Paper
The history of infectious disease modelling essentially begins with the papers by Ross on malaria [1-5]. These models assume that the dynamics of malaria can most simply be characterized by two equations that describe the prevalence of malaria in the human and mosquito hosts. This structure has formed the central core of models for malaria and most other vector-borne diseases for the last century with occasional additions acknowledging important aetiological details. We partially add to this tradition by describing a malaria model that provides for vital dynamics in the vector and the possibility of super-infection in the human host; reinfection of asymptomatic hosts before they have cleared a prior infection. These key features of malaria aetiology create the potential for break points in the prevalence of infected hosts, sudden transitions that seem to characterize malarias response to control in different locations. We show that this potential for critical transitions is a general and underappreciated feature of any model for vector borne diseases with incomplete immunity and asymptomatic patients, including the canonical Ross-McDonald model. Ignoring these details of the hosts immune response to infection can potentially lead to serious misunderstanding in the interpretation of malaria distribution patterns and the design of control schemes for other vector-borne diseases.
