## Physical Sciences 2

#### Presentation Title

Analyzing the Spread of the Zika Infection in Puerto Rico

#### Faculty Mentor

Dr. Anael Verdugo

#### Start Date

18-11-2017 2:00 PM

#### End Date

18-11-2017 2:15 PM

9-285

#### Session

Physical Sciences 2

Oral Talk

#### Subject Area

physical_mathematical_sciences

#### Abstract

The Zika virus is being investigated due to its recent outbreak in Latin America. Within the last year, Zika infection case counts have risen in various states throughout America, with the largest case count centered in Puerto Rico. Although properties of the virus have been identified – including its mode of transmission and link to birth defects – the infection’s subtle symptoms make the illness difficult to diagnose. Given that the infection was previously perceived as a mild illness, the disease’s dynamics remain unknown. As simple models graze over the unique behaviors diseases exhibit, this work aims to create a robust model that analyzes disease transmission from an evolutionary perspective. We intertwine compartmentalizing techniques inspired by the Susceptible-Infected-Recovered (SIR) model, where a population is categorized into subpopulations based on their health status, with the ordinary differential equations of the Replicator-Mutator (RM) model to describe the interactions between the three subgroups. Applying the RM model to the Zika virus, we analyze the model’s dynamics and assess its ability to model the Zika infection’s geographic spread. Through MATLAB, we produce simulations of our equations to define our model’s parameters, giving us a mathematical description of the three subpopulations’ growth. Lastly, by using linear stability analysis we identify the model’s fixed points to analyze the subpopulations’ long-term behavior. Ultimately, by examining this model’s dynamics we aim to give insight into the infection’s outbreak cycle.

#### Summary of research results to be presented

We have identified the RM model’s best-fit curve with respect to the infected subpopulation’s experimental curve, which was formulated by the Centers for Disease Control and Prevention’s case count data on the Zika infection. We mimic the experimental curve’s behavior, namely capturing the initial increase in the infected population’s size and steep increase in size from August to December 2017. The parameters that provide this similar behavior were chosen as values for our model. According to these parameters, the Zika infection exhibits a low infection and recovery rate. When our RM model’s simulations were extended to 25 months, the predicted behavior demonstrates that the susceptible population will become nonexistent, while the number of infected individuals will grow to encapsulate the majority of the Puerto Rican population. Furthermore, our simulations indicate that the infection rate is faster than the recovery rate, evidenced by the steep decrease in the susceptible population in comparison to the recovered population.

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COinS

Nov 18th, 2:00 PM Nov 18th, 2:15 PM

Analyzing the Spread of the Zika Infection in Puerto Rico

9-285

The Zika virus is being investigated due to its recent outbreak in Latin America. Within the last year, Zika infection case counts have risen in various states throughout America, with the largest case count centered in Puerto Rico. Although properties of the virus have been identified – including its mode of transmission and link to birth defects – the infection’s subtle symptoms make the illness difficult to diagnose. Given that the infection was previously perceived as a mild illness, the disease’s dynamics remain unknown. As simple models graze over the unique behaviors diseases exhibit, this work aims to create a robust model that analyzes disease transmission from an evolutionary perspective. We intertwine compartmentalizing techniques inspired by the Susceptible-Infected-Recovered (SIR) model, where a population is categorized into subpopulations based on their health status, with the ordinary differential equations of the Replicator-Mutator (RM) model to describe the interactions between the three subgroups. Applying the RM model to the Zika virus, we analyze the model’s dynamics and assess its ability to model the Zika infection’s geographic spread. Through MATLAB, we produce simulations of our equations to define our model’s parameters, giving us a mathematical description of the three subpopulations’ growth. Lastly, by using linear stability analysis we identify the model’s fixed points to analyze the subpopulations’ long-term behavior. Ultimately, by examining this model’s dynamics we aim to give insight into the infection’s outbreak cycle.