Mathematical model for pneumonia dynamics with carriers

Joseph, Mugisha; Oleche, Paul Odhiambo

doi:10.12988/ijma.2013.35109

Cited by 19 publications

(8 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Pneumonia is an infection that inflames the air sacs with pus or fluid in one or both lungs. Different types of microorganisms, including fungi, viruses, and bacteria, can cause pneumonia (Otieno et al, 2012). The most prevalent causes in any person who contracts pneumonia are Streptococcus pneumoniae, a pneumonia bacterium, and viruses.…”

Section: Introductionmentioning

confidence: 99%

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

Diah¹,

Aziz²

2022

JICT

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

Diah¹,

Aziz²

2022

JICT

View full text Add to dashboard Cite

show abstract

“…Several studies have been carried out to investigate the transmission dynamics of pneumonia. For example, [9] formulated a mathematical model to examine the role of carriers and recovery measures in the pneumonia transmission dynamics among children under five years of age. Also, [10] developed a model for childhood pneumonia dynamics to investigate the role of treatment and natural immunity in pneumonia transmission dynamics.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control in Two Strain Pneumonia Transmission Dynamics

Swai

Shaban

Marijani

2021

Journal of Applied Mathematics

View full text Add to dashboard Cite

A mathematical model for the transmission dynamics of pneumonia disease in the presence of drug resistance is formulated. Intervention strategies, namely, vaccination, public health education, and treatment are implemented. We compute the effective reproduction numbers and establish the local stability of the equilibria of the model. Global stability of the disease-free equilibrium is obtained through the comparison method. On the other hand, we apply the Lyapunov method to show that the drug-resistant equilibrium is globally asymptotically stable under some feasible biological conditions. Furthermore, we apply optimal control theory to the model aiming at minimizing the number of infections from drug-sensitive and drug-resistant strains. The necessary conditions for the optimal solutions of the model were derived by using Pontryagin’s Maximum Principle. The optimal controls are characterized in terms of the optimality system, which is solved numerically for several scenarios to investigate the best strategy. The incremental cost-effectiveness analysis technique is used to find the most cost-effective strategy, and it is observed that the vaccination program is the most cost-effective strategy in case of limited resources. However, results show that implementing the three strategies simultaneously provides the best results in controlling the disease.

show abstract

“…Pneumonia is an infection in the lung when alveoli are filled up with inflammatory cells (Otieno et al, 2012). According to Otieno et al (2012), the disease can be caused by microorganisms such as parasites, fungi, bacteria and viruses.…”

Section: Introductionmentioning

confidence: 99%

“…Bacteria has been recognized to be the main cause that lead someone to get pneumonia, especially streptococcus pneumoniae (pneumococcus) (Otieno et al, 2012). General symptoms for those who have contact with pneumonia will have high grade fever, chills, sweating, coughing with yellow or green or blood-stained sputum, shortness of breath and chest pain.…”

Section: Introductionmentioning

confidence: 99%

The Relative Risk Estimation of Pneumonia in Malaysia using Standardized Morbidity Ratio (SMR)

Diah¹

2021

ASMScJ

View full text Add to dashboard Cite

Pneumonia is the most serious inflammatory disease of the respiratory system which cause millions of deaths worldwide especially for children under age five and older adults. The numbers of pneumonia cases reported keep on increasing from year to year in Malaysia. Moreover, this type of disease can become outbreak if it is not controlled. Besides using as prevention strategies for a disease risk, statistical modelling of disease mapping can also be used in monitoring as it clearly shows risk areas. The objective of this paper is to estimate the value of relative risk for pneumonia transmission by using Standardized Morbidity Ratio (SMR) method which is the conventional statistic method used in disease mapping and subsequently propose a disease risk map to show the pneumonia risk areas. Pneumonia data in Malaysia is used in estimating the relative risk. The results show that, Terengganu has the highest risk of contracting pneumonia while Pulau Pinang shows the lowest risk.

show abstract

Mathematical model for pneumonia dynamics with carriers

Cited by 19 publications

References 16 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

Optimal Control in Two Strain Pneumonia Transmission Dynamics

The Relative Risk Estimation of Pneumonia in Malaysia using Standardized Morbidity Ratio (SMR)

Contact Info

Product

Resources

About