Antiviral resistance and the control of pandemic influenza: the roles of stochasticity, evolution and model details

Abstract

Antiviral drugs, most notably the neuraminidase inhibitors, are an important component of control strategies aimed to prevent or limit any future influenza pandemic. The potential large-scale use of antiviral drugs brings with it the danger of drug resistance evolution. A number of recent studies have shown that the emergence of drug-resistant influenza could undermine the usefulness of antiviral drugs for the control of an epidemic or pandemic outbreak. While these studies have provided important insights, the inherently stochastic nature of resistance generation and spread, as well as the potential for ongoing evolution of the resistant strain have not been fully addressed. Here, we study a stochastic model of drug resistance emergence and consecutive evolution of the resistant strain in response to antiviral control during an influenza pandemic. We find that taking into consideration the ongoing evolution of the resistant strain does not increase the probability of resistance emergence; however, it increases the total number of infecteds if a resistant outbreak occurs. Our study further shows that taking stochasticity into account leads to results that can differ from deterministic models. Specifically, we find that rapid and strong control cannot only contain a drug sensitive outbreak, it can also prevent a resistant outbreak from occurring. We find that the best control strategy is early intervention heavily based on prophylaxis at a level that leads to outbreak containment. If containment is not possible, mitigation works best at intermediate levels of antiviral control. Finally, we show that the results are not very sensitive to the way resistance generation is modeled.

Fig. 1

Schematic of the compartmental model describing the infection dynamics. The compartments are susceptibles, S, persons infected with the drug sensitive strain that are untreated, I_u, persons infected with the drug sensitive strain that receive treatment, I_t, and persons infected with the first, second and third resistant strain, I₁, I₂ and I₃. The first resistant strain is the one initially generated, ongoing evolution leads to further mutations that increase fitness of the resistant strain, resulting in I₂ and subsequently in I₃. Table 1 show the possible transitions and their propensities, Table 2 summarizes the model parameters. Further details are given in the text.

Fig. 2

Attack rate in the absence and presence of compensatory mutations. Control starts after the indicated number of infections have occurred, with treatment and prophylaxis chosen at equal levels, (f_t = f_p). Control can only mitigate the outbreak (R_f = 1.2). Attack rate is defined as the total number of infecteds divided by the population size. Boxplots are results from 2000 stochastic simulations, lines show results from the equivalent deterministic model. The black boxes and solid line are results in the absence of ongoing evolution through compensatory mutations, the gray boxes and dashed line show results in the presence of ongoing evolution. The dotted line shows the attack rate in the absence of control. The resistant strains have R₁ = 1.5, R₂ = 1.75 and R₃ = 2.0, for the case with compensatory mutations, c₁ = c₂ = c_t.

Fig. 3

Probability of resistance emergence and attack rate in the absence and presence of compensatory mutations. Control is strong enough to contain the sensitive outbreak (R_f = 0.8). Left: Probability of resistance emergence in the absence (black) and presence (gray) of compensatory mutations. Resistance is considered to have emerged if at least 5% of the total number of infections that have occurred during the outbreak are resistant infecteds (a higher/lower percentage leads to a right/left shift of the curves). Right: Solid lines show attack rate averaged over all 2000 stochastic simulations, dashed lines show attack rate averaged only over those simulations where a (resistant) outbreak occurred. The variance in attack rate for the stochastic simulations when an outbreak occurs is very small, we therefore only plot the mean instead of showing boxplots. These mean values agree closely with the deterministic results (not plotted). Rest as explained previously.

Fig. 4

Different evolutionary trajectories of the resistant strain. Control is strong enough to contain the sensitive outbreak (R_f = 0.8), as previously shown in Figure 3. Left: Probability of resistance emergence for the 3-step evolutionary trajectory previously shown in Figure 3 (solid line), a 1-step process with c_t = 10⁻³ as before and R′ = 1.7 (dashed line), and a 1-step process with c′ = 10⁻⁴ leading to a strain with fitness R′ = 2 (dash-dotted). Right: Average attack rate. Attack rate here and in the following figures is the average over all stochastic simulations, independent of the occurrence of a resistant outbreak.

Fig. 5

Probability of resistance emergence and attack rate for different control strategies. Control starts after the indicated number of infections have occurred. It leads to R_f = 0.8, which is strong enough to contain the outbreak caused by the sensitive strain. Control strategies are: only treatment (solid line), equal levels of prophylaxis and treatment (dashed line) and only prophylaxis (dash-dotted line). Evolution through compensatory mutations is included.

Fig. 6

Average attack rate for different levels of control. Treatment and prophylaxis are chosen equal (f = f_p+f_t). Control starts after the indicated number of infections have occurred. Control can only reduce, not contain the outbreak caused by the sensitive strain. The solid, dashed and dash-dotted lines show results for R_f = 1.5, R_f = 1.35 and R_f = 1.2. Black lines are total attack rate, gray lines indicate fraction of cases caused by the resistant strains. Evolution through compensatory mutations is included as previously described.

Fig. 7

Attack rate for varying levels of control. Control starts after 500 infected cases have occurred, treatment and prophylaxis are used equally (f = f_t = f_p). Left: control strength is varied from 0 to 1 and kept constant throughout the outbreak. The vertical dotted line indicates the level of control for which R_f = 1. Right: Low level of control (f = 0.1) for the indicated number of days, followed by a switch to strong control (f = 0.9). The horizontal dotted line indicates the minimum attack rate obtained for the constant treatment schedule. Evolution through compensatory mutations is included.

Fig. 8

Probability of resistance emergence and attack rate for different implementation of resistance generation. Control based on treatment only (black) or prophylaxis only (gray) for the model with resistance generation as used here (solid) and as used in previous studies (dashed). See text for details on the two model implementations. Evolution through compensatory mutations is included.