Transmission Dynamics of Some Epidemiological Patch Models

As we known, infectious diseases can be transmitted from one region to another due to extensive travel and migration. Meanwhile, different regions have different demographic and epidemiological characteristics. To capture these features, multi-patch epidemic models have been developed to study disease transmission in heterogeneous environments. In Chapter 1, a susceptible-infectious-susceptible patch model with nonconstant transmission coefficients is formulated to investigate the effect of media coverage and human movement on the spread of infectious diseases among patches. In chapter 2, I propose a multi-patch model to study the effects of population dispersal on the spatial spread of malaria between patches. In Chapter 3, based on the classical Ross-Macdonald model, I propose a periodic malaria model to incorporate the effects of temporal and spatial heterogeneity in disease transmission. Chapter 4 is devoted to studying the spatial spread of Rift Valley fever in Egypt. In summary, I propose several epidemic patch models to study the effects of human movement on the spatial spread of infectious diseases. The analytical and numerical results suggest that the migration of humans can influence disease spread in a complicated way and to control or eliminate an infectious disease we need global and regional strategies