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STABILITY OF A CLASS OF DISCRETE-TIME PATHOGEN INFECTION MODELS WITH LATENTLY INFECTED CELLS

  • ELAIW, A.M. (DEPARTMENT OF MATHEMATICS, KING ABDULAZIZ UNIVERSITY) ;
  • ALSHAIKH, M.A. (DEPARTMENT OF MATHEMATICS, KING ABDULAZIZ UNIVERSITY)
  • Received : 2018.02.23
  • Accepted : 2018.12.11
  • Published : 2018.12.25

Abstract

This paper studies the global stability of a class of discrete-time pathogen infection models with latently infected cells. The rate of pathogens infect the susceptible cells is taken as bilinear, saturation and general. The continuous-time models are discretized by using nonstandard finite difference scheme. The basic and global properties of the models are established. The global stability analysis of the equilibria is performed using Lyapunov method. The theoretical results are illustrated by numerical simulations.

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FIGURE 1. The simulation of susceptible cells of system (5.1)-(5.4) for Case(I).

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FIGURE 2. The simulation of latently infected cells of system (5.1)-(5.4) for Case(I).

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FIGURE 3. The simulation of actively infected cells of system (5.1)-(5.4) for Case(I).

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FIGURE 4. The simulation of pathogens of system (5.1)-(5.4) for Case(I).

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FIGURE 5. The simulation of susceptible cells of system (5.1)-(5.4) for Case(II).

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FIGURE 6. The simulation of latently infected cells of system (5.1)-(5.4) for Case(II).

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FIGURE 7. The simulation of actively infected cells of system (5.1)-(5.4) for Case(II).

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FIGURE 8. The simulation of pathogens of system (5.1)-(5.4) for Case(II).

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FIGURE 9. The simulation of susceptible cells of system (5.1)-(5.4) for Case(III).

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FIGURE 10. The simulation of latently infected cells of system (5.1)-(5.4) for Case(III).

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FIGURE 11. The simulation of actively infected cells of system (5.1)-(5.4) for Case(III).

E1TAAE_2018_v22n4_253_f0012.png 이미지

FIGURE 12. The simulation of pathogens of system (5.1)-(5.4) for Case(III).

TABLE 1. The values of R0 for system (5.1)-(5.4) with different values of λ.

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