Models of spatio-temporal dynamics in malaria1

The development of mathematical models has been very useful in the study of the dynamics of infectious diseases. However, there is a scarcity of models which take into account the spatial heterogeneity of the environment. The few models developed indicate that, when the environment is fragmented, an increase in mobility between the patches enhances the persistence of the disease. We develop a model which describes the dynamics of malaria in time in a heterogeneous environment. As expected, fragmenting the environment decreases the likelihood of establishment of the disease in comparison with a homogeneous environment. Two types of mobility patterns are considered in the fragmented environment: migration between patches with no return, and visitation in which the individuals return to their patch of origin after visiting other patches. When compared with the fragmented environment without mobility, the time elapsed to reach the equilibrium decreases with both patterns of mobility; however, the chances of establishment and the equilibrium prevalence are the same with the migration pattern and higher with the visitation pattern. It is concluded that the effects of mobility in heterogeneous environments is not a simple matter, and depends on the patterns of mobility. The relevance of these findings to the design of control strategies is discussed.