The usefulness of mathematics in agriculture, for the environment and in contrasting diseases: insights from a wide range of simple models

Mathematics has been applied to physics and engineering in the last few centuries, substantially contributing to the various phases of the industrial revolution. Its application to biology is instead relatively more recent. In this paper we provide an overview of some problems in a few fields mainly related to ecology. The models discussed help in fighting pests in agriculture to improve crop harvesting and to combat the phenomenon of alien species invasions, that due to worldwide trading and climate changes is affecting the temperate regions, threatening the survival of the native species. A pair of examples related to primary oxygen production and fallacies of our linear way of thinking are also presented, to stress the fact that raising temperatures entail huge unforeseen problems. Finally we delve briefly in the vaste field of epidemiology, that would deserve a review on its own, to discuss models for diseases in the environment and one instance related epidemics affecting humans, prompted by the important role of asymptomatics played in them.