# Research

Are you a student interested in becoming involved in research at the interface of mathematics and biology? Contact me via e-mail! **m.robert@usciences.edu**.

Note: Although my expertise is in infectious disease modeling, I would be happy to work with students in other systems, biological and non-biological. Students interested in quantitative research in biology, chemistry, pharmacy, and/or the social sciences are invited to contact me as well! If you are interested in research outside the domain of my interests, please have a basic idea of what particular applications you might be interested in.

My research is focused on utilizing mathematical models to develop a better understanding of the various processes underlying infectious disease dynamics. My work to date has been more narrowly focused on mosquito-borne diseases such as dengue, chikungunya, and Zika. Each of these three diseases are vectored primarily by *Aedes aegypti* mosquitoes. Dengue has been established throughout Southeast Asia, Africa, and the Americas for decades; chikungunya and Zika have only recently experienced global spread with the first reports of the two viruses in the Western Hemisphere occurring in 2013 and 2015, respectively. Emergence and spread of these viruses is driven by expansion of the vector distribution, urbanization, and increases in global travel. All three viruses are often imported into populations that are currently naïve to the diseases but could potentially sustain local transmission. There are no prophylactic treatments or vaccines for chikungunya or Zika, and currently licensed vaccines for dengue have incomplete efficacy at protecting against the multiple strains of the virus. Control of the viruses relies upon control of the vectors, although effective, sustainable vector control programs are rare, so novel control alternatives are being investigated.

My work covers various facets of the dynamics of vector-borne disease spread and control. Below, I describe some projects in more detail. Articles for published work can be found on the Publications page.

**Understanding Emergence and Spread of Vector-Borne Disease in Naïve Populations**

Mathematical models are valuable tools for understanding the factors that contribute to the introduction and emergence of a disease in populations that have rarely or never been affected by the disease. Often, data is not available to parameterize models until after a disease has begun to spread in a population. I am interested in developing a model framework to study the potential for emergence and spread of disease in naïve populations by utilizing what data is available. By doing so, we can better understand some factors that potentially lead to successful emergence and pinpoint gaps in the data that need to be addressed in order to develop a better understanding of the potential for emergence and outbreaks.

**Understanding the Influence of Environmental Factors on Disease Emergence and Spread **

Transmission and spread of viruses such as dengue, chikungunya, and Zika depend upon interactions among humans, mosquitoes, the virus, and the environment. In particular, the rate of mosquito development and the mosquito lifespan fluctuate with changes in temperature. Temperature also impacts the extrinsic incubation period (EIP) of the virus within the mosquito host. However, the optimal temperature for EIP and the optimal temperature for mosquito development and survival are not necessarily the same. I am interested in developing models to investigate the influence of both inter-annual and diurnal temperature fluctuations on the transmission of viruses and the ability of introductions of dengue to lead to outbreaks. Such modeling exercises can be used to inform experiments to better quantify the relationship between temperature and characteristics of the virus and mosquito life history. This, in turn, can help parameterize models for studying the spread of viruses.

**Optimizing Integrated Strategies to Control Vector-Borne Diseases**

As novel approaches for controlling vector-borne diseases are being developed, it is important to understand how these approaches can be integrated with traditional methods to most efficiently reduce disease incidence. I am interested in utilizing the tools of optimal control theory to study and develop integrated pest management strategies for controlling vector-borne diseases.

**Using Mathematical Models as Aids in Experimental Design**

Statistical models are often used to guide experiments and assess experimental outcomes. While mathematical models are also used quite frequently to assess experimental outcomes (e.g. parameter estimation), it is less appreciated that these models can play a role in the design of experiments. I am interested in using models as tools for guiding the development of experiments, exploring the full potential of experimental designs, and identifying any limitations of experimental designs.

**Assessing GPM Control Strategies**

A number of novel methods for controlling disease vectors have been proposed in recent years. Among them are methods that fall under a broader category of pest control known as Genetic Pest Management (GPM). GPM strategies aim to release insects that have genetic material that alters either their ability to produce viable offspring (population suppression) or ability to transmit disease (population replacement). These strategies must be evaluated thoroughly before releases can occur in native populations. I am interested in using mathematical models to help to determine release strategies that will result in the desired outcome (population suppression or population replacement) as well as predict the effects of any potential shortcomings of the strategies.

**Assessing control strategies involving the release of Wolbachia-infected mosquitoes**

Another novel approach to reducing dengue transmission is the release of Ae. aegypti infected with the bacterium Wolbachia. Research has shown that Wolbachia infection shortens the adult life of mosquitoes and reduces their ability to transmit the dengue virus. Releases of Wolbachia-infected mosquitoes could result in a population of mosquitoes unable to transmit dengue, which would in turn result in decreased incidence of the disease. Models of Wolbachia often predict that successful invasion will result if the infection is introduced above some frequency in the native population. In practice, however, successful invasion could be limited by spatial heterogeneity, movement of mosquitoes, and stochastic effects, among other things. I am interested in using models to assess the role that these and other effects could have on the ability of Wolbachia infection to successfully invade.

**Summer of 2012 REU and UBM Program at NCSU**

In the summer of 2012 I mentored 8 undergraduate students at NCSU along with Alun Lloyd and Tim Antonelli. The students worked on three separate projects developing mathematical models to investigate the impact on wild populations of disease-vectoring mosquitoes of releasing mosquitoes infected with the bacterium *Wolbachia*.

REU and UBM 2012 Students present their research!