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A rhombic
planform nonlinear stability analysis of a noncytopathic
EIAV-target cell limited interaction-dispersion-chemotaxis
quasiequilibrium model system
David J. Wollkind, Bonni Dichone and Sandra E. Auttelet |
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Vol. 18 (2025), No. 5, 779–812
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Abstract |
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A noncytopathic EIAV-target cell limited interaction dynamical model system is extended by including the spatial effects of dispersion and chemotaxis. A linear stability analysis of its two equilibrium states and both one-dimensional longitudinal and two-dimensional rhombic planform nonlinear stability analyses of the infectious state are performed on a quasiequilibrium version of this model system. This system only depends on two dimensionless ratios: the basic reproductive number and a chemotaxis coefficient, which is a measure of the attraction of the uninfected target cells to density gradients in the infected target cells. For sufficiently large values of the chemotaxis coefficient, a morphological infection sequence of the uninfected state to sparse homogeneous distributions and isolated spots to periodic spots to dense homogeneous distributions is predicted as the basic reproductive number increases from zero. The patterned region is identified with the occurrence of petechial hemorrhages or minute blood-red spots on the anemic mucous membranes of horses during the chronic degree phase of EIAV infectiousness. The concept of higher threshold rhombic patterns based on the mean density deviation level of the infected target cells is introduced to make the interpretation of spots in the periodic patterning region. The distance between these adjacent spots decreases as the basic reproductive number increases, consistent with this predicted morphological infection sequence. |
Keywords
spatial diffusion effects, equilibrium approximation,
Turing instabilities, spots versus stripes, petechiation
patterns
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Mathematical Subject Classification
Primary: 35B35, 35B36, 35K57, 35Q56, 92C17
Secondary: 92D30
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Milestones
Received: 15 August 2023
Revised: 18 April 2024
Accepted: 22 April 2024
Published: 13 November 2025
Communicated by Martin Bohner
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Authors |
| David J. Wollkind | |
| Department of Mathematics Washington State University Pullman, WA United States |
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| Bonni Dichone | |
| Department of Mathematics Gonzaga University Spokane, WA United States |
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| Sandra E. Auttelet | |
| Department of Mathematics Washington State University Pullman, WA United States |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
