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Global Stability of Pneumococcal Pneumonia with Awareness and Saturated Treatment

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  • Fulgensia Kamugisha Mbabazi
  • J. Y. T. Mugisha
  • Mark Kimathi

Abstract

Pneumocccal pneumonia, a secondary bacterial infection that follows influenza A infection, is responsible for morbidity and mortality in children, elderly, and immunocomprised groups. A mathematical model to study the global stability of pneumococcal pneumonia with awareness and saturated treatment is presented. The basic reproduction number, R0, is computed using the next generation matrix method. The results show that if R0 1 the endemic steady state is globally attractive; thus, the disease would persist in the population. The quadratic‐linear and Goh–Voltera Lyapunov functionals approach are used to prove the global stabilities of the disease‐free and endemic steady states, respectively. The sensitivity analysis of R0 on model parameters shows that, it is positively sensitive to the maximal effective rate before antibiotic resistance awareness, rate of relapse encountered in administering treatment, and loss of information by aware susceptible individuals. Contrarily, the sensitivity analysis of R0 on model parameters is negatively sensitive to recovery rate due to treatment and the rate at which unaware susceptible individuals become aware. The numerical analysis of the model shows that awareness about antibiotic resistance and treatment plays a significant role in the control of pneumococcal pneumonia.

Suggested Citation

  • Fulgensia Kamugisha Mbabazi & J. Y. T. Mugisha & Mark Kimathi, 2020. "Global Stability of Pneumococcal Pneumonia with Awareness and Saturated Treatment," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnljam:v:2020:y:2020:i:1:n:3243957
    DOI: 10.1155/2020/3243957
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    References listed on IDEAS

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    3. Mohammed Kizito & Julius Tumwiine, 2018. "A Mathematical Model of Treatment and Vaccination Interventions of Pneumococcal Pneumonia Infection Dynamics," Journal of Applied Mathematics, John Wiley & Sons, vol. 2018(1).
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    Cited by:

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