Abstract
Many organisms face a wide variety of biotic and abiotic stressors which reduce individual survival, interacting synergistically to further reduce fitness.
Abstract
Here we studied the e↵ects of two such synergistically interacting stressors; immunotoxicant exposure and parasite infection. We model the dynamics of a within-host infection and the associated immune response of an individual.
Abstract
We consider both the indirect sub-lethal e↵ects on immunosuppression and the direct e↵ects on health and mortality of individuals exposed to toxicants.
Abstract
We demonstrate that sub-lethal exposure to toxicants can promote infection through the suppression of the immune system. This happens through the depletion of the immune response which causes rapid proliferation in parasite ⇤ Corresponding author. E-mail address: r.booton@she eld.ac.uk.
Abstract
load. In addition, high toxicant exposure can alter cellular regulation and cause the breakdown of normal healthy tissue, from which we infer higher mortality risk of the host. We classify this breakdown into three phases of increasing toxicant stress, and demonstrate the range of conditions under which toxicant exposure causes failure at the within-host level. These phases are determined by the relationship between the immunity status, overall cellular health and the level of toxicant exposure. We discuss the implications of our model in the context of individual honey bee health. Our model provides an assessment of how pesticide stress and infection interact to cause the synergistic breakdown of the within-host dynamics of individual honey bees.
Introduction
X. We denote the total parasite/pathogen density as Y . The total number 69 of cells within the model represents a general susceptible subset of animal 70 tissue cells. As a motivating example, our model can be thought of describ-71 ing the midgut epithelial cells of the honey bee X under a Nosema ceranae 72 infection Y [67] with associated immune response Z, although we also pro-73 pose that our model can be thought of describing any interaction between 74 any immunotoxicant and associated parasite or pathogen in a general host. 75 Toxicants can be lethally toxic to individuals at high enough exposure [18, 76 19, 20] . In addition various functions associated with the immune response 77 are damaged by toxicants [39, 40, 41, 42, 43, 68, 69, 70, 44] . We model 78 both the direct lethality (denoted by parameter r) and indirect sub-lethal 79 immunotoxicity (denoted by parameter h) e↵ects of toxicant exposure Q. 80 For simplicity, we assume fast dynamics of virus replication compared to the 81 replication of other immune or within-host cells resulting in the formulation 82 of the model (Figure 1) icant exposure (denoted by subscript A). Two possible outcomes are possible. 126 First the infection is removed entirely by the immune system, in which case 127 the total within-host cells and total immunity each reach a constant level at 128 the disease free equilibrium (DFE):
Introduction
where d and c b represent the ratio of total production to total removal of 
Introduction
so that the addition of any toxicant reduces the total within-host cells by 146 rQ d and reduces the immune function by hQ b . Secondly the model predicts an infected individual under toxicant exposure represented by the EE:
Introduction
In this case, the parasite density grows rapidly as a result of the toxicant 150 suppressing the immune system. The introduction of the toxicant reduces 151 both within-host cells and immunity in both an infection-free and infected 152 individual, but an initial parasite infection is required for an infection to 153 grow.
154
The e↵ect of toxicant exposure on the net change of within-host cells, 155 parasite density and immunity within the individual is summarised in Table   156 1.
157
Next we assume that the indirect (sub-lethal) e↵ects of toxicant exposure 171
157
The model predicts that the initial state of an immune response is able to 173 counter any infection. However, as the toxicant load is increased, the immune 174 system is gradually depleted. Through a weakened immune suppression, this 175 enables the parasite density to increase.
176
Phase
176
The second phase begins at the point of maximum infection and where the In phase three, the immune system has been destroyed and the parasite 183 infection is no longer present leaving only a small fraction of within-host cells.
184
Finally, the lethality of the toxicant causes the mortality of the individual 185 honey bee and production of new cells ceases.
186
Thus we have calculated the conditions under which the within-host dy-187 namics change according to the level of toxicant exposure. By understanding the relationship between the parameters in the model and toxicant stress, we can make some biological interpretations. We predict that the ratio of the (Figure 5a ). We highlight this limi-283 tation of our theoretical work but argue that condition (3) have a greater impact on suppressing the immune system.
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The framework provided in this study focuses on the failure of the immune Black dots show the stable endemic equilibrium, white dots show the unstable disease-free equilibria and lines show the convergence from initial conditions. Parameters as in Table 2 and we assume an initial immune response (Z = 10) and an initial amount of within-host cells (X > 0), and either zero or positive parasite density (Y 0). Figure 5 : The mechanism of parasite infection under increasing toxicant exposure with aggressive direct mortality. In (a), the total density of immune function (blue), parasite load (red) and within-host cells (black) change as an individual honey bee is subject to higher toxicant loads. In (b), the total % parasite infection (black) changes as the toxicant load is increased. Parameters taken from 

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