To be completed by Erin Human African Trypanosomiasis (HAT) This work considers the effects of using "host-only" transmission models such as the quasi-equilibrium assumption upon disease dynamics and also the effect of omitting the latency period upon epidemic predictions. Some of Kat’s work focuses on the simplifications that are often made to reduce the complexity of models. Even when only considering just one specific disease the variations in the disease within different populations may lead to changes in not just the parameterisation, but also of how one may wish to take the modelling approach. Unsurprisingly models from the literature range greatly from deterministic to stochastic, endemic (including birth and death rates) or epidemic (an outbreak of limited duration), incorporating spatial spread, spatial heterogeneity, latency periods, age structure, acquisition and loss of immunity, multiple strains and many others. There are many different types of mathematical model for vector-borne disease transmission ideally these are sought to be kept mathematically tractable and as simple as possible whilst retaining the general dynamics of the biological system. Modelling the Dynamics of Vector-Borne Diseases Typically mathematical models of vector-borne diseases are based upon a two-population SI(R) model exhibiting “criss-cross” infection terms, where and are the force of infection of terms for hosts and vectors respectively:ĭependent upon the disease and population being modelled, this may be adapted to incorporate other more specific features.
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