Research Proposal Tharindu

7/30/2019 Research Proposal Tharindu

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M.Phil / Ph.D. Research Proposal, Faculty of Science, University of Colombo

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Program

PhD

Department

Departments

of

Mathematics

Index No.

Name:Mr.WPTM

Wickramaarachchi

Signature E-mail:

[email protected]

Phone:

0718377861

Title:

Developing a mathematical model to study dynamics of Dengue epidemics and controllability of

transmission of Dengue

Name(s) of supervisor(s) Institute Signature E-mail / Phone

Dr. SSN Perera University of

Colombo

[email protected]

Phone:0715352616

Introduction

Dengue is one of the most prevalent viruses by mosquitoes where increasing incidence and severity

claims it as a worrisome disease. This virus is common throughout the tropics and subtropics. Outbreaks

have occurred in the US Virgin Islands, Cuba and Central America. Also it is increasing in Asia and

Africa. According to the World Health Organization, there are an estimated 50 million cases of denguefever with 500,000 cases of dengue hemorrhagic fever requiring hospitalization each year. Nearly 40%

of the worlds population lives in an area endemic with dengue.

Dengue fever is caused by family of viruses that are transmitted by Aedes mosquitoes. Though its claim

classic form causes flu-like symptoms and is not life-threatening, more severe forms as dengue

hemorrhagic fever (DHF) and dengue shock syndrome (DSS) can be fatal, especially in children.

During the past few years, the characteristics of dengue in Sri Lanka appear to have changed. For

instance, a decade ago, children were predominantly affected, but in recent years clinicians have seen

increasing numbers of adult dengue patients, with both significant morbidity and increasing number ofadult deaths due to dengue. Therefore, it is very important to investigate, how this virus spreads while

considering their age, gender and other demographic factors with the attitudes of the government and

people.

As far as disease control, its entomological aspect is very important. Mosquito phase is to be approached

to block the transmission cycle. Socio-economic impact of control measures is the major concern in

national health care administration.

In literature, many Mathematical models are available to study the transmission of dengue. But all these

models are based on the forward simulation. That is given a set of parameters the simulation results areobtained. Yet, given the task the optimal control strategies for transmission of dengue, have not been

attended in literature.
mailto:[email protected]:[email protected]


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Objectives of the Research

Identify the optimal control strategy to control the transmission of dengue is the major objective of this

research. Meantime the following sub objectives will also be achieved.1. Identify the quantification of factors affecting the transmission of dengue.2. Study dynamics of dengue with respect to range of parameter values and their patterns.3. Carry out model based analysis to investigate effectiveness of disease control strategies.4. Identification of cost functional in order to minimize the investment in further transmission of

dengue.

Methodology

Dynamics of dengue can be formulated via a system of ODEs/PDEs.Thus, model equations can be

infused the approaches mentioned above (i.e. age-specific, gender-specific,etc).Using field

data/literature, parameter values will be identified and sensitivity of model with respect to externalvariables will be studied by defining set of sensitivity equations and using phase portrait. In our

approach the parameter values will be allowed to vary within reliable bounds. Thus, range modeling is

the typical approach here. It is important in two ways. First, effect of varying dynamics can beincorporated better than in a classical deterministic approach. On the other hand, it would minimize the

burden of lack of data, where fully stochastic model is not possible. Using multiple regression, neura

network or Hybrid models, dengue disease patterns with respect to measured direct parameters as well

as auxiliary parameters such as human behavior and social welfare potential will be recognized.Enumerating the impact of human awareness and subsequent response is a challenging task as it is

infused with many other time-specific and regional factors. Thus Fuzzy logic and Fuzzy integrals will be

suitable here to model the behavior of humans in controllability of dengue.

Based on the obtained results control measures will be identified. Cost functional will be identified to

recognize control strategies with respect to control parameters. Characteristics of the cost functional will

be aimed to minimize the investment in diseases control and the risk of further transmission. Based onthe cost functional and respective constraints, the Lagrangian Functional will be set up together with

optimization techniques. State, Adjoint, Control systems will be set up and suitable optimization

algorithm will be applied to solve the problem.

Time Frame

Task Year 1 Year 2 Year 3

Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4

1 Literature review

2 Study the transmission of dengue(Simple)

3 Identify the quantification factors of dengue

4 Study the dynamics of dengue(advanced)5 Identification of patterns in the parameters

6 Data collection

7 Estimating the parameter values

8 Simulation

9 Identifying the cost functional and constraints.

10 Identifying and recommending optimal controlstrategies for transmission of dengue

11 Thesis writing


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References

[1] M Derouich, A Boutayeb and EH Twizell (2003), A model for dengue fever, Biomedical

Engineering Online - pp 1-10.

[2] Puntani Pongsumpun (2006), Transmission model for dengue disease with and without the effect of

extrinsic incubation period, KMITL Sci.Tech.J. Vol 6 No.2 - pp 74-82.

[3] N Nuraini, E Soewono and KA Sidarto (2007), A Mathematical model of dengue internaltransmission process, J.Indones.Math.Soc (MIHMI) Vol 13 No.1 - pp 123-132.

[4] P.Pongsumpun (2008),Mathematical model of dengue disease with the incubation period of virus, PPongsumpun, World Academy of Science, Engineering and Technology - pp 328-332.

Research Proposal Tharindu

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