When resistance to anticancer or antimicrobial drugs evolves in a patient, highly effective chemotherapy can fail, threatening patient health and lifespan. Standard practice is to treat aggressively, effectively eliminating drug-sensitive target cells as quickly as possible. This prevents sensitive cells from acquiring resistance de novo but also eliminates populations that can competitively suppress resistant populations. Here we analyse that evolutionary trade-off and consider recent suggestions that treatment regimens aimed at containing rather than eliminating tumours or infections might more effectively delay the emergence of resistance. Our general mathematical analysis shows that there are situations in which regimens aimed at containment will outperform standard practice even if there is no fitness cost of resistance, and, in those cases, the time to treatment failure can be more than doubled. But, there are also situations in which containment will make a bad prognosis worse. Our analysis identifies thresholds that define these situations and thus can guide treatment decisions. The analysis also suggests a variety of interventions that could be used in conjunction with cytotoxic drugs to inhibit the emergence of resistance. Fundamental principles determine, across a wide range of disease settings, the circumstances under which standard practice best delays resistance emergence—and when it can be bettered.

We extend the existing work on the time-optimal control of the basic SIR epidemic model with mass action contact rate. Previous results have focused on minimizing an objective function that is a linear combination of the cost associated with using control and either the outbreak size or the infectious burden. We instead, provide analytic solutions for the control that minimizes the outbreak size (or infectious burden) under the assumption that there are limited control resources. We provide optimal control policies for an isolation only model, a vaccination only model and a combined isolation-vaccination model (or mixed model). The optimal policies described here contain many interesting features especially when compared to previous analyses. For example, under certain circumstances the optimal isolation only policy is not unique. Furthermore the optimal mixed policy is not simply a combination of the optimal isolation only policy and the optimal vaccination only policy. The results presented here also highlight a number of areas that warrant further study and emphasize that time-optimal control of the basic SIR model is still not fully understood.

The macaque malaria parasite Plasmodium knowlesi has recently emerged as an important zoonosis in Southeast Asia. Infections are typically mild but can cause severe disease, achieving parasite densities similar to fatal Plasmodium falciparum infections. We show that a primate-adapted P. knowlesi parasite proliferates poorly in human blood due to a strong preference for young red blood cells. We establish a continuous in vitro culture system by using human blood enriched for young cells. Mathematical modeling predicts that parasite adaptation for invasion of older red blood cells is a likely mechanism leading to high parasite densities in clinical infections. Consistent with this model, we find that P. knowlesi can adapt to invade a wider age range of red blood cells, resulting in proliferation in normal human blood. Such cellular niche expansion may increase pathogenesis in humans and will be a key feature to monitor as P. knowlesi emerges in human populations.