In any discussion of the great challenges facing humanity in addressing global environmental problems, a small number of topics automatically rise to the top: climate change, the loss of biodiversity, and the sustainability of the services ecosystems provide us. But no threats to human welfare are more urgent than those posed by infectious diseases; we suffer already the devastating consequences of the emergence of new diseases such as HIV, the reemergence of old ones such as tuberculosis, and simply the increasing toll of endemic diseases such as malaria. Non-human animals play fundamental roles in the spread of many of these diseases – as reservoirs, as vectors, and as cauldrons for the creation of new types. Land-use practices and environmental management both affect the persistence and spread of endemic diseases, such as malaria. Furthermore, as animal populations increase their ranges, due to climate change and human-facilitated alien introductions, the potential for disease spread also increases. These factors, together with the increasing mobility of the human population, conspire to make these environmental problems of great and immediate concern.

Using a dynamic model of the control of an infectious disease, we derive the conditions under which eradication will be optimal. When eradication is feasible, the optimal program requires either a low vaccination rate or eradication. A high vaccination rate is never optimal. Under special conditions, the results are especially stark: the optimal policy is either not to vaccinate at all or to eradicate. Our analysis yields a cost–benefit rule for eradication, which we apply to the current initiative to eradicate polio.

In the epidemiological literature, the eradication of a wildlife disease through culling is usually described in terms of a constant hunting rate to simulate the selective removal of animals from the population. By using simple SI (susceptible–infected) models, it is easy to prove that, if the hunting rate is high enough, the population eventually drops below a critical threshold level under which the pathogen is deemed to be extinct. However, hunting costs as well as the monetary benefits of disease control are almost systematically neglected. Moreover, the hunting rate is usually assumed to be constant over time, while in reality health authorities can implement more flexible culling policies. In this work we examine a class of more realistic time-variant culling strategies in a cost–benefit framework. Culling strategies differ in the way decisions are made about when and how much to cull; that is, whether hunting occurs when disease prevalence, host population density, or the number of carcasses exceeds (or is below) a given threshold. For each culling strategy, the optimal value of the control parameters and the hunting rate are those that minimize the sum of the culling costs and the sanitary costs associated with infection over a specific period of time. Classical swine fever (CSF) in wild boar populations has been taken as a reference example because of its potential economic impact on industrialized and developing countries.

We show that the optimal time-flexible culling strategy is invariably more efficient than the best traditional strategy in which the hunting rate is held constant through time. We also show that the type of hunting strategy that is selected as optimal depends on the shape of the cost functions.

Plant pathogens are quite destructive to cash crops throughout the world, resulting in potentially devastating financial losses. This work expands recently developed optimal control theory for an integrodifference model to a mathematical system which includes an integrodifference component. This system models a highly simplified plant pathogen system for which the optimal harvesting scheme is derived. An adjoint system is introduced to characterize the optimal harvesting pattern. This analysis shows that, while it may not be possible to prevent losses upon discovery of the pathogen in an area, it is theoretically possible to significantly cut those losses by culling an area around the initial infection.

We study the effects of development and climate change on infectious diseases in Sub-Saharan Africa. Infant mortality and infectious disease are closely related, but there are better data for the former. In an international cross-section, per capita income, literacy, and absolute poverty significantly affect infant mortality. We use scenarios of these three determinants and of climate change to project the future incidence of malaria, assuming it to change proportionally to infant mortality. Malaria deaths will first increase, because of population growth and climate change, but then fall, because of development. This pattern is robust to the choice of scenario, parameters, and starting conditions; and it holds for diarrhoea, schistosomiasis, and dengue fever as well. However, the timing and level of the mortality peak is very sensitive to assumptions. Climate change is important in the medium term, but dominated in the long term by development. As climate can only be changed with a substantial delay, development is the preferred strategy to reduce infectious diseases even if they are exacerbated by climate change. Development can, in particular, support the needed strengthening of disease control programs in the short run and thereby increase the capacity to cope with projected increases in infectious diseases over the medium to long term. This conclusion must, however, be viewed with caution, because development, even of the sort envisioned in the underlying socio-economic scenarios, is by no means certain.

The fields of epidemiological disease modeling and economics have tended to work independently of each other despite their common reliance on the language of mathematics and exploration of similar questions related to human behavior and infectious disease. This paper explores the benefits of incorporating simple economic principles of individual behavior and resource optimization into epidemiological models, reviews related research, and indicates how future cross-discipline collaborations can generate more accurate models of disease and its control to guide policy makers.