Abstract: Mathematical models can be used to describe the
dynamics of the spread of infectious disease between susceptibles
and infectious populations. Dengue fever is a re-emerging disease in
the tropical and subtropical regions of the world. Its incidence has
increased fourfold since 1970 and outbreaks are now reported quite
frequently from many parts of the world. In dengue endemic regions,
more cases of dengue infection in pregnancy and infancy are being
found due to the increasing incidence. It has been reported that
dengue infection was vertically transmitted to the infants. Primary
dengue infection is associated with mild to high fever, headache,
muscle pain and skin rash. Immune response includes IgM antibodies
produced by the 5th day of symptoms and persist for 30-60 days. IgG
antibodies appear on the 14th day and persist for life. Secondary
infections often result in high fever and in many cases with
hemorrhagic events and circulatory failure. In the present paper, a
mathematical model is proposed to simulate the succession of dengue
disease transmission in pregnancy and infancy. Stability analysis of
the equilibrium points is carried out and a simulation is given for the
different sets of parameter. Moreover, the bifurcation diagrams of our
model are discussed. The controlling of this disease in infant cases is
introduced in the term of the threshold condition.
Abstract: Leptospirosis is recognized as an important zoonosis
in tropical regions well as an important animal disease with
substantial loss in production. In this study, the model for the
transmission of the Leptospirosis disease to human population are
discussed. Model is described the vector population dynamics and
the Leptospirosis transmission to the human population are
discussed. Local analysis of equilibria are given. We confirm the
results by using numerical results.
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.