8486/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.aquaculture.2006.02.076
emerging diseases. It increases the risk of infection establishment and spread, resulting in serious economic
or ecological problems in aquaculture species (Murray
and Peeler, 2005). Great potential benefits would be gained from any appropriate management able to control the spread of the infectious diseases and eliminate it from the aquaculture species populations. On the other hand, mitigation of environmental stressors that increase the risk of host susceptibility to the spread of emerging disease, however, poses a significant challenge to the design of a realistic control strategy.
Sindermann (1990), LaPatra (1998), and Lafferty and Kuris (1999) have reviewed and evaluated comprehensively the pollution-associated diseases of marine fish and shellfish, indicating that there are several diseases for which a relationship with pollution seems evident. There are a number of other diseases for which a relationship with pollution is also indicated. Furthermore, there is some evidence that certain latent viral infections may be provoked into potency by environmental stressors involved in host– pathogen–environment interactions. These suggest that pollution stress can be a major contributing factor in the occurrence of some diseases in degraded habits.
There is evidence both from field observations and experimental studies of significant correlations between increased heavy-metal pollutants and
in-creased mortality in aquaculture species. Hetrick et
al. (1979) demonstrated that exposure to increased copper (Cu) concentrations may be immunosuppres-sive by an increased susceptibility to infectious hematopoietic necrosis virus (IHNV) by rainbow trout (Oncorhynchus mykiss) exposed to Cu compared
with control animals. Carballo et al. (1995)
demon-strated that increased susceptibilities to Saprolegnia parasitica infection were observed for ammonia (71%), Cu (57%), nitrite (50%), and cyanide (33%)
in rainbow trout.Chou et al. (1998)demonstrated that
an increase in heavy-metal stresses such as Cu, cad-mium (Cd), mercury (Hg), and zinc (Zn) has a marked effect on the susceptibility of hard clam (Meretrix lusoria) to a low pathogenic infectious pancreatic necrosis virus (IPNV)-like aquaculture birnavirus
infec-tion. Chou et al. (1999) further indicated that an
infectious pancreatic necrosis virus (IPNV) with only low pathogenicity could cause high mortality in groupers (Epinephelus sp.) when combined with heavy-metal
stressors such as Zn, Cd, and Cu.Arkoosh et al. (1991,
1994, 1998, 2001)andLoge et al. (2005)revealed that pollution-associated immunodysfunction in juvenile Chinook salmon (Oncorhynchus tshawytscha) may
lead to increased susceptibility to infection by a virulent marine pathogen Vibrio anguillarum.
Smith et al. (2005) suggested that the theoretical tools of ecology and epidemiology may be the cornerstone in constructing future program aimed at preventing and controlling infectious diseases through-out the world. Analysis of infectious disease ecology and host–pathogen interactions including pathogen transmission and disease manifestations are central to successful control strategies. From ecotoxicological point of view, environmental chemical stresses affect ecological endpoints such as intrinsic rates of increase, carrying capacity, and density dependence of
popula-tions involving in density–toxicant interacpopula-tions (Sibly et
al., 2000; Forbes et al., 2001; Hendriks et al., 2005). Here we intend to develop a framework focusing on constructing a mechanistic model by incorporating relevant principles from ecotoxicology into an epide-miological dynamics. We try to link the interplay relationships between disease transmission and envi-ronmental stressor variability that may contribute to a better understanding of the factors that ultimately affect recruitment of aquaculture species populations.
The purpose of this study is to construct a density and environmental stressor dependent host–pathogen model to evaluate the potential impact of heavy-metal stresses on the population dynamics of disease transmission in aquaculture species. To investigate the possible relation-ships between heavy-metals exposure and infectious disease mortality in aquaculture species, we focus on the disease-induced mortalities that occur before and after exposure to stressors that alter host susceptibility to infectious disease. The mortality profiles are based on two serial two-step processes involving exposure to heavy metals and then pathogen as well as exposure to pathogen and then heavy metals. The available data are adopted from the published laboratory disease challenge studies.
