Free-Virus and Cell-to-Cell Transmission in Models of Equine Infectious Anemia Virus Infection

Research published in Mathematical Biosciences looked at the role of cell-to-cell transmission of equine infectious anemia virus. The article “Free-Virus and Cell-to-Cell Transmission in Models of Equine Infectious Anemia Virus Infection” is available for purchase on


  • We examine the role of cell-to-cell transmission among two competing virus strains
  • We consider an antibody neutralization sensitive strain and a resistant strain
  • Long-term dynamics depend on the ratio of cell-to-cell vs. free-virus transmission
  • Interventions that only block free virus transmission may lead to resistance
  • Those that block cell-to-cell transfer could lower R0 and development of resistance


Equine infectious anemia virus (EIAV) is a lentivirus in the retrovirus family that infects horses and ponies. Two strains, referred to as the sensitive strain and the resistant strain, have been isolated from an experimentally-infected pony. The sensitive strain is vulnerable to neutralization by antibodies whereas the resistant strain is neutralization-insensitive. The sensitive strain mutates to the resistant strain. EIAV may infect healthy target cells via free virus or alternatively, directly from an infected target cell through cell-to-cell transfer. The proportion of transmission from free-virus or from cell-to-cell transmission is unknown. A system of ordinary differential equations (ODEs) is formulated for the virus-cell dynamics of EIAV. In addition, a Markov chain model and a branching process approximation near the infection-free equilibrium (IFE) are formulated. The basic reproduction number R0R0 is defined as the maximum of two reproduction numbers, R0sR0s and R0r,R0r, one for the sensitive strain and one for the resistant strain. The IFE is shown to be globally asymptotically stable for the ODE model in a special case when the basic reproduction number is less than one. In addition, two endemic equilibria exist, a coexistence equilibrium and a resistant strain equilibrium. It is shown that if R0>1,R0>1, the infection persists with at least one of the two strains. However, for small infectious doses, the sensitive strain and the resistant strain may not persist in the Markov chain model. Parameter values applicable to EIAV are used to illustrate the dynamics of the ODE and the Markov chain models. The examples highlight the importance of the proportion of cell-to-cell versus free-virus transmission that either leads to infection clearance or to infection persistence with either coexistence of both strains or to dominance by the resistant strain.


L.J.S. Allen, Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas; E. J. Schwartz, School of Biological Sciences and Department of Mathematics, Washington State University, Pullman, Washington.

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