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In this paper, we have rigorously analyzed a model to find the effective control strategies on the transmission dynamics of a vector-borne disease. It is proved that the global dynamics of the disease are completely determined by the basic reproduction number. The numerical simulations (using MatLab and Maple) of the model reveal that the precautionary measures at the aquatic and adult stage decrease the number of new cases of dengue virus. Numerical simulation indicates that if we take the precautionary measures seriously then it would be more effective than even giving the treatment to the infected individuals.

Vector-borne diseases rely upon organisms, named vectors, such as mosquitoes, ticks or sandflies that have an active role in the transmission of a pathogen from one host to the other. Every year there are more than 1 billion cases and over 1 million deaths from vector-borne diseases such as malaria, dengue, schistosomiasis, human African try-panosomiasis, leishmaniasis, Chagas disease, yellow fever, Japanese encephalitis and onchocerciasis, globally. Since dengue is related with our previous work, so over here we consider the Dengue transmission model. Dengue is endemic in more than 110 countries [

Dengue fever is an infectious tropical disease caused by the dengue virus. Dengue is transmitted by several species of mosquito within the genus Aedes, principally Aedes aegypti. The virus has four different types [

According to the World Tourism Organization, 2,012,077 USA tourists visited Thailand during 1 January 2001 and 31 December 2004, giving a rate of 3.5 dengue infection per 1 million visitors to Thailand. Personnel deployed in dengue-endemic areas during humanitarian emergencies then are regular travelers, since they usually live in areas without vector control activities or air conditioning, and usually stay in those areas longer than do tourists. During a 5-month deployment as a part of the United Nations Mission in Haiti, 32% of 249 personal with febrile illness had dengue [

Several mathematical models have been developed in the literature to gain-insights into the transmission dynamics of dengue in a community [

The dengue virus follows two main modes of transmission: human to mosquito and mosquito to human [

mutually-exclusive sub-populations of susceptible humans

Similarly, the total vector population at time t, denoted by

where the modification parameter

Variables | Description |
---|---|

Susceptible humans | |

Exposed humans | |

Infected humans | |

Migrated class of individuals comes from different parts of the world to the host country and contains the virus of dengue | |

Treated humans | |

Recovered individuals | |

Aquatic class | |

Susceptible mosquitoes | |

Exposed mosquitoes | |

Infected mosquitoes |

The associated basic reproduction number, denoted by

where ρ is the spectral radius of

where,

The square root in the expression for R_{0} arises from the two generations required for an infectious vector or host to reproduce itself.

The model (2) is simulated, using the parameter values given in

_{V} at which the vector individuals transfer from exposed class to infected class increases and at the same time if we have the effective precautionary measures the we would be able to control the disease spread and no endemic will occur, otherwise the disease burden will increases.

6000 | 500 | 300 | 50 | 290 | 280 | 1,000,000 | 10,000 | 5000 | 3000 |

Parameter | Description | Baseline values |
---|---|---|

π_{H} | Recruitment rate of humans | 20 day^{−1} [ |

π_{V} | Recruitment rate of vectors | 5000 day^{−1} [ |

Natural death rate of humans | 67 years [ | |

_{HV} | Natural death rate of vectors Contact rate from host to vector | [^{−1} [ |

C_{VH} | Contact rate from vector to host | 0.375 day^{−1} [ |

σ_{H} | Exposed individuals with develop clinical symptoms | |

of dengue disease move to infectious class at that rate | (0, 1) day^{−1} | |

σ_{V} | Exposed vectors develop symptom of disease and | |

move to infections class at this rate | (0, 1) assumed | |

τ_{H} | Rate of treatment | Variable |

δ_{H} | Disease induced death | 10^{−1} day^{−1} [ |

π_{2} | Migrated population | Variable |

µ_{1}, µ_{2} | Transition rates between E_{H} and I_{H} classes | Variable |

γ_{1} | Transfer rate from treatment class to recovery class | 0.1428 day^{−1} [ |

δ_{V} | Disease induced death rate for infectious | negligible |

γ_{m} | is the mean aquatic transition rate | Variable |

C_{a} | Control effect rate | Variable |

η_{H}, η_{V} | Modification parameters | [0, 1] [ |

C_{m} | Control effect rate | Variable |

θ_{c} | Extrinsic incubation rate of vector | Variable |

fective vector control rate

Mosquitoes are the carriers that can cause a virus infection to human. Aim of our current study is to make people conscious about vector-bone disease cause. Numerical simulation depicts that if we take the precautionary measures more seriously it would be more effective than even giving the treatment to the infected individuals. Numerical simulations reveal that the spread of dengue virus can be controlled more effectively, if we take the precautionary measures at the aquatic and adult stages.

SaddamHossain,JannatumNayeem,ChandranathPodder, (2015) Effective Control Strategies on the Transmission Dynamics of a Vector-Borne Disease. Open Journal of Modelling and Simulation,03,111-119. doi: 10.4236/ojmsi.2015.33012