2. Materials and methods
2.1. Modeling effects of environmental stress and epidemic on host population
We derive a nonlinear population model to take into account ecologically, toxicologically, and epidemiolog-ically relevant factors in aquacultural systems. The proposed model indicates a strong correspondence between transmission of infectious disease and variabil-ity of metal stressors. To address this issue, we incorporate standard ecotoxicological theory for chem-ical exposure into an epidemiologchem-ical framework.
We begin with an analysis of the dynamics of host– pathogen interactions in a homogeneous host population subjected to an environmental chemical stress of exposed concentration C. We do this by studying the ability of a lethal waterborne pathogen with the exposed
concentration-dependent virulence α(C) and the
trans-missibility β(C), to invade an aquaculture species
population in a polluted aquacultural system. The waterborne pathogen spreads in an epidemic fashion throughout each generation before reproductive matu-rity is attained. The survivors then go on to reproduce, each producing on average offspring characterized by a population growth rate as a function of exposed concentration (λ(C)) that survive to emerge as adults
at the start of the next generation (Anderson and May,
1991). The numbers of adults in successive generations
could be characterized by a first-order nonlinear
difference equation (Anderson and May, 1991),
Nðt þ 1Þ ¼ kðCÞNðtÞð1−IðNðtÞÞÞ; ð1Þ
where N(t+1) and N(t) are the population size in generations of t and t + 1 (number individual or denotes
as ind), λ(C) is the exposed concentration-dependent
finite rate of increase or is called the asymptotic
population growth rate (ind ind− 1 day− 1), and I(N(t))
is the fraction of the population infected by the epidemic
in generation t. The λ(C) is the analogy of “r,” the
intrinsic rate of increase: r(C) = lnλ(C). The fraction of
surviving to reproduce is 1− I in that the fraction I is
given by a simple extension of the
Kermack–McKen-drick (K&M) model (Anderson and May, 1991). Here
we modified K&M model to a more appropriate form to include the effect of C,
1−I ¼ expð−INðtÞ=NTðCÞÞ; ð2Þ
where NT(C) is an exposed concentration-dependent
threshold population size and can be determined by the
transmissibility, β(C), and the virulence, α(C) of the
pathogen as: NT(C) =α(C)/β(C). If N(t) is below
threshold magnitude (N(t) < NT(C)), the pathogen cannot
spread: I = 0, whereas N(t) is above threshold (N(t) > NT
(C)), the pathogen dose spread: I≠ 0. The K&M
epidemic model has been extensively analyzed and
reviewed in the mathematical literature (Diekmann et
al., 1995).
A fundamental concept in epidemic dynamics is the
basic reproductive number (Anderson and May, 1991),
R0, quantifying the transmissibility of any pathogen. R0
is defined as the average number of secondary cases generated by a typical primary case at the start of the epidemic in an entirely susceptible population. In the
absence of the effects of chemical stressors on host
susceptibility, R0> 1 implies that the epidemic is
spreading within a population and that incidence is
increasing, whereas R0< 1 means that the disease is
dying out. An average R0of 1 means the disease is in
endemic equilibrium within the population. R0
essen-tially determines the rate of spread of an epidemic and how intensive a policy will need to be to control the
epidemic. In light of the concept of R0, the total
proportion of uninfected population during the epidemic
(1−I) is seen to depend only on pollution-associated R0,
R0(C), as described in Eq. (2) (Anderson and May,
1991),
1−I ¼ expð−R0ðCÞIÞ: ð3Þ
Eq. (3) is based on the theoretical relationship between
epidemic (I) and R0(C) assuming a homogeneous and
unstructured population. We optimally fitted Eq. (3) to
the plot of relationships between I and R0 based on
Anderson and May (1991)for R0ranging from 0.98 to 5 by using a nonlinear regression technique, resulting in
1−I ¼ expð1:63−1:66R0ðCÞÞ; 0:98 < R0ðCÞ < 5;
r2¼ 0:99: ð4Þ
We note that for R0(C) > 5, 1−I=exp(−R0(C))⋘1
(Swinton, 1998).
We summarize Eqs. (1)–(4) to obtain an expression to describe the effects of pollution-associated infectious disease on host density,
Nðt þ 1Þ ¼ NðtÞexpðlnkðCÞ þ 1:63−1:66R0ðCÞÞ;
0:98 < R0ðCÞ < 5: ð5Þ
On the other hand, for R0(C) > 5, N(t + 1) = N(t)exp(r
(C)−R0(C)).
