Abstract: We used mathematical model to study the
transmission of dengue disease. The model is developed in which
the human population is separated into two populations, pregnant and
non-pregnant humans. The dynamical analysis method is used for
analyzing this modified model. Two equilibrium states are found and
the conditions for stability of theses two equilibrium states are
established. Numerical results are shown for each equilibrium state.
The basic reproduction numbers are found and they are compared by
using numerical simulations.
Abstract: An important technique in stability theory for
differential equations is known as the direct method of Lyapunov. In
this work we deal global stability properties of Leptospirosis
transmission model by age group in Thailand. First we consider the
data from Division of Epidemiology Ministry of Public Health,
Thailand between 1997-2011. Then we construct the mathematical
model for leptospirosis transmission by eight age groups. The
Lyapunov functions are used for our model which takes the forms of
an Ordinary Differential Equation system. The globally
asymptotically for equilibrium states are analyzed.
Abstract: Dengue, a disease found in most tropical and
subtropical areas of the world. It has become the most common
arboviral disease of humans. This disease is caused by any of four
serotypes of dengue virus (DEN1-DEN4). In many endemic
countries, the average age of getting dengue infection is shifting
upwards, dengue in pregnancy and infancy are likely to be
encountered more frequently. The dynamics of the disease is studied
by a compartmental model involving ordinary differential equations
for the pregnant, infant human and the vector populations. The
stability of each equilibrium point is given. The epidemic dynamic is
discussed. Moreover, the numerical results are shown for difference
values of dengue antibody.
Abstract: In this paper we develop and analyze the model for
the spread of Leptospirosis by age group in Thailand, between 1997
and 2010 by using mathematical modeling and computer simulation.
Leptospirosis is caused by pathogenic spirochetes of the genus
Leptospira. It is a zoonotic disease of global importance and an
emerging health problem in Thailand. In Thailand, leptospirosis is a
reportable disease, the top three age groups are 23.31% in 35-44
years olds group, 22.76% in 25-34 year olds group, 17.60% in 45-54
year olds group from reported leptospirosis between 1997 and 2010,
with a peak in 35-44 year olds group. Our paper, the Leptosipirosis
transmission by age group in Thailand is studied on the mathematical
model. Some analytical and simulation results are presented.
Abstract: Mathematical models can be used to describe the
transmission of disease. Dengue disease is the most significant
mosquito-borne viral disease of human. It now a leading cause of
childhood deaths and hospitalizations in many countries. Variations
in environmental conditions, especially seasonal climatic parameters,
effect to the transmission of dengue viruses the dengue viruses and
their principal mosquito vector, Aedes aegypti. A transmission model
for dengue disease is discussed in this paper. We assume that the
human and vector populations are constant. We showed that the local
stability is completely determined by the threshold parameter, 0 B . If
0 B is less than one, the disease free equilibrium state is stable. If
0 B is more than one, a unique endemic equilibrium state exists and
is stable. The numerical results are shown for the different values of
the transmission probability from vector to human populations.