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WHY THE COMPLEX SYSTEM ANALYSIS APPROACH IS
MORE COMPATIBLE THAN CLASSICAL SIR MODEL IN
DENGUE TRANSMISSION
DILRUK GALLAGE
Abstract.
Background: Dengue, which is transmitted predominately by the
mosquito
Aedes aegypti, has become a global problem since 1950s and is
endemic inmore than 100 countries. There are about 100 million
people infected yearly.Here in Sri Lanka, the disease usually
occurs as epidemics following monsoon
seasons. Since no specific medical treatment or vaccine is
available, one possi-ble way is to analyze mathematical models of
transmission of dengue disease.
Aims: The aim of this work is to realize why the complex system
analysisapproach is more compatible with the transmission dynamics
of infectious dis-eases than classical model approach.
Methods: Here we monthly varied the effect of incubation period
(EIP) of aclassical SIR-model and investigate the behavior of the
transmission of denguedisease. However EIP is not the only
parameter varied but other param-
eters may be varied with time according to climate factors.
Runge-KuttaMethod is used here to solve system of ordinary
differential equations numeri-
cally (namely ode45 solver in MATLAB) to simulate our
mathematical models.
Results: Although the trajectory of infectious human population
of classicalmodel with fixed EIP is convergent (ie. the disease
will die out), it is not the
case in model with varying EIP.
Conclusions: : It is believed that the classical modeling
approach is not suit-
able for decision making processes for controlling diseases. The
reason this is
not true is that because of classical models used with fixed
parameters (butgenerally parameters are varied with climatic
factors) to study the transmission
dengue disease, the results are very far from the reality.
However, consider-ing complex system analysis approach we are able
to attain better results for
transmission of disease than we do with classical model
approach.
Received by the editors March 11, 2013.Key words and phrases.
dengue , mathematical models, extrinsic incubation period
(EIP),
SIR-model, Runge-Kutta Method, ordinary differential
equations.
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MATHEMATICAL MODELING AND DENGUE 3
2. Transmission model with varying the effect of EIP
The following graph is a blowout of above graph.
A blowout of fixed effect of EIP is shown below
Why I varied incubation period in mosquitoes is it has a strong
relationship withclimate factors. Therefore the incubation period
in mosquitoes varies with time.Its not a fixed value in nature.Here
we only varied one parameter, incubation period. But other
parameter may bevaried with time according to climate factors such
as temperature, relative humidify,rain fall... But in classical
models, we considered those are fixed values. In thereality, it is
not.
Department of Mathematics & University of Colombo
E-mail address: [email protected]
