A Bistable Switch in Virus Dynamics Can Explain the Differences in Disease Outcome Following SIV Infections in Rhesus Macaques

Abstract

Experimental studies have shown that the size and infectious-stage of viral inoculum influence disease outcomes in rhesus macaques infected with simian immunodeficiency virus. The possible contribution to disease outcome of antibody developed after transmission and/or present in the inoculum in free or bound form is not understood. In this study, we develop a mathematical model of virus-antibody immune complex formation and use it to predict their role in transmission and protection. The model exhibits a bistable switch between clearance and persistence states. We fitted it to temporal virus data and estimated the parameter values for free virus infectivity rate and antibody carrying capacity for which the model transitions between virus clearance and persistence when the initial conditions (in particular the ratio of immune complexes to free virus) vary. We used these results to quantify the minimum virus amount in the inoculum needed to establish persistent infections in the presence and absence of protective antibodies.

Keywords: SIV; bistable dynamics; immune complexes; mathematical model; stochastic model.

Figure 1

(Left) Basin of attraction for V_T given by (6) vs. data; (Right) Free antibody (solid lines); recipient immune complexes (dashed lines) and donor immune complexes (dotted lines) for V(0) = 20/300 vRNA copies per ml, X_D(0) = 0 vRNA copies per ml (black) and V(0) = 2/300 vRNA copies per ml, X_D(0) = 0 vRNA copies per ml (gray). Note that antibody populations are identical regardless of initial conditions (solid black and gray lines overlap).

Figure 2

V_T given by (6) at steady state vs. i for: (Left) V(0) = i/300 vRNA copies per ml, X_D(0) = 0 vRNA copies per ml and median parameters in Table 2; (Right) V(0) = i/300 vRNA copies per ml, X_D(0) = 7.8 × i/300 vRNA copies per ml and median parameters in Table 3.

Figure 3

(Left) V_T given by (6) vs. data; (Right) Free antibody (solid lines), recipient immune complexes (dashed lines) and donor immune complexes (dotted lines): for V(0)+X_D(0) = 1500/300 vRNA copies per ml, X_D(0)/V(0) = 7.8 (black) and V(0)+X_D(0) = 150/300 vRNA copies per ml, X_D(0)/V(0) = 7.8 (gray). Note that antibody populations are identical regardless of initial conditions (solid black and gray lines overlap) but the immune complexes differ.

Figure 4

Asymptotic behavior for the V_T solutions of (6) for median parameters in Table 3 as the initial vRNA and X_D(0)/V(0) are varied. The blue region (left of the curve) corresponds to extinction asymptotic concentrations V_T = 0 copies per ml. The yellow region (right of the curve) corresponds to persistence asymptotic concentrations $V_T=6.9\times 10^6$ copies per ml.

Figure 5

(Left) V_T given by (6) vs. data; (Right) Free antibody (solid lines), recipient immune complexes (dashed lines) and donor immune complexes (dotted lines) for V(0) = 20/300 vRNA copies per ml, X_D(0) = 0 vRNA copies per ml and $A_D(0)=7.4\times 10^9$ molecules per ml.

Figure 6

The probability of virus persistence for (Left) ramp-up-stage and (Right) set-point-stage vRNA data under the assumption of the burst stochastic model (9). The red circles account for the probability of persistence for high inocula, while the blue stars account for the probability of persistence for low inocula.