Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays

Mbabazi, Fulgensia Kamugisha; Mugisha, Johnny; Kimathi, Mark

doi:10.1155/2019/3757036

Cited by 4 publications

(3 citation statements)

References 41 publications

(40 reference statements)

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“…Recently, Soliman and Bueno (2018) used the basic Susceptible-Infected-Recovered (SIR) model to analyse and predict the transmission rate of pneumonia in the Philippines. Mbabazi et al (2019) formulated a Susceptible-Vaccinated-Exposed-Carrier-Infected (SVECI) model, which was a time delay model for pneumonia. From the literature, there were only two studies on pneumonia disease that used the stochastic model (Smith et al, 1993;Melegaro et al, 2002).…”

Section: Related Studiesmentioning

confidence: 99%

The Comparison between Standardized Mortality Ratio, Poisson-Gamma and Stochastic Sic Model for Pneumonia Disease Mapping in Malaysia

Diah¹,

Aziz²

2022

JICT

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Pneumonia is one of the primary causes of death from infectious diseases. Traditionally, its spread has been tracked based on thetotal number of cases reported, with no concern for geographical distribution. Disease mapping is among the ways public health andthe government can monitor diseases as a preventative strategy. Clear pictures of the risk areas can be seen using this method. Relative risk estimation is a significant part of disease mapping that needs to be considered when studying disease occurrence. This paper aimed to estimate the relative risk values for pneumonia based on three models and compare the results. The approaches used in this study were Standardized Morbidity Ratio (SMR), Poisson-gamma, and discrete time-space stochastic Susceptible-Infected-Carriers (SIC) models, which were applied in estimating the relative risk values. Results showed that Kuala Lumpur was classified as a very low-risk area for pneumonia incidence when using the SMR and Poisson-gamma models. In contrast, Selangor was identified as a very low-risk area when using the discrete time-space stochastic SIC model. Putrajaya was categorised as a very high-risk area in the results of all three types of methods. In conclusion, this stochastic SIC model demonstrated better performance than the conventional models.

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Section: Related Studiesmentioning

confidence: 99%

The Comparison between Standardized Mortality Ratio, Poisson-Gamma and Stochastic Sic Model for Pneumonia Disease Mapping in Malaysia

Diah¹,

Aziz²

2022

JICT

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“…In 2019, Tilahun et al analysed a coinfection mathematical model for pneumonia and bacterial meningitis [ 16 ]. Mbabazi et al, in 2019, proposed a pneumococcal pneumonia model with time delays mathematically, Hopf-bifurcation was analysed [ 17 ]. In 2020, Otoo et al analysed a model of pneumonia spread by bacteria.…”

Section: Literature Surveymentioning

confidence: 99%

Modeling the transmission dynamics of delayed pneumonia-like diseases with a sensitivity of parameters

et al. 2021

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Pneumonia is a highly transmitted disease in children. According to the World Health Organization (WHO), the most affected regions include South Asia and sub-Saharan Africa. 15% deaths of children are due to pneumonia. In 2017, 0.88 million children were killed under the age of five years. An analysis of pneumonia disease is performed with the help of a delayed mathematical modelling technique. The epidemiological system contemplates subpopulations of susceptible, carriers, infected and recovered individuals, along with nonlinear interactions between the members of those subpopulations. The positivity and the boundedness of the ongoing problem for nonnegative initial data are thoroughly proved. The system possesses pneumonia-free and pneumonia existing equilibrium points, whose stability is studied rigorously. Moreover, the numerical simulations confirm the validity of these theoretical results.

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“…In 2019, Tilahun et al [17] analyzed a co-infection mathematical model for the bacterial disease of pneumonia and meningitis. In 2019, Mbabazi et al [18] proposed a mathematical model of pneumococcal pneumonia with time delays and performed Hopf-bifurcation analysis. In 2020, Otoo et al [19] analyzed a model of pneumonia spread by bacteria.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Pneumonia Model via Efficient Computing Techniques

Abodayeh¹,

Raza²,

Rafiq³

et al. 2022

Computers, Materials &Amp; Continua

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Pneumonia is a highly transmissible disease in children. According to the World Health Organization (WHO), the most affected regions include south Asia and sub-Saharan Africa. Worldwide, 15% of pediatric deaths can be attributed to pneumonia. Computing techniques have a significant role in science, engineering, and many other fields. In this study, we focused on the efficiency of numerical techniques via computer programs. We studied the dynamics of the pneumonia-like infections of epidemic models using numerical techniques. We discuss two types of analysis: dynamical and numerical. The dynamical analysis included positivity, boundedness, local stability, reproduction number, and equilibria of the model. We also discuss well-known computing techniques including Euler, Runge Kutta, and non-standard finite difference (NSFD) for the model. The non-standard finite difference (NSFD) technique shows convergence to the true equilibrium points of the model for any time step size. However, Euler and Runge Kutta do not work well over large time intervals. Computing techniques are the suitable tool for crosschecking the theoretical analysis of the model.

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Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays

Cited by 4 publications

References 41 publications

The Comparison between Standardized Mortality Ratio, Poisson-Gamma and Stochastic Sic Model for Pneumonia Disease Mapping in Malaysia

The Comparison between Standardized Mortality Ratio, Poisson-Gamma and Stochastic Sic Model for Pneumonia Disease Mapping in Malaysia

Modeling the transmission dynamics of delayed pneumonia-like diseases with a sensitivity of parameters

Analysis of Pneumonia Model via Efficient Computing Techniques

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