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Backward bifurcation in a malaria transmission model.

Yanyuan Xing1,2, Zhiming Guo1, Jian Liu1

  • 1School of Mathematics and Information Science, Guangzhou University, Guangzhou, People's Republic of China.

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|May 29, 2020
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Summary

This study introduces a malaria transmission model highlighting limited resource impacts. The research explores disease dynamics, stability, and potential backward bifurcation in human and mosquito populations.

Keywords:
92D30Global stabilitybackward bifurcationbasic reproductive numberlimited resourcemalaria transmission

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Disease Modeling

Background:

  • Malaria remains a significant global health challenge, necessitating robust transmission models.
  • Understanding the influence of resource limitations on disease dynamics is crucial for effective control strategies.

Purpose of the Study:

  • To develop and analyze a mathematical model for malaria transmission dynamics.
  • To investigate the impact of limited resources on disease spread in human and mosquito populations.
  • To determine conditions for disease eradication and persistence.

Main Methods:

  • Formulation of a compartmental mathematical model for malaria transmission.
  • Derivation of the basic reproductive number (R0).
  • Analysis of model equilibria and stability using bifurcation theory.
  • Numerical simulations to validate analytical findings.

Main Results:

  • The model characterizes malaria transmission dynamics considering resource limitations.
  • Conditions for the existence of a disease-free equilibrium and endemic equilibria were established.
  • The model demonstrates the possibility of backward bifurcation, where a stable disease-free state coexists with an endemic state.
  • Conditions for global asymptotic stability of both disease-free and endemic equilibria were determined.

Conclusions:

  • Limited resources can significantly influence malaria transmission patterns.
  • The potential for backward bifurcation highlights complex disease dynamics and challenges in eradication.
  • The model provides valuable insights for public health interventions and resource allocation in malaria control programs.