Time-dependent population size N(t) in Eq. (1) is conventionally modeled by the well-known Verhulst–
Pearl logistic equation (Tsoularis and Wallace, 2002),
given by N tð þ 1Þ ¼ N tð Þexp r0 1−NðtÞ K ; ð6Þ
where r0is a parameter representing per capita growth
rate defined as1/N × dN/dt, and K is the population's carrying capacity (ind). Here we assume that environ-mental stressor affects population size N by reducing the
per capita growth rate r0(C) as a function of the exposure
concentration C. In addition to an inhibition of the per
capita growth rate (r0), chemical stressor and disease
functions of C and R0. We analogize Eqs. (5) and (6) to
estimate per capita growth rate (r0(C)) and carrying
capacity (K(R0,C)) from key epidemiological parameter
(R0(C)) (Gerber et al., 2005),
K Rð 0; CÞu
lnkðCÞ þ 1:63
R0ðCÞ ; ð7Þ
r0ðCÞulnkðCÞ þ 1:63: ð8Þ
Eqs. (7) and (8) describe the effects of environmental chemical stressor on the host susceptibility
characteriz-ing byλ(C) and R0(C).
2.2. Pollution-associated population dynamics of disease model
Here we use a mechanistic model allowing us to explore the effects of environmental chemical stressor on the pollution-associated population dynamics of disease transmission. To achieve this purpose, we modify the standard susceptible-infectious-recovered (SIR) structure to a disease-induced mortality-based susceptible-infectious-mortality (SIM) model to provide a mechanistic bridge between theoretical models and empirical data. The SIR class of models is a cornerstone of ecological epidemiology providing a simple
mecha-nistic model for microparasite dynamics (Anderson and
May, 1991; Lafferty and Holt, 2003; Loge et al., 2005). We denote the number of infectious host at time t by
Y(t). The force of infection, λF, that is the infection
pressure experienced by one susceptible individual, is
then given byλF=β(C)Y(t). We use a deterministic SIM
model with homogeneous mixing to estimate the force of infection. The dynamics of the susceptible (X), the infected (Y) and the mortality state (Z) for aquaculture species exposed to a pollution-associated disease can be described as
dX
dt ¼ −b Cð ÞYX ; ð9Þ
dY
dt ¼ b Cð ÞYX −a Cð ÞY; ð10Þ
dZ
dt ¼ a Cð ÞY: ð11Þ
After determining β(C) and α(C), the
pollution-associated basic reproductive number (R0(C)) can be
calculated using the formula (Anderson and May, 1991),
R0ð Þ ¼C
Nð0ÞbðCÞ
aðCÞ ; ð12Þ
where N(0) is the initial host population size (ind). Therefore, the carrying capacity in terms of disease parameter and environmental chemical stressor can be obtained as
K Rð 0; CÞ ¼ aðCÞbðCÞ
ðlnkðCÞ þ 1:63Þ
N : ð13Þ
Once the interplay of environmental chemical-driven stress and disease dynamics is taken into account, a nonlinear population model that achieves this by explicitly taking into account epidemiological dynamics (i.e., changes in the abundance of susceptible host, per capita growth rate, and disease transmission rate) could all be reconstructed as N tð þ 1Þ ¼ N tð Þexp lnk Cð ð Þ þ 1:63Þ 1− 1:63þlnkðCÞ1:66 NbðCÞ=aðCÞ 0 @ 1 A 2 4 3 5: ð14Þ The nonlinear nature of Eq. (14) revels that pollution-associated population dynamics of disease model could be characterized in terms of chemical stressor concen-tration (C), pollution-associated population growth rate (λ(C)), transmissibility (β(C)), and disease-specific
mortality rate α(C). Eqs. (9)–(11) thus provide a
simplified yet fully specified mechanistic model for the pollution-associated dynamics of disease transmis-sion. Eqs. (9)–(11) can link Eq. (14) to represent a novel and quantitative analysis of the effects of environmental stressor on host susceptibility and subsequently modu-lation of disease dynamics in aquaculture species populations.
