Numerical Modeling of Dengue Disease with Incubation Period of Virus

M. Rafiq, M. O. Ahmad

Abstract


Now a days, Numerical models have great importance in epidemiology. It helps us to understand the transmission dynamics of infectious diseases in a very comprehensive way. In disease epidemiology, vector- host models are important because many diseases are spreading through vectors. Mosquitoes are vectors of dengue disease which spread the disease in a population. The infectious vectors infect the hosts while infectious hosts infect to vectors .Two main groups of dengue patients are Infected and Infectious. The susceptible mosquitoes can get dengue infection from infectious humans but not from infected ones. Humans can be categorized into Susceptible, infected, infectious and recovered ones while mosquitoes are susceptible, infected and infectious. Susceptible individual can transfer dengue infection from diseased mosquitoes only. The transmission dynamics of “Dengue Fever” with incubation period of virus has been analyzed in this paper. Using standard methods for analyzing a system, the stability of equilibrium points of the model has been determined. Finally a numerical model has been constructed for the same problem and numerical experiments are performed for different values of discretization parameter ‘ ’.Results are compared with well-known numerical scheme i.e. Runge-Kutta method of order four (RK4). Unlike RK4 which fails for large time steps, the developed scheme gives results that converged to true steady states for any time step used

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References


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