Bhattarai, Rosahn

English

ScholarWorks @ Georgia State University

Abstract for Using Predator Carrying Capacity for a Pathogenic Vector-Dynamic Differential Model Schistosomiasis, also known as bilharzia or “snail fever”, is a parasitic disease carried by freshwater snails that has affected 240 million people in as many as 78 countries worldwide, with a majority of cases in sub-Saharan Africa.  Schistosomiasis is transmitted by contact with contaminated fresh water (rivers, lakes and ponds) inhabited by snails carrying the parasite, which are kept in check by freshwater prawns (predators). The parasites grow in the human bodies and produce eggs which are eventually released by humans into the water, completing the cycle.  We adapt a classical Ross-MacDonald model to account for predator-prey interaction between these three populations, with the snail population divided into infected and uninfected individuals.  Other features of the model include predator and prey carrying capacity, a fixed human population and mass-action assumption for the interaction terms.  Our model exhibits oscillatory behavior for the predator and prey populations, while slowly reducing prey (infected) numbers, which is a new finding that is in agreement with experimental data.  This points out to avenues of reducing the threat of infection with Schistosomiasis by increasing the negative impact the predator population has on the infected snails.  Future research will focus on introducing more detailed components for this ecological system, such as other natural predators for snails and detailed spatial interactions. 

Using Predator Carrying Capacity for a Pathogenic Vector-Dynamic Differential Model

Bhattarai, Rosahn P

VCU Scholars Compass

Virginia Commonwealth UniversityVCU Scholars CompassBiology and Medicine Through MathematicsConference 2016May 21st, 5:30 PM - 8:00 PMUsing Predator Carrying Capacity for a PathogenicVector-Dynamic Differential ModelRosahn P. BhattaraiGeorgia State University, rbhattarai1@student.gsu.eduFollow this and additional works at: http://scholarscompass.vcu.edu/bammPart of the Dynamic Systems Commons, Ordinary Differential Equations and Applied DynamicsCommons, and the Parasitic Diseases CommonsThis Event is brought to you for free and open access by the Dept. of Mathematics and Applied Mathematics at VCU Scholars Compass. It has beenaccepted for inclusion in Biology and Medicine Through Mathematics Conference by an authorized administrator of VCU Scholars Compass. Formore information, please contact libcompass@vcu.edu.http://scholarscompass.vcu.edu/bamm/2016/May21/17Abstract for Using Predator Carrying Capacity for a Pathogenic Vector-Dynamic Differential Model Schistosomiasis, also known as bilharzia or “snail fever”, is a parasitic disease carried by freshwater snails that has affected 240 million people in as many as 78 countries worldwide, with a majority of cases in sub-Saharan Africa.  Schistosomiasis is transmitted by contact with contaminated fresh water (rivers, lakes and ponds) inhabited by snails carrying the parasite, which are kept in check by freshwater prawns (predators). The parasites grow in the human bodies and produce eggs which are eventually released by humans into the water, completing the cycle.  We adapt a classical Ross-MacDonald model to account for predator-prey interaction between these three populations, with the snail population divided into infected and uninfected individuals.  Other features of the model include predator and prey carrying capacity, a fixed human population and mass-action assumption for the interaction terms.  Our model exhibits oscillatory behavior for the predator and prey populations, while slowly reducing prey (infected) numbers, which is a new finding that is in agreement with experimental data.  This points out to avenues of reducing the threat of infection with Schistosomiasis by increasing the negative impact the predator population has on the infected snails.  Future research will focus on introducing more detailed components for this ecological system, such as other natural predators for snails and detailed spatial interactions. 

Georgia State University

Abstract for Using Predator Carrying Capacity for a 
Pathogenic Vector-Dynamic Differential Model 
Schistosomiasis, also known as bilharzia or “snail fever”, is a parasitic 
disease carried by freshwater snails that has affected 240 million people in as 
many as 78 countries worldwide, with a majority of cases in sub-Saharan 
Africa.  Schistosomiasis is transmitted by contact with contaminated fresh water 
(rivers, lakes and ponds) inhabited by snails carrying the parasite, which are 
kept in check by freshwater prawns (predators). The parasites grow in the 
human bodies and produce eggs which are eventually released by humans into 
the water, completing the cycle.  We adapt a classical Ross-MacDonald model 
to account for predator-prey interaction between these three populations, with 
the snail population divided into infected and uninfected individuals.  Other 
features of the model include predator and prey carrying capacity, a fixed 
human population and mass-action assumption for the interaction terms.  Our 
model exhibits oscillatory behavior for the predator and prey populations, while 
slowly reducing prey (infected) numbers, which is a new finding that is in 
agreement with experimental data.  This points out to avenues of reducing the 
threat of infection with Schistosomiasis by increasing the negative impact the 
predator population has on the infected snails.  Future research will focus on 
introducing more detailed components for this ecological system, such as other 
natural predators for snails and detailed spatial interactions. 


http://scholarscompass.vcu.edu/cgi/viewcontent.cgi?article=1008&context=bamm

Using Predator Carrying Capacity for a Pathogenic Vector-Dynamic Differential Model

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