2.3. Model calibration
Thanks to the excellent published data of the
cumulative incidence of mortality, the model (Eqs. (9)–
(11) and (14)) can be tested and evaluated. The published data is adopted from the laboratory disease challenge experiments in studying the effects of heavy-metal cations on the susceptibility of hard clam (M. lusoria)
al. (2001) have extensively reviewed the infectivity of aquabirnavirus to various marine fish species.
Chou et al. (1998) indicated that the hard clam M. lusoria that are cultured in Taiwan have suffered high mortality each spring/summer since 1969. Environmen-tal factors such as pollution and infectious disease have been implicated, yet no single factor has been shown to lead directly to larger scale death of the cultured hard
clam.Chou et al. (1998)conducted two experiments to
examine the effects of heavy metals on the disease transmission in hard clam. In experiment I (denoting as V + metal ion), a group of 60 clams was immersed in birnavirus solution (CV-TS-1 virus) for 24 h and subsequently exposed to one of the heavy metals of
Zn2+, Cd2+, Cu2+, and Hg2+. In experiment II (denoting
as metal ion + V), clams were exposed to one of the heavy metals for 7 days and then infected with the CV-TS-1 virus in that controls were only exposed to heavy metals. CV-TS-1 is an aquaculture birnavirus that can be isolated from the gills of hard clam in southern Taiwan and is serologically similar to Ab type of IPNV that is a
low pathogenicity to fish (Lo et al., 1988). The major
results in experiment I indicated that cumulative mortalities of clams were 20–50% in most of the experimental groups after 5 weeks, whereas in exper-iment II, the survival time shortened and the mortalities ranged from 65% to 90%.
The proposed model was applied to cumulative mortality data to obtain estimates of the model
parameters of β(C), α(C), and R0(C). Practically,
McCallum et al. (2001) have rigorously outlined the method to estimate transmission rate. We first discretely
estimated the λF by fitting Eq. (9) to the cumulative
mortality curves byΔS=(1−ΔM(%))N where M(%) is
the percent of cumulative mortality. By the definition of
β(C)=λF/Y =λF/(M(%)N), the stressor-specific
transmis-sion rate (β(C)) can be estimated. We then estimate
simultaneously the mortality-based R0(C) and α(C) by
optimal fitting R0(C) =β(C)N/α(C) to published
mor-tality curves at conditions of N = 60 and constantβ(C)
estimates. Finally, the relationships of β(C)−C and
α(C)−C over a wide range of exposed metal ion concentrations in a specific functional form can be characterized.
Optimal statistical models were selected on the basis of least squared criterion from a set of generalized linear and nonlinear autoregression models provided by TableCurve 2D package (Version 5, AISN Software Inc., Mapleton, OR, USA) fitted to the data. A value of p < 0.05 was judged significant. We used a Monte Carlo simulation to quantify our uncertainty concerning transmissibility (β) and disease-specific mortality rate.
We used the Kolmogorov–Smirnov (K-S) statistics to
optimize the goodness-of-fit of distributions. We employed Crystal Ball software (Version 2000.2, Decisioneering, Inc., Denver, CO, USA) to analyze data and to estimate distribution parameters. For this study, 10,000 iterations are sufficient to ensure stability of results.
3. Results
3.1. Effects of metal stress on host susceptibility to infection
The estimated median transmission rates are 0.026
(V + 0.1 ppm Cu2+) and 0.018 (0.1 ppm Cu2++ V),
0.0085 (V + 0.005 ppm Hg2+) and 0.0197 (0.005 ppm
Hg2++ V), and 0.0077 (V + 0.05 ppm Cd2+) and
0.0127 day− 1ind− 1(0.05 ppm Cd2++ V), respectively,
for experiments I and II. The results indicate that the estimated stressor-specific transmission rates are higher in the experiment II settings than that of experiment I,
but not for Cu2+–virus system (Fig. 1andTable 1). On
the other hand, the median mortality rates are estimated
to be 1.56 (V + 0.1 ppm Cu2+) and 1.06 (0.1 ppm
Cu2++ V), 0.52 (V + 0.005 ppm Hg2+) and 1.16
(0.005 ppm Hg2++ V), and 0.47 (V + 0.05 ppm Cd2+)
and 0.73 day− 1 (0.05 ppm Cd2++ V), respectively, for
experiments I and II (Fig. 1and Table 1).Fig. 1 also
depicts the fitted transmission and mortality rate functions in a range of metal ion concentrations based on the limited available data.
