### June 2016 - Present

# DYNAMICS AND TOPOLOGY OF ZIKA VIRUS EPIDEMICS

CONFERENCES:

Poster presentation at NetSciX2017

Poster presentation at Complenet 2018

ABSTRACT:

This research provides a generative approach to modeling and analyzing Zika Virus epidemics over a coupled system of human and mosquito populations. We advance a network generation scheme referred to as the Sexual Contact Network (SCN). The SCN consists of several sub-networks, each characterized by a specific sexual behavior (based on the type and number of partners). The human population is viewed as heterogeneous and is represented by a sexual network across which the virus spreads following a Susceptible, Exposed, Infected, and Recovered (SEIR) dynamics model. The mosquitoes are modeled as a homogeneous population across which the virus spreads following a Susceptible, Exposed, and Infected (SEI) dynamics model. The passing of the virus from humans to mosquitoes and vice-versa is captured by a two-way coupling between the populations.

This model straddles the gap between theoretical probability distribution and data-driven approach, by only accepting the most fundamental and easily accessible data points as parameters of the generative model. These parameters include the basic epidemiological rates of the virus, rough percentages of the composition of the SCN that can typically be acquired from public data sources, and information about the mosquito population.

This proposed model should be utilized when there is a lack of data as it relies on generative equations and the resulting simulations, as opposed to other models which tend to be highly accurate, but require large amounts of available data. For many Zika-stricken regions, there is a dearth of information, particularly during the initial breakout period when the virus is discovered. This period is also when epidemiologists could most benefit from a computational tool to aid in key decision-making, such as resource allocation.

Based on these input parameters, the model proposed by this research stochastically generates realizations of SCN's, runs deterministic SEIR single species epidemic simulations over the SCN's, and runs deterministic SEIR-SEI interspecies epidemics over the coupled human-mosquito systems. Once the network and epidemic data is simulated, the data analysis method proposed in this research finds the Graph Laplacian of the SCN's, the total time for the infection to cease spreading, the diffusion constants associated with each SCN's Graph Laplacian, and the peak infections of each node of the SCN during the epidemic. These variables are collected for both the single species and interspecies simulations. Then, they are combined, weighted, subtracted, and normalized to find the total difference in spread, due to the mosquitoes vs. the SCN.

The results of the simulations and subsequent analyses indicate that the difference in the spread of the virus, with and without mosquitoes present, across various SCN’s is heavily impacted by the location of the original outbreak of the virus in the SCN, as well as the overall connectivity of the SCN. As expected, for SCN’s with more disconnected components, e.g. fully monogamous or abstinent sample populations, the mosquitoes have a larger net effect in the spread of the virus than in fully connected networks, e.g. networks generated from power law distributions that typically form one large component, where the virus will eventually diffuse given enough time.

The interesting results emerge when simulating SCN’s based on realistic demographic parameters, whose connectivity is difficult to capture. The above process of analysis yields preliminary results that reduce the dimensionality of these SCNs’ connectivity information. Instead of requiring their full adjacency matrices to convey a meaningful measure of their connectivity information, a useful amount of information is conveyed in the difference in spread of the virus due to mosquitoes. Essentially this difference in spread represents an underlying feature of the overall connectivity of a SCN. It achieves this by relating the simulated epidemic spread of a virus over the SCN to the closed-form diffusion process over the same SCN, via its Graph Laplacian that captures the algebraic connectivity of the SCN. By simulating both the single species and coupled population systems, over the same SCN, and comparing them via this diffusion process, the difference in their spread of the virus can be attributed to mosquitoes. This attribution establishes the link between the spread of the virus due to mosquitoes and the connectivity information of the respective networks.

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