ZIKV has affected many countries around the world, causing a variety of consequences. Several strategies, including awareness campaigns to promote travel safety to tropical regions, personal protection and vector control, have been implemented to limit its spread. Mathematical models have been used to better understand the dynamics of Zika and to assess the efficacy of interventions. In this thesis, Zika infection compartmental models have been developed to investigate various aspects of the dis ease. The first model incorporates human movement between rural areas and nearby forests, to investigate the role of human movement in the spread of ZIKV infections in human and mosquito populations. Proportions of both susceptible and infected humans living in rural areas are assumed to move to nearby forest areas. Direct, indirect, and vertical transmission routes are incorporated for all populations. The second model describes the spread of the disease in three interacting populations, namely, human, vector (mosquitoes), and non-human primate (monkeys) inhabiting forests area. It aims to investigate the role of non-human primates in the disease transmission dynam ics. Human movement between rural and forest areas has been also considered. It is assumed that the ZIKV spreads within the non-human primate population, which in turn acts as a reservoir of infection, and is then transmitted to the human population through infected mosquitoes. The proposed model incorporates vertical transmission and direct transmission in all populations. The third model represents a multi-patch model for the spread of ZIKV infection taking into account direct and indirect transmissions along with vertical transmission. The model is fitted to a data set collected from two neighboring countries Brazil and Colombia to estimate some of its parameters. The fourth model investigates the transmission dynamics of the co-infection of Malaria and Zika. The potential interactions between these diseases and their implications for public health and the potential effectiveness of various intervention strategies have been explored. The analysis of the models include positivity and boundedness of solutions, derivation of the basic reproduction numbers, existence and stability analysis of the equilibrium points, and bifurcation analysis are performed. Also, sensitivity analysis of the basic reproduction number to models' parameters has been presented and discussed. The effect of some model parameters on the disease transmission dynamics has been carried out numerically and presented graphically in each mod