The timing and targeting of treatment in influenza pandemics influences the emergence of resistance in structured populations

Abstract

Antiviral resistance in influenza is rampant and has the possibility of causing major morbidity and mortality. Previous models have identified treatment regimes to minimize total infections and keep resistance low. However, the bulk of these studies have ignored stochasticity and heterogeneous contact structures. Here we develop a network model of influenza transmission with treatment and resistance, and present both standard mean-field approximations as well as simulated dynamics. We find differences in the final epidemic sizes for identical transmission parameters (bistability) leading to different optimal treatment timing depending on the number initially infected. We also find, contrary to previous results, that treatment targeted by number of contacts per individual (node degree) gives rise to more resistance at lower levels of treatment than non-targeted treatment. Finally we highlight important differences between the two methods of analysis (mean-field versus stochastic simulations), and show where traditional mean-field approximations fail. Our results have important implications not only for the timing and distribution of influenza chemotherapy, but also for mathematical epidemiological modeling in general. Antiviral resistance in influenza may carry large consequences for pandemic mitigation efforts, and models ignoring contact heterogeneity and stochasticity may provide misleading policy recommendations.

Figure 1. Final epidemic sizes depend on treatment levels and relative transmissibility.

Figure shows the final epidemic size for various treatment levels when wild-type and resistant strains have differing transmissibilities. Treatment is only preferable when the wild-type strain is more transmissible than the resistant strain (i.e.: ). Model details given in . Parameters: , and , , and .

Figure 2. Final epidemic size and demonstration of the critical manifold.

Results of the mean-field approximations. Panel a shows the final infected proportion as a function of for all infections () (red line), wild-type without treatment () (black line) and wild-type without mutation () (blue line). Panel b demonstrates the critical manifold leading to dependence on initial conditions (dashed grey line). Treatment in the red region (“Dangerous Treatment”) results in emergence of resistance, while treatment in the green region (“Efficient Treatment”) can lead to eradication. Parameters: .

Figure 3. Treatment timing above and below critical manifold.

Effects of treatment when initial conditions are above (panels b, c, d) and below (panels e, f, g) the critical manifold. Panel a is replicated from Figure 2, with each dot corresponding to the panels at right. Solid lines correspond to mean-field approximations, and points correspond to means of 100,000 simulations on networks of size 250,000. Horizontal black line corresponds to a mean of 1 infected individual in a network of 250,000 over 100,000 simulations. With no treatment the disease reaches a maximum and decays (panels b and e). Treatment is only effective early in the simulations when the initial conditions are under the critical manifold (panel f compared to panel c) as opposed to when the initial conditions are over the critical manifold (panel g compared to panel d). Parameters: , , , , , , and .

Figure 4. Comparison of random and targeted treatment.

Panel a shows the final size for wild-type, resistant and both infections as a function of percentage treated, , for targeted (dashed lines) and non-targeted (solid lines) treatment regimes. We see a transition from wild-type to resistant infections at a lower treatment percentage in the targeted treatment regime. Panel b shows the percent of total infection that is the resistant strain for the targeted (dashed line) and non-targeted (solid line) treatment. Parameters: , , , , and .