Mathematical Biosciences and Engineering, 2014, 11(4): 995-1001. doi: 10.3934/mbe.2014.11.995.

Primary: 92D25, 92D30; Secondary: 37G99.

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A note on global stability for malaria infections model with latencies

1. School of Mathematical Science, Heilongjiang University, Harbin 150080
2. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo 153-8914

A recent paper [Y. Xiao and X. Zou, On latencies in malaria infections and their impact on the disease dynamics, Math. Biosci. Eng., 10(2) 2013, 463-481.] presented a mathematical model to investigate the spread of malaria. The model is obtained by modifying the classic Ross-Macdonald model by incorporating latencies both for human beings and female mosquitoes. It is realistic to consider the new model with latencies differing from individuals to individuals. However, the analysis in that paper did not resolve the global malaria disease dynamics when $\Re_0>1$. The authors just showed global stability of endemic equilibrium for two specific probability functions: exponential functions and step functions. Here, we show that if there is no recovery, the endemic equilibrium is globally stable for $\Re_0>1$ without other additional conditions. The approach used here, is to use a direct Lyapunov functional and Lyapunov-LaSalle invariance principle.
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Keywords Global stability; malaria infection; latency distribution; Lyapunov functional.

Citation: Jinliang Wang, Jingmei Pang, Toshikazu Kuniya. A note on global stability for malaria infections model with latencies. Mathematical Biosciences and Engineering, 2014, 11(4): 995-1001. doi: 10.3934/mbe.2014.11.995

References

  • 1. Funkcial. Ekvac., 31 (1988), 331-347.
  • 2. in Mathematical Population Dynamics: Analysis of Heterogeneity, I. Theory of Epidemics (eds. O. Arino et al.), Wuerz, Winnepeg, Canada, (1995), 33-50.
  • 3. Applied Mathematical Science, New York, 1993.
  • 4. Funkcial. Ekvac., 21 (1978), 11-41.
  • 5. Comm. Pure Appl. Math., 38 (1985), 733-753.
  • 6. J. Math. Biol., 63 (2011), 125-139.
  • 7. SIAM J. Appl. Math., 70 (2010), 2693-2708.
  • 8. Math. Biosci. Eng., 1 (2004), 57-60.
  • 9. Bull. Math. Biol., 68 (2006), 615-626.
  • 10. Regional Conference Series in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1976.
  • 11. W. A. Benjamin Inc., New York, 1971.
  • 12. Nonlinear Anal. RWA., 11 (2010), 55-59.
  • 13. Math. Biosci. Eng., 6 (2009), 603-610.
  • 14. Princeton University Press, Princeton, NJ, 2003.
  • 15. Math. Med. Biol., 29 (2012), 283-300.
  • 16. Math. Biosci. Eng., 4 (2007), 205-219.
  • 17. Math. Biosci. Eng., 10 (2013), 463-481.

 

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  • 2. Jinliang Wang, Xinxin Tian, Xia Wang, Stability analysis for delayed viral infection model with multitarget cells and general incidence rate, International Journal of Biomathematics, 2016, 09, 01, 1650007, 10.1142/S1793524516500078

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