**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**5

# Dengue disease Related Publications

##### 5 Dengue Disease Mapping with Standardized Morbidity Ratio and Poisson-gamma Model: An Analysis of Dengue Disease in Perak, Malaysia

**Authors:**
N. A. Samat,
S. H. Mohd Imam Ma’arof

**Abstract:**

Dengue disease is an infectious vector-borne viral disease that is commonly found in tropical and sub-tropical regions, especially in urban and semi-urban areas, around the world and including Malaysia. There is no currently available vaccine or chemotherapy for the prevention or treatment of dengue disease. Therefore prevention and treatment of the disease depend on vector surveillance and control measures. Disease risk mapping has been recognized as an important tool in the prevention and control strategies for diseases. The choice of statistical model used for relative risk estimation is important as a good model will subsequently produce a good disease risk map. Therefore, the aim of this study is to estimate the relative risk for dengue disease based initially on the most common statistic used in disease mapping called Standardized Morbidity Ratio (SMR) and one of the earliest applications of Bayesian methodology called Poisson-gamma model. This paper begins by providing a review of the SMR method, which we then apply to dengue data of Perak, Malaysia. We then fit an extension of the SMR method, which is the Poisson-gamma model. Both results are displayed and compared using graph, tables and maps. Results of the analysis shows that the latter method gives a better relative risk estimates compared with using the SMR. The Poisson-gamma model has been demonstrated can overcome the problem of SMR when there is no observed dengue cases in certain regions. However, covariate adjustment in this model is difficult and there is no possibility for allowing spatial correlation between risks in adjacent areas. The drawbacks of this model have motivated many researchers to propose other alternative methods for estimating the risk.

**Keywords:**
disease mapping,
Dengue disease,
Standardized
Morbidity Ratio,
Poisson-gamma model,
Relative risk

##### 4 Numerical Analysis of the SIR-SI Differential Equations with Application to Dengue Disease Mapping in Kuala Lumpur, Malaysia

**Authors:**
N. A. Samat,
D. F. Percy

**Abstract:**

The main aim of this study is to describe and introduce a method of numerical analysis in obtaining approximate solutions for the SIR-SI differential equations (susceptible-infectiverecovered for human populations; susceptible-infective for vector populations) that represent a model for dengue disease transmission. Firstly, we describe the ordinary differential equations for the SIR-SI disease transmission models. Then, we introduce the numerical analysis of solutions of this continuous time, discrete space SIR-SI model by simplifying the continuous time scale to a densely populated, discrete time scale. This is followed by the application of this numerical analysis of solutions of the SIR-SI differential equations to the estimation of relative risk using continuous time, discrete space dengue data of Kuala Lumpur, Malaysia. Finally, we present the results of the analysis, comparing and displaying the results in graphs, table and maps. Results of the numerical analysis of solutions that we implemented offers a useful and potentially superior model for estimating relative risks based on continuous time, discrete space data for vector borne infectious diseases specifically for dengue disease.

**Keywords:**
disease mapping,
Dengue disease,
numerical
analysis,
SIR-SI differential equations

##### 3 Mathematical Modeling for Dengue Transmission with the Effect of Season

**Authors:**
R. Kongnuy.,
P. Pongsumpun

**Abstract:**

**Keywords:**
mathematical model,
season,
Dengue disease,
threshold parameters

##### 2 Analysis of Model in Pregnant and Non-Pregnant Dengue Patients

**Authors:**
R. Kongnuy,
P. Pongsumpun

**Abstract:**

**Keywords:**
pregnancy,
Equilibrium states,
Dengue disease,
basic reproductive number

##### 1 Analysis of a Mathematical Model for Dengue Disease in Pregnant Cases

**Authors:**
Rujira Kongnuy,
Puntani Pongsumpun,
I-Ming Tang

**Abstract:**

Dengue fever is an important human arboviral disease. Outbreaks are now reported quite often from many parts of the world. The number of cases involving pregnant women and infant cases are increasing every year. The illness is often severe and complications may occur. Deaths often occur because of the difficulties in early diagnosis and in the improper management of the diseases. Dengue antibodies from pregnant women are passed on to infants and this protects the infants from dengue infections. Antibodies from the mother are transferred to the fetus when it is still in the womb. In this study, we formulate a mathematical model to describe the transmission of this disease in pregnant women. The model is formulated by dividing the human population into pregnant women and non-pregnant human (men and non-pregnant women). Each class is subdivided into susceptible (S), infectious (I) and recovered (R) subclasses. We apply standard dynamical analysis to our model. Conditions for the local stability of the equilibrium points are given. The numerical simulations are shown. The bifurcation diagrams of our model are discussed. The control of this disease in pregnant women is discussed in terms of the threshold conditions.

**Keywords:**
pregnancy,
mathematical model,
local stability,
Dengue disease