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A mathematical model for feral cat ecology with application to disease.
 Date Issued:
 2016
 Abstract/Description:
 We formulate and analyze a mathematical model for feral cats living in an isolated colony. The model contains compartments for kittens, adult females and adult males. Kittens are born at a rate proportional to the population of adult females and mature at equal rates into adult females and adult males. Adults compete with each other in a manner analogous to LotkaVolterra competition. This competition comes in four forms, classified by gender. Native house cats, and their effects are also considered, including additional competition and abandonment into the feral population. Control measures are also modeled in the form of percapita removal rates. We compute the net reproduction number (R_0) for the colony and consider its influence. In the absence of abandonment, if R_0(>)1, the population always persists at a positive equilibrium and if R_0 (<)= 1, the population always tends toward local extinction. This work will be referred to as the core model.The model is then expanded to include a set of colonies (patches) such as those in the core model (this time neglecting the effect of abandonment). Adult females and kittens remain in their native patch while adult males spend a fixed proportion of their time in each patch. Adult females experience competition from both the adult females living in the same patch as well as the visiting adult males. The proportion of adult males in patch j suffer competition from both adult females resident to that patch as well the proportion of adult males also in the patch. We formulate a net reproduction number for each patch (a patch reproduction number) R_j. If R_j(>)1 for at least one patch, then the collective population always persists at some nontrivial (but possibly semitrivial) steady state. We consider the number of possible steady states and their properties. This work will be referred to as the patch model.Finally, the core model is expanded to include the introduction of the feline leukemia virus. Since this disease has many modes of transmission, each of which depends on the host's gender and lifestage, we regard this as a model disease. A basic reproduction number R_0 for the disease is defined and analyzed. Vaccination terms are included and their role in disease propagation is analyzed. Necessary and sufficient conditions are given under which the diseasefree equilibrium is stable.
Title:  A mathematical model for feral cat ecology with application to disease. 
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Name(s): 
Sharpe, Jeff, Author Nevai, A, Committee Chair Shuai, Zhisheng, Committee Member Qi, Yuanwei, Committee Member QuintanaAscencio, Pedro, Committee Member University of Central Florida, Degree Grantor 

Type of Resource:  text  
Date Issued:  2016  
Publisher:  University of Central Florida  
Language(s):  English  
Abstract/Description:  We formulate and analyze a mathematical model for feral cats living in an isolated colony. The model contains compartments for kittens, adult females and adult males. Kittens are born at a rate proportional to the population of adult females and mature at equal rates into adult females and adult males. Adults compete with each other in a manner analogous to LotkaVolterra competition. This competition comes in four forms, classified by gender. Native house cats, and their effects are also considered, including additional competition and abandonment into the feral population. Control measures are also modeled in the form of percapita removal rates. We compute the net reproduction number (R_0) for the colony and consider its influence. In the absence of abandonment, if R_0(>)1, the population always persists at a positive equilibrium and if R_0 (<)= 1, the population always tends toward local extinction. This work will be referred to as the core model.The model is then expanded to include a set of colonies (patches) such as those in the core model (this time neglecting the effect of abandonment). Adult females and kittens remain in their native patch while adult males spend a fixed proportion of their time in each patch. Adult females experience competition from both the adult females living in the same patch as well as the visiting adult males. The proportion of adult males in patch j suffer competition from both adult females resident to that patch as well the proportion of adult males also in the patch. We formulate a net reproduction number for each patch (a patch reproduction number) R_j. If R_j(>)1 for at least one patch, then the collective population always persists at some nontrivial (but possibly semitrivial) steady state. We consider the number of possible steady states and their properties. This work will be referred to as the patch model.Finally, the core model is expanded to include the introduction of the feline leukemia virus. Since this disease has many modes of transmission, each of which depends on the host's gender and lifestage, we regard this as a model disease. A basic reproduction number R_0 for the disease is defined and analyzed. Vaccination terms are included and their role in disease propagation is analyzed. Necessary and sufficient conditions are given under which the diseasefree equilibrium is stable.  
Identifier:  CFE0006502 (IID), ucf:51389 (fedora)  
Note(s): 
20161201 Ph.D. Sciences, Mathematics Doctoral This record was generated from author submitted information. 

Subject(s):  Ecology model  Felis catus  feral cat  heterogeneous populations  ordinary differential equations  spatial heterogeneity  basic reproductive number  disease control  diseasefree equilibrium  epidemic model  feline leukemia virus  FeLV  
Persistent Link to This Record:  http://purl.flvc.org/ucf/fd/CFE0006502  
Restrictions on Access:  public 20161215  
Host Institution:  UCF 