# P. Pongsumpun

## Publications

##### 12 Local Stability Analysis of Age Structural Model for Herpes Zoster in Thailand

**Authors:**
P. Pongsumpun

**Abstract:**

Herpes zoster is a disease that manifests as a dermatological condition. The characteristic of this disease is an irritating skin rash with blisters. This is often limited to one side of body. From the data of Herpes zoster cases in Thailand, we found that age structure effects to the transmission of this disease. In this study, we construct the age structural model of Herpes zoster in Thailand. The local stability analysis of this model is given. The numerical solutions are shown to confirm the analytical results.

**Keywords:**
Numerical Solution,
local stability,
herpes zoster,
Age structural model

##### 11 Dynamical Network Transmission of H1N1 Virus at the Local Level Transmission Model

**Authors:**
P. Pongsumpun

**Abstract:**

**Keywords:**
Simulation,
Dynamical network,
H1N1virus,
local level

##### 10 Mathematical Model for the Transmission of Leptospirosis in Juvennile and Adults Humans

**Authors:**
P. Pongsumpun

**Abstract:**

**Keywords:**
mathematical model,
leptospirosis,
Adult human,
juvenile human

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

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

**Abstract:**

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

##### 8 Mathematical Model for the Transmission of Two Plasmodium Malaria

**Authors:**
P. Pongsumpun

**Abstract:**

**Keywords:**
Malaria,
mathematical model,
threshold condition,
Dynamical analysis

##### 7 Dynamical Transmission Model of Chikungunya in Thailand

**Authors:**
P. Pongsumpun

**Abstract:**

**Keywords:**
Chikunkunya,
dynamical model,
Endemic region,
Routh-Hurwitz criteria

##### 6 Swine Flu Transmission Model in Risk and Non-Risk Human Population

**Authors:**
P. Pongsumpun

**Abstract:**

**Keywords:**
mathematical model,
steady state,
Swine flu,
threshold condition

##### 5 Dengue Transmission Model between Infantand Pregnant Woman with Antibody

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

**Abstract:**

**Keywords:**
mathematical model,
infant,
Dengue antibody,
pregnant human

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

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

**Abstract:**

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

##### 3 Mathematical Model of Dengue Disease with the Incubation Period of Virus

**Authors:**
P. Pongsumpun

**Abstract:**

**Keywords:**
local stability,
Transmission model,
intrinsic incubation period,
extrinsic incubation period,
basic reproductive number,
equilibriumstates

##### 2 Plasmodium Vivax Malaria Transmission in a Network of Villages

**Authors:**
P. Pongsumpun,
I. M. Tang

**Abstract:**

**Keywords:**
household,
Plasmodium Vivax malaria,
local level,
dynamical model

##### 1 Transmission Model for Plasmodium Vivax Malaria: Conditions for Bifurcation

**Authors:**
P. Pongsumpun,
I.M. Tang

**Abstract:**

Plasmodium vivax malaria differs from P. falciparum malaria in that a person suffering from P. vivax infection can suffer relapses of the disease. This is due the parasite being able to remain dormant in the liver of the patients where it is able to re-infect the patient after a passage of time. During this stage, the patient is classified as being in the dormant class. The model to describe the transmission of P. vivax malaria consists of a human population divided into four classes, the susceptible, the infected, the dormant and the recovered. The effect of a time delay on the transmission of this disease is studied. The time delay is the period in which the P. vivax parasite develops inside the mosquito (vector) before the vector becomes infectious (i.e., pass on the infection). We analyze our model by using standard dynamic modeling method. Two stable equilibrium states, a disease free state E0 and an endemic state E1, are found to be possible. It is found that the E0 state is stable when a newly defined basic reproduction number G is less than one. If G is greater than one the endemic state E1 is stable. The conditions for the endemic equilibrium state E1 to be a stable spiral node are established. For realistic values of the parameters in the model, it is found that solutions in phase space are trajectories spiraling into the endemic state. It is shown that the limit cycle and chaotic behaviors can only be achieved with unrealistic parameter values.

**Keywords:**
Hopf Bifurcation,
Time Delay,
local stability,
plasmodium vivax,
Equilibrium states,
limit cyclebehavior