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A Household Model of Cockroach Infestation and Its Effects on Atopic Asthma Symptoms

Asthma is a chronic respiratory condition which affects 25 million people in the United States.
According to the Center for Disease Control and Prevention (CDC) asthma is a significant health
and economic concern, and also causes 270 deaths per month. Cockroaches are among the most
common indoor pests, with its allergen being present in 63% of U.S. households. Improper extermination
of cockroaches and the associated allergens has been shown to increase the occurrence
of atopic asthma, a type of asthma triggered by the exposure to allergens. In this work, a household
model was developed to study the dynamics of cockroach infestation in a neighborhood of houses
with individuals sensitized to the cockroach allergen. The impact of extermination and removal of
allergens in a household with recurrent atopic asthma was evaluated. Equilibria for the system
with and without the influx or migration of cockroaches are determined, including equilibria in
which both cockroaches and asthma are present. The average number of secondary infestations
that can be produced by the presence of a single infestation in a population of households without
cockroaches and asthma was calculated. Numerical simulations on the model and sensitivity analysis
on the basic reproductive number were used to examine the impact of key parameter values.
Numerical backward bifurcations for a set of parameters were obtained and the results showed that
it is more effective to prevent infestation of cockroaches, rather to attempt to remove cockroaches
once they have infested a house. A mathematical study of cockroach infestations and their effect on
atopic asthma has not been done. Therefore, this model will assist in educating the general public
about the importance of pest control and its relationship with asthma.

Article Number: MTBI-14-02M



Ana Lucıa Campana - Universidad de Los Andes, Bogota D.C., Colombia

Karen Funderburk - Arizona State University, Tempe, Arizona

Amandeep Kaur - California State University, Bakersfield

Patricia Puente - Texas Woman’s University, Denton, Texas

Karen Rıos-Soto - University of Puerto Rico, Mayaguez

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