Arsha Sherly

• Mechanistic disease spread models for different vector borne diseases have been studied from the 19th century. The relevance of mathematical modeling and numerical simulation of disease spread is increasing nowadays. This thesis focuses on the compartmental models of the vector-borne diseases that are also transmitted directly among humans. An example of such an arboviral disease that falls under this category is the Zika Virus disease. The study begins with a compartmental SIRUV model and its mathematical analysis. The non-trivial relationship between the basic reproduction number obtained through two methods have been discussed. The analytical results that are mathematically proven for this model are numerically verified. Another SIRUV model is presented by considering a different formulation of the model parameters and the newly obtained model is shown to be clearly incorporating the dependence on the ratio of mosquito population size to human population size in the disease spread. In order to incorporate the spatial as well as temporal dynamics of the disease spread, a meta-population model based on the SIRUV model was developed. The space domain under consideration are divided into patches which may denote mutually exclusive spatial entities like administrative areas, districts, provinces, cities, states or even countries. The research focused only on the short term movements or commuting behavior of humans across the patches. This is incorportated in the multi-patch meta-population model using a matrix of residence time fractions of humans in each patches. Mathematically simplified analytical results are deduced by which it is shown that, for an exemplary scenario that is numerically studied, the multi-patch model also admits the threshold properties that the single patch SIRUV model holds. The relevance of commuting behavior of humans in the disease spread has been presented using the numerical results from this model. The local and non-local commuting are incorporated into the meta-population model in a numerical example. Later, a PDE model is developed from the multi-patch model.