We estimate the pollution-associated basic
reproduc-tive number (R0(C)) by fitting a deterministic SIM
model to the cumulative mortality data. The median values are approximately 0.99–1.03 for both
experi-ments I and II (Fig. 2) in that the highest R0(C) occurs at
the condition of 0.05 ppm Cu2++ virus (R0(C) = 1.03).
Our results also reveal that the epidemic will spread throughout the hard clam population when the
mortal-ity-based R0(C) estimate greater than 0.98 in a
pollution-associated disease environment. Data availability led us to model the effects of metal on the susceptibility of hard clam to birnavirus infection.
3.2. Pollution-associated dynamics of disease with a density-dependent process
The model predicts cumulative mortality profiles that were significantly fitted with the published cumulative mortality data at selected experimental settings for
experiments I and II (Fig. 3). The stressor-specific
0 0.005 0.01 0.015 0.02 0.025 0.03 0 0.4 0.8 1.2 1.6 0 0.05 0.1 0 0.002 0.004 0.006 0.008 0.01 0 0.02 0.04 0.06 0.08 0.1 0 0.02 0.04 0.06 0.08 0.1 0 0.002 0.004 0.006 0.008 0.01 Transmission rate, β β (d -1 ind -1) 0 0.004 0.008 0.012 0.016 0.02 0 0.02 0.04 0.06 0.08 0.1 0 0.4 0.8 1.2 0 0.05 0.1 Mortality rate, α α (d -1) A B C D α β β 0 0.002 0.004 0.006 0.008 0.01 0 0.2 0.4 0.6 0 0.005 0.01 0 0.005 0.01 0.015 0.02 0.025 0 0.005 0.01 0 0.5 1 1.5 0 0.005 0.01 E F G H 0 0.2 0.4 0.6 0 0.05 0.1 0 0.003 0.006 0.009 0.012 0.015 0 0.02 0.04 0.06 0.08 0.1 0 0.4 0.8 0 0.05 0.1 I J K L Virus + Cu2+ Data Fitted model Virus + Hg2+ Virus + Cd2+ Cu2+ + virus Hg2+ + virus Cd2+ + virus
Metal ion concentration (ppm)
β β β α α α α α α
Fig. 1. Estimated stressor-specific disease transmission rate for virus added Cu2+, Hg2+, Cd2+(A, E, I), for Cu2+, Hg2+, Cd2+added virus (B, F, J) and
mortality rate for virus added Cu2+, Hg2+, Cd2+(C, G, K), for Cu2+, Hg2+, Cd2+added virus (D, H, L) profiles as the function of metal ion
concentration based on the published cumulative mortality data obtained from the laboratory disease challenge experiments (Chou et al., 1998) in that the best fitted models for different experimental settings are shown inTable 1.
exponential growth model: ln(N(t + 1)/N(t)) = r(C) to the
data (Fig. 4).
