TY - GEN
T1 - A Mathematical Model of the Spread of Pneumococcal Pneumonia Disease by Considering Vaccine and Hospital Care Interventions
AU - Alya, Jilan
AU - Aldila, Dipo
AU - Rusin, Rahmi
N1 - Funding Information:
This research is funded by Universitas Indonesia with PUTI KI Q2 research grant scheme (ID Number : NKB-775/UN2.RST/HKP.05.00/2020)
Publisher Copyright:
© 2022 American Institute of Physics Inc.. All rights reserved.
PY - 2022/8/2
Y1 - 2022/8/2
N2 - Pneumococcal pneumonia is a type of community-acquired pneumonia which is an acute respiratory infection caused by Streptococcus pneumoniae bacteria. In this study, a mathematical model on the spread of Pneumococcal pneumonia is constructed by considering vaccination and hospital care interventions. The model is formed by dividing the human population based on their health status. We consider several things in the model's construction, such as asymptomatic individuals, the latent phase during infection, and interventions of vaccination and hospitalization. Analytical studies are carried out to find and analyze the existence and local stability of the equilibrium points, determining the basic reproduction number (R0), and investigate the type of bifurcation of the model. We find that the model exhibits a forward bifurcation when R0 = 1. These result means that we have to reduce the value of R0 as large as possible using vaccination and/or hospitalization to avoid the existence of Pneumococcal pneumonia in the community. Several numerical experiments are shown to see the visualization of the model. The simulation results show that the rate of vaccination and the rate of hospitalization only have a very significant effect at the beginning in reducing the value of R0, but not as significant when the value of the two rates given is large enough. It is also concluded that an increase in the rate of vaccination is more successful in reducing the number of individuals infected with Pneumococcal pneumonia compared to an increase in the rate of hospitalization. Thus, it will be more effective for intervention in the field to rely on vaccination compared to hospitalization. The type of vaccine used in the vaccination process also has a significant effect in reducing the value of R0. This is because the elasticity value of the parameter ζ, which is the infection reduction value because the effectiveness of the vaccine, has the most significant effect in reducing the value of R0 compared to the parameters that indicate the rate of vaccination and the rate of hospitalization.
AB - Pneumococcal pneumonia is a type of community-acquired pneumonia which is an acute respiratory infection caused by Streptococcus pneumoniae bacteria. In this study, a mathematical model on the spread of Pneumococcal pneumonia is constructed by considering vaccination and hospital care interventions. The model is formed by dividing the human population based on their health status. We consider several things in the model's construction, such as asymptomatic individuals, the latent phase during infection, and interventions of vaccination and hospitalization. Analytical studies are carried out to find and analyze the existence and local stability of the equilibrium points, determining the basic reproduction number (R0), and investigate the type of bifurcation of the model. We find that the model exhibits a forward bifurcation when R0 = 1. These result means that we have to reduce the value of R0 as large as possible using vaccination and/or hospitalization to avoid the existence of Pneumococcal pneumonia in the community. Several numerical experiments are shown to see the visualization of the model. The simulation results show that the rate of vaccination and the rate of hospitalization only have a very significant effect at the beginning in reducing the value of R0, but not as significant when the value of the two rates given is large enough. It is also concluded that an increase in the rate of vaccination is more successful in reducing the number of individuals infected with Pneumococcal pneumonia compared to an increase in the rate of hospitalization. Thus, it will be more effective for intervention in the field to rely on vaccination compared to hospitalization. The type of vaccine used in the vaccination process also has a significant effect in reducing the value of R0. This is because the elasticity value of the parameter ζ, which is the infection reduction value because the effectiveness of the vaccine, has the most significant effect in reducing the value of R0 compared to the parameters that indicate the rate of vaccination and the rate of hospitalization.
KW - equilibrium points
KW - mathematical model
KW - Pneumococcal pneumonia
KW - SIR
UR - http://www.scopus.com/inward/record.url?scp=85136789929&partnerID=8YFLogxK
U2 - 10.1063/5.0082709
DO - 10.1063/5.0082709
M3 - Conference contribution
AN - SCOPUS:85136789929
T3 - AIP Conference Proceedings
BT - 8th Symposium on Biomathematics, Symomath 2021
A2 - Megawati, Noorma Yulia
A2 - Susyanto, Nanang
A2 - Ertiningsih, Dwi
A2 - Sari, Eminugroho Ratna
A2 - Saptaningtyas, Fitriana Yuli
A2 - Tantrawan, Made
A2 - Amalia, Oki Almas
A2 - Susiana, null
PB - American Institute of Physics Inc.
T2 - 8th Symposium on Biomathematics: Bridging Mathematics and Covid-19 Through Multidisciplinary Collaboration, Symomath 2021
Y2 - 16 July 2021 through 17 July 2021
ER -
