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 disease-free steady state is locally asymptotically stable; thus, pneumococcal pneumonia would be eradicated in the population. On the other hand, 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.
Highlights
Pneumonia is one of the severe forms of pneumococcal diseases caused by pneumococcus [1]
We propose and analyze a mathematical model for pneumococcal pneumonia disease with awareness about antibiotic resistance and saturated treatment. e aim of this study is to investigate the impact of awareness about antibiotic resistance and treatment on the incidence and control of pneumococcal pneumonia in the human population
Model Description and Formulation. e total population under consideration is N(t), comprising four classes with the susceptible and infectious individuals, each partitioned into two. e susceptible class consists of the aware susceptible individuals Sa(t) who have had a chance to attend the available antibiotic resistance awareness programs and the unaware susceptible individuals Su(t) who have never heard of the prevailing programs or have heard of the existing programs but have not responded. e infectious class consists of infected individuals receiving treatment I(t) and infected individuals but resistant to first line treatment R(t)
Summary
Pneumonia is one of the severe forms of pneumococcal diseases caused by pneumococcus [1]. Private individual information, and appropriate treatment have proven to be among control measures undertaken by health institutions and the public to reduce the spread of most infectious diseases. Roy et al [27] studied the effect of awareness programs in controlling the disease HIV/AIDS and found out that increased awareness campaign during high infection is likely to delay the inception of infection among aware compared with unaware population. We propose and analyze a mathematical model for pneumococcal pneumonia disease with awareness about antibiotic resistance and saturated treatment. A relapse of resistant individuals, a modified saturated treatment, and a reduced disease transmission rate with the effect of antibiotic resistance awareness through media are added.
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