Population dynamics of disease differed significantly from different experimental settings of V + metal ion and metal ion + V. Our results indicate that the effective times that cause 50% population mortality (ET50) are more shortened in metal ion + V settings than that of V + metal ion. The results show that ET50s are around 6
(0.1 ppm Cu2++ V) and 9 days (V + 0.1 ppm Cu2+), 20
(0.05 ppm Cd2++ V) and 37 days (V + 0.05 ppm Cd2+),
and 11 (0.005 ppm Hg2++ V) and 46 days (V +
0.005 ppm Hg2+), respectively, based on the initial
N = 60 hard clams (Fig. 5). The pollution-associated
disease dynamics experiences most different response curves in hard clam population exposed to viral infection in combination with environmental metal
stressors (Fig. 6). Fig. 6 can also be used to predict
the effective reduction in percent mortality for hard clam Table 1
Estimated functional forms of stressor-specific transmission and mortality rates associated with their median (95% CI) estimates based on the published mortality data obtained from the laboratory disease challenge experiments (Chou et al., 1998)
Transmission rate,β (day− 1ind− 1) Mortality rate,α (day− 1)
a b r2 Median (95% CI) a b r2 Median (95% CI)
Virus + 0.1 ppm Cu2+a 0.0347 898.094 0.999 0.0262 (0.0238–0.0287) 2.033 16.042 0.999 1.556 (1.409–1.701) 0.1 ppm Cu2++ virusa 0.0194 8024.233 0.988 0.0183 (0.0149–0.021) 1.118 154.868 0.987 1.057 (0.869–1.234) Virus + 0.005 ppm Hg2+a 0.00980 136,136.233 0.994 0.00852 (0.00736–0.00960) 0.594 2264.239 0.994 0.517 (0.444–0.582) 0.005 ppm Hg2++ virusa 0.0231 49,903.576 0.992 0.0197 (0.0165–0.0226) 1.357 874.249 0.992 1.161 (0.970–1.337) Virus + 0.05 ppm Cd2+a 0.00963 8495.577 0.993 0.00774 (0.00632–0.00907) 0.581 143.429 0.993 0.468 (0.380–0.548) 0.05 ppm Cd2++ virusb 0.0127 0.000199 0.994 0.0127 (0.0116–0.0121) 0.763 0.0120 0.994 0.727 (0.697–0.758)
aBest fitted model: y = a(1−1/(1+abx)) (seeFig. 1A–J). b Best fitted model: y = a + b ln x (seeFig. 1K–L).
0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Median 25%-75% 2.5%-97.5% Experimental setting A B D F E C 0.98
Basic reproductive number
, R
0
Fig. 2. Box and whisker plot representations of the basic reproductive number (R0) for different experimental settings. (A) V + 0.05 ppm Cu2+, (B)
population continuous exposure to specific pollution-associated disease settings in the condition of metal ion
concentration ranging from 0.01 to 0.1 ppm (V–Cu2+
and V–Cd2+) and 0.001–0.01 (V–Hg2+) during
resi-dence times ranging from 0 to 100 days.
A sensitivity analysis is performed to show that the pollution-associated disease dynamics is density
depen-dent (Fig. 7). Fig. 7 reveals that the higher the
population number, the higher the cumulative incidence, and hence, the mortality in that the time to peak infection and mortality shortens is associated with a drop in the mortality along with a decrease in clam size. The result suggests that rearing size or density itself is sufficient to manipulate the level of disease from acute to chronic.
4. Discussion
4.1. Impact of metal stressors on dynamics of disease transmission
Our model supports the theory that in a hard clam–
birnavirus–metal stressor system, environmental metal stressor is an important determinant affecting population dynamics of disease transmission. It implicates that the control measures may be achieved through mitigation of not only pathogen virulence, but also chemical stressors in host–pathogen interactions that play a central role in determining the dynamics and persistence of aquacul-ture species populations.
Chou et al. (1998, 1999)suggested that in the metal ion + virus and virus + metal ion experiments, the immune system of fish/shellfish effectively eliminated the virus in most of the unstressed species. When the virus was not eliminated, even low virus levels were sufficiently high to cause death in most cases, whereas the increased susceptibility of fish/shellfish exposed to Time (days) Cumulative mortality 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 7 14 21 28 35 Fitted model Data of virus+0.1ppmCu(II) Data of virus+0.01ppmHg(II) Data of virus+0.1ppmCd(II) 0 0.2 0.4 0.6 0.8 1 0 7 14 21 28 Fitted model Data of 0.05ppmCu(II)+virus Data of 0.01ppmHg(II)+virus Data of 0.01ppmCd(II)+virus A B
Fig. 3. Proposed pollution-associated population dynamics of disease model tested against the published cumulative data of (A) experiment I: virus + metal ion and (B) experiment II: metal ion + virus.
