I am interested in using systems of ordinary differential equations to study the spread of infectious diseases and the impact of mitigation strategies. I have developed simple and age-structured mathematical models for various diseases including HIV, smallpox, influenza, and malaria. I am also interested in understanding the impact that reactive community and individual behavior may have on the spread of diseases. Our research has shown that behavioral changes can significantly reduce the spread and shorten the epidemic.
We studied the effects of education, temporarily effective vaccines, and therapies on HIV transmission in homosexuals with genetic heterogeneity (i.e., a mutant allele Delta32 of CCR5 chemokine receptor gene, which provides partial or full resistance to HIV in 10% of Caucasian populations). Our results show that combined interventions are more effective than single intervention strategies; however, genetic resistance may increase the spread by prolonging the infected period of slow progressors.
Facemask can be effective in preventing airborne infections. We studied the impact of compliance, effectiveness, and influenza severity and showed that facemasks can reduce the transmission and allow for more time to develop pharmaceutical interventions. In addition, facemasks can reduce the economic impacts by keeping schools open and decreasing the spread.
Bed nets have played an important role in the fight against malaria. However, improper handling and human behavior (e.g., lack of usage) have diminish their effectiveness. We investigated the impact of insecticide-treated bed nets and identified the threshold needed to eliminate malaria using a simple mathematical model. We shoed that bed nets have a positive impact in reducing disease burden.
The impact of changes in human behavior, specifically a reduction in the number of contacts, can change the dynamics of disease transmission. We studied the impact of behavioral changes in response to a smallpox outbreak and showed that disease is highly sensitive to how rapidly people reduce their contacts. Models that do not include reactive changes in behavior will overestimate the impact of infectious diseases.