Generalized Epidemic Dynamic Models with Delays for Hierarchic Network Populations

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The recent advances in modern technology in communication, transportation and several other areas of life have many positive significant impacts in several areas of human life. Some negative indirect byproducts of these advances have also emerged. For instance, the rapid, effective and efficient global human transportation means in modern times indirectly initiates and accelerates the outbreaks of epidemics and pandemic. Epidemic dynamic models in mathematical biology incorporate two general types of delays in the epidemic process to improve the reality of the models namely:- (1) the disease latency which can be the incubation period of the disease or the period of infectiousness etc., and (2) the immunity period of the disease which can be natural infection induced immunity or artificial immunity. Furthermore, the influence of the random fluctuating environment is also included into the epidemic dynamic models to add to the reality of the models. In this talk, two general types of epidemic dynamic models are presented based on the mode of disease transmission- (1) a generalized epidemic dynamic model for diseases with direct human to human transmission, for example, influenza etc., (2) a generalized epidemic dynamic model for a vector-borne disease, for example, Zika-virus or malaria etc. I will show how to represent the human mobility process, the two general forms of delays and the random environmental fluctuations in the epidemic dynamic process for a hierarchic population exhibiting two levels of human interaction, i.e. an interregional and an intra-regional level. For example, human interaction at two levels in a country- intra-regional level between counties, and interregional level between states. The epidemic dynamic models are expressed as systems of stochastic differential equations. The epidemic dynamic models are investigated for the eradication of the disease from the population and the influence of the human mobility process on the eradication of the disease are characterized for several real life scenarios. Numerical simulation results are presented for a real life scenario.


Joint Mathematics and Statistics Colloquiums, Department of Mathematical Sciences, Georgia Southern University


Statesboro, GA