Y = -0.3X R2 = 0.999 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 0 0.02 0.04 0.06 0.08 0.1 -0.002 -0.0015 -0.001 -0.0005 0 0 0.002 0.004 0.006 0.008 0.01
Intrinsic growth rate,
r (d
-1)
Metal ion concentration (ppm)
Cu2+ Cd2+ Y=-0.00287-0.00005lnX R2=0.973 Hg2+ -0.0032 -0.0024 -0.0016 -0.0008 0 0 0.02 0.04 0.06 0.08 0.1 Y = -0.00192-0.000033lnX R2 = 0.994 A B C
Fig. 4. Best fitted stressor-specific intrinsic growth rate profiles as a function of metal ion concentrations of (A) Cu2+, (B) Hg2+, and (C) Cd2+,
heavy metal was due to their incapability of eliminat-ing the virus. These considerations support the theory that aquaculture species exposed to chemical stressors are immunosuppressed, and that this suppression may be associated with an increase in disease susceptibility and mortality. It results in the idea that immunosup-pressed species may allocate greater energy and resources for defending themselves against infection and reducing resources for other vital physiological
functions such as growth and reproduction (Arkoosh et
al., 1998).
In light of the effect of immunomodulating chemicals on immunocompetence of aquaculture species, host immunity has a key role in the nonlinear population dynamics of disease transmission. In the future work, we may use a nonlinear population model that takes into account immunity and pollution-associated disease transmission to show the relationships between disease transmission and environmental stressor variability. Here, we have shown that the existence of immunomo-dulating heavy metals that increases in disease trans-mission resulting in increased susceptibility of aqua-culture species to infections. Once the interplay of environmental stressors and disease dynamics is taken into account, clear evidence emerges for a role of environmental stressors variability in the dynamics of disease transmission.
4.2. Effects of host density on pollution-associated disease epidemics
There is accumulating empirical evidence that the density-dependent process may play a large part in spreading the disease among aquaculture species population. For instance, density dependence was
detected in the spread of IPNV (Bebak-Williams et al.,
2002a,b) and IHNV (Ogut and Reno, 2004) in rainbow trout as well as in the furunculosis epidemics in Chinook
salmon (Ogut et al., 2004, 2005).
Density dependence and frequency dependence are familiar mechanisms in population biology to determine
disease transmission (McCallum et al., 2001; Begon et
al., 2002; Gerber et al., 2005). Swinton (1998) and
McCallum et al. (2001) indicated that in discrete compact neighborhoods, numbers rather than densities are appropriate. A fish/shellfish population in a tank that is closed with infectious units and a homogeneous contact structure can be considered a perfect example of
such a neighborhood (Begon et al., 2002). In the
modeling of birnavirus transmission in hard clams, we used the simple SIM model with numbers to simulate CV-TS-1 epidemics. Hence, the proposed simple SIM model was capable of predicting the population dynamics of disease in aquaculture species population. Our model indicates that a decrease in host size causes a significant decrease in the mortality rate and an even larger decrease in the transmission coefficient. It suggests that host size or density is a key factor and should be evaluated carefully to decrease disease transmission in aquaculture species populations. Our proposed model provides an invaluable tool to control
0 10 20 30 40 50 60 Cu2+ 0.1ppm + virus 0 10 20 30 40 50 60 0 20 40 60 80 100 Virus + 0.1ppm A B 0 10 20 30 40 50 60 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 10 20 30 40 50 60 Virus + 0.005ppm 0.005ppm + virus Hg2+ C D 0.05ppm + virus Virus + 0.05ppm Cd2+ E F 0 10 20 30 40 50 60 0 20 40 60 80 100 0 10 20 30 40 50 60 0 20 40 60 80 100 Time (days) Population size, N (number)
Fig. 5. Simulations of pollution-associated population dynamics of disease in different disease challenge experimental settings based on the initial hard clams number = 60: (A) 0.1 ppm Cu2++ virus, (B) virus + 0.1 ppm Cu2+, (C) 0.005 ppm Hg2++ virus, (D) virus + 0.005 ppm Hg2+, (E) 0.05 ppm Cd2++ virus, and (F) virus + 0.05 ppm Cd2+.
and eliminate diseases that could threaten the survival of aquaculture species in a pollution-associated disease environment.
