Publication Date



Open access

Embargo Period


Degree Type


Degree Name

Doctor of Philosophy (PHD)


Mathematics (Arts and Sciences)

Date of Defense


First Committee Member

Shigui Ruan

Second Committee Member

Robert Stephen Cantrell

Third Committee Member

Chris Cosner

Fourth Committee Member

John Beier


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.


mathematical epidemiology; patch model; malaria; basic reproduction number; persistence; Rift Valley fever