Abstract:
In this thesis, a new deterministic model for the Dengue disease is developed and
analyzed with the homotopy perturbation transform method. The model comprises
six compartments namely human population susceptible class S(t), exposed class
E(t), infected class I(t), recovered class R(t) and vector population namely virus-free
vectors U(t) and virus-carrying vectors V(t). The qualitative behavior of this model
is analyzed by a deterministic approach, invariant region, the existence of equilibrium
points(disease-free and endemic equilibrium), the basic reproduction number, sensitivity
analysis , and their local stability were checked. The results of the analysis showed
that the basic reproduction number is less than one, then the disease free equilibrium
point is stable. Some values of the parameters were estimated from data collected from
Dire Dawa Dil Chora Hospital, some from related published articles, and others were
assumed. Moreover, the homotopy perturbation transform method is used to solve the
system of initial value problems of the developed model by using the Laplace transform,
inverse Laplace, the homotopy perturbation method, and a nonlinear coupled equation
decomposed by He's polynomial method. The homotopy perturbation transform method
(HPTM), which competes with ODE45, enables us to obtain an approximate of the
solution in a small number of iterations. This increases the number of iterations,
increases convergence, and complements the solution of ODE45. The Homotopy
perturbation transform method is one of alternative method to solve the system of
linear and nonlinear di erential equations. Furthermore, numerical simulation was
done using parameter values to taste the impact of basic parameters and the results
of the simulation were displayed graphically using the MATLAB computer software
program. Numerical results showed that decreasing the contact rate and exposed rate
between humans and vectors helps to reduce the spread of dengue disease.