The value of R0(C) for a pollution-associated
infection with a population can be estimated from knowledge of the biological characteristics of the disease, such as host density or size, characteristics of immunomodulating chemicals, and rates of infection and host mortality. Some factors determining the
magnitude of R0(C) are specific to the parasite itself
(e.g., mechanisms of transfer and stability in the environment), whereas others are specific to the host (e.g., host density, size, species, behavior) or
environ-ment (temperature, flow rate, water quality) (Ogut et al.,
2004). Under the controlled conditions provided, effects
of all parameters related to the disease-causing agent and the host are summarized under the parameter transmission coefficient (β), which is essential in the
calculation of R0(C). In our application, any reduction in
the value of R0(C) below 0.98 will act to reduce disease
prevalence and incidence to a level at which infection cannot be sustained and the pathogen will be eliminated
from the population. Hence, the condition R0(C) = 0.98
in the hard clam–birnavirus–metal system indicates a transmission threshold below which the disease agent is unable to maintain itself within the host population.
0 0.2 0.4 0.6 0.8 1 Virus + 0.01ppmCu(II) Virus + 0.05ppmCu(II) Virus + 0.1ppmCu(II) 0 0.2 0.4 0.6 0.8 1 0.01ppmCu(II) + virus 0.05ppmCu(II) + virus 0.1ppmCu(II) + virus 0 0.2 0.4 0.6 0.8 1 Virus + 0.001ppmHg(II) Virus + 0.005ppmHg(II) Virus + 0.01ppmHg(II) 0 0.2 0.4 0.6 0.8 1 0.001ppmHg(II) + virus 0.005ppmHg(II) + virus 0.01ppmHg(II) + virus 0 0.2 0.4 0.6 0.8 1 Virus + 0.01ppmCd(II) Virus + 0.05ppmCd(II) Virus + 0.1ppmCd(II) 0 0.2 0.4 0.6 0.8 1 0.01ppmCd(II) + virus 0.1ppmCd(II) + virus 0.05ppmCd(II) + virus Time (days) A B C D E F 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 N (t )/ N (0)
Our results also indicate that the value of NT is dynamic according to factors related to host, pathogen and environment. For example, in the hard clam–
birnavirus–metal system with virus+0.1 ppm Cu2+
(Fig. 7), larger than 50 animals could be required to
initiate an epizootic. The value of NTis important and
could serve as a starting point optimal for aquaculture
species under the defined conditions (Ogut et al., 2004).
4.3. Implications in management strategies
Chemical stressors may affect population size N by
reducing the growth rate r0(C) as a function of the
exposure concentration C. Here the experimental data we adopted were conducted and measured by using adult hard clams (3 months old). Therefore, we did not take into account the larval quality and survival. To explicitly assess the role of pollution-associated disease in analyses of growth/survival risks for aquaculture species of protection concern, information on host
density dependence, pathogen R0(C), and probability of
pathogen arrival will need to be included in conven-tional management models. Further management actions for aquaculture species exposed to pollution-associated disease environment may involve manipu-lating environmental stressors to reduce the host susceptibility to infections. For such situations, a pollution-associated population dynamics of disease model explicitly will be essential to predict how much manipulation is necessary to increase population persistence. The interaction of selected immunomodu-lating chemicals with the regulation of immunologically and toxicologically relevant genes and force of infection associated with the dynamics of host–pathogen
inter-actions within the pollution-associated infectious
dis-ease scenarios should also be included (Loge et al.,
2005).
Our proposed approach represents an integration of relevant principles of ecology, toxicology, and epide-miology associated with the available data to date. It also provides a mechanistic-based quantitative repre-sentation of the potential magnitude of pollution-associated disease-induced mortalities and the direc-tion for future management of general aquaculture species. Future work should explicitly compare the predictability of models based solely on immunomo-dulating chemicals on intrinsic rate of increase and carrying capacity. Our results suggest that predicting schemes will require the consideration of both environmental stressor variability and the host size or density. Given that the time series on susceptible levels are rarely available, approaches presented here are crucial in the attempt to predict and anticipate the future size of outbreaks of emerging infectious
diseases in aquaculture (Murray and Peeler, 2005).
Therefore, to be integrated with susceptibility levels associated with pathogen manipulation in the future work is encouraged.
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