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. Here we show that a primate-adapted P. knowlesi parasite proliferates poorly in human blood due to a strong preference for young red blood cells (RBCs). We establish a continuous in vitro culture system by using human blood enriched for young cells. Mathematical modelling predicts that parasite adaptation for invasion of older RBCs 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 RBCs, 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.

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. 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 prevent sensitive cells from acquiring resistance by eliminating them as quickly as possible with aggressive chemotherapy. This approach, however, prevents sensitive cells from competitively suppressing any resistant cells that are present. Consequently, it has been suggested that where resistance emergence threatens patient health, aggressive therapies should be replaced with approaches aimed at containing the infection or cancer. Here we show that there is no “one-size-fits-all” solution. Containment can improve some situations, but it can also make things worse. Our analysis delineates the details that determine when containment is the best choice—and when aggressive treatment is better.

The application of evolutionary and ecological principles to cancer prevention and treatment, as well as recognizing cancer as a selection force in nature, has gained impetus over the last 50 years. Following the initial theoretical approaches that combined knowledge from interdisciplinary fields, it became clear that using the eco‐evolutionary framework is of key importance to understand cancer. We are now at a pivotal point where accumulating evidence starts to steer the future directions of the discipline and allows us to underpin the key challenges that remain to be addressed. Here, we aim to assess current advancements in the field and to suggest future directions for research. First, we summarize cancer research areas that, so far, have assimilated ecological and evolutionary principles into their approaches and illustrate their key importance. Then, we assembled 33 experts and identified 84 key questions, organized around nine major themes, to pave the foundations for research to come. We highlight the urgent need for broadening the portfolio of research directions to stimulate novel approaches at the interface of oncology and ecological and evolutionary sciences. We conclude that progressive and efficient cross‐disciplinary collaborations that draw on the expertise of the fields of ecology, evolution and cancer are essential in order to efficiently address current and future questions about cancer.

Standard infectious disease practice calls for aggressive drug treatment that rapidly eliminates the pathogen population before resistance can emerge. When resistance is absent, this elimination strategy can lead to complete cure. However, when resistance is already present, removing drug-sensitive cells as quickly as possible removes competitive barriers that may slow the growth of resistant cells. In contrast to the elimination strategy, a containment strategy aims to maintain the maximum tolerable number of pathogens, exploiting competitive suppression to achieve chronic control. Here, we combine in vitro experiments in computer-controlled bioreactors with mathematical modeling to investigate whether containment strategies can delay failure of antibiotic treatment regimens. To do so, we measured the “escape time” required for drug-resistant Escherichia coli populations to eclipse a threshold density maintained by adaptive antibiotic dosing. Populations containing only resistant cells rapidly escape the threshold density, but we found that matched resistant populations that also contain the maximum possible number of sensitive cells could be contained for significantly longer. The increase in escape time occurs only when the threshold density—the acceptable bacterial burden—is sufficiently high, an effect that mathematical models attribute to increased competition. The findings provide decisive experimental confirmation that maintaining the maximum number of sensitive cells can be used to contain resistance when the size of the population is sufficiently large.