Mathematical modelling of pneumonia dynamics of children under the age of five

Idowu, Kabir Oluwatobi; L.M, Erinle-Ibrahim

doi:10.21203/rs.3.rs-194578/v1

“…However, the model with the quarantined individual, hospitalized individuals, and control interventions (personal protection, effort used to hospitalize/Isolate the infectious not hospitalized, and effort used in spraying of the environment) has not been considered (Oluwatobi and Erinle-Ibrahim, 2021). Therefore, we presented a dynamical system for corona virus and also a control model for the disease.…”

Section: Figure 1 Diagram Showing the Shape Of Covid-19mentioning

confidence: 99%

“…This portion of the paper focuses on computational methods for the built-in optimization framework using a fourth-order Runge-Kutta with a forward-backward sweep approach that is exceedingly effective, helpful, and dependable. Many writers concerned with efficient simulation and dynamic systems have used this adaptive approach (Erinle et al, 2021;Madubueze, et al, 2020). The initial conditions for the state variables are as follows: S(0) =216746934, E(0) = 1000011, Q(0) = 2554, I(0) = 2494, H(0) = 2715, R(0) = 249246, and V(0) = 0.…”

Section: Numerical Simulationmentioning

confidence: 99%

Qualitative Analysis of the Transmission Dynamics and Optimal Control of Covid-19

Idowu

¹

,

Loyinmi

²

2023

Preprint

Self Cite

0

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Globally, the COVID-19 presents a serious concern to the wellbeing of people. COVID-19 was first detected in Wuhan, China. The disease became a source of concern for Nigerians after the country registered its first case in February 2020. Currently, the country has recorded 255,103 confirmed cases, 249,246 recovered cases, and 3,142 deaths as of March 21, 2022. We proposed a SEQIHRV model to investigate the spread of coronavirus disease in Nigeria. This model defines the infection dynamics' transmission routes as well as effect of contaminated surfaces on the human population. Unfortunately, the virus's propagation and mortality from COVID-19 is increasing daily. Therefore, it is required to manage and control the flow of the infection. The impact of control measures as time-dependent interventions was investigated in this study utilizing optimization technique to determine their effects on the spread of Corona virus. The basic reproduction was calculated and used to calcite the sensitive parameters affecting the system, which revealed the key parameters leading to COVID-19 propagation. The control optimization of the sytem was performed using Pontryagin's maximum principle to determine the best approach for controlling the spread. The discoveries from the simulation showed that the combination of all four control approaches will help to reduce infection to zero in the population.

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“…In 2021, Wafula et al presented an article describing optimal control treatment by developing a deterministic mathematical model pneumonia–HIV coinfection incorporating the use of anti-pneumonia and ART treatment interventions as controls [ 26 ]. Oluwatobi et al studied the effect of treatment of pneumonia infection and investigated the basic and effective reproduction numbers existence and the stability of equilibrium points [ 27 ]. Epidemiology has a significant role in different disciplines like medicine, engineering, chemistry, physics, economics and many more.…”

Section: Literature Surveymentioning

confidence: 99%

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

Naveed

¹

,

Băleanu

²

,

Raza

³

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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“…Several models has been developed to investigate the flow of infectious diseases and the effect of control interventions on such disease [8,3] Erinle-Ibrahim, Idowu and Sulola, 2021) and some studies are particular about COVID-19 [9,10,11,12]. In [12], the SEIQCRW model were presented.…”

Section: Introductionmentioning

confidence: 99%

“…However, the model with the quarantined individual, hospitalized individuals, and control interventions (personal protection, effort used to hospitalize/Isolate the infectious not hospitalized, and effort used in spraying of the environment) has not been considered [8]. Therefore, we presented a dynamical system for corona virus and also a control model for the disease.…”

Section: Introductionmentioning

confidence: 99%

Qualitative Analysis of the Transmission Dynamics and Optimal Control of Covid-19

Idowu,

Loyinmi

2023

EJSMT

1

0

View full text Add to dashboard Cite

Globally, the COVID-19 presents a serious concern to the wellbeing of people. COVID-19 was first detected in Wuhan, China. The disease became a source of concern for Nigerians after the country registered its first case in February 2020. Currently, the country has recorded 255,103 confirmed cases, 249,246 recovered cases, and 3,142 deaths as of March 21, 2022. We proposed a SEQIHRV model to investigate the spread of coronavirus disease in Nigeria. This model defines the infection dynamics' transmission routes as well as effect of contaminated surfaces on the human population. Unfortunately, the virus's propagation and mortality from COVID-19 is increasing daily. Therefore, it is required to manage and control the flow of the infection. The impact of control measures as time-dependent interventions was investigated in this study utilizing optimization technique to determine their effects on the spread of Corona virus. The basic reproduction was calculated and used to calcite the sensitive parameters affecting the system, which revealed the key parameters leading to COVID-19 propagation. The control optimization of the sytem was performed using Pontryagin's maximum principle to determine the best approach for controlling the spread. The discoveries from the simulation showed that the combination of all four control approaches will help to reduce infection to zero in the population.

show abstract

Mathematical modelling of pneumonia dynamics of children under the age of five

Cited by 5 publications

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Qualitative Analysis of the Transmission Dynamics and Optimal Control of Covid-19

Qualitative Analysis of the Transmission Dynamics and Optimal Control of Covid-19

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

Qualitative Analysis of the Transmission Dynamics and Optimal Control of Covid-19

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