### Abstract

In the present investigation, three mathematical models on a common single strain mosquito-transmitted diseases are considered. The first one is based on ordinary differential equations, and other two models are based on fractional order differential equations. The proposed models are validated using published monthly dengue incidence data from two provinces of Venezuela during the period 1999-2002. We estimate several parameters of these models like the order of the fractional derivatives (in case of two fractional order systems), the biting rate of mosquito, two probabilities of infection, mosquito recruitment and mortality rates, etc., from the data. The basic reproduction number, R_{0}, for the ODE system is estimated using the data. For two fractional order systems, an upper bound for, R_{0}, is derived and its value is obtained using the published data. The force of infection, and the effective reproduction number, R(t), for the three models are estimated using the data. Sensitivity analysis of the mosquito memory parameter with some important responses is worked out. We use Akaike Information Criterion (AIC) to identify the best model among the three proposed models. It is observed that the model with memory in both the host, and the vector population provides a better agreement with epidemic data. Finally, we provide a control strategy for the vector-borne disease, dengue, using the memory of the host, and the vector.

Original language | English |
---|---|

Pages (from-to) | 18-36 |

Number of pages | 19 |

Journal | Mathematical Biosciences |

Volume | 263 |

DOIs | |

Publication status | Published - May 1 2015 |

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### Keywords

- Fractional order differential equations
- Mathematical model
- Parameter estimation
- Reproduction number
- Single strain mosquito-transmitted diseases

### ASJC Scopus subject areas

- Statistics and Probability
- Medicine(all)
- Modelling and Simulation
- Immunology and Microbiology(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics

### Cite this

*Mathematical Biosciences*,

*263*, 18-36. https://doi.org/10.1016/j.mbs.2015.01.009

**A generic model for a single strain mosquito-transmitted disease with memory on the host and the vector.** / Sardar, Tridip; Rana, Sourav; Bhattacharya, Sabyasachi; Al-Khaled, Kamel; Chattopadhyay, Joydev.

Research output: Contribution to journal › Article

*Mathematical Biosciences*, vol. 263, pp. 18-36. https://doi.org/10.1016/j.mbs.2015.01.009

}

TY - JOUR

T1 - A generic model for a single strain mosquito-transmitted disease with memory on the host and the vector

AU - Sardar, Tridip

AU - Rana, Sourav

AU - Bhattacharya, Sabyasachi

AU - Al-Khaled, Kamel

AU - Chattopadhyay, Joydev

PY - 2015/5/1

Y1 - 2015/5/1

N2 - In the present investigation, three mathematical models on a common single strain mosquito-transmitted diseases are considered. The first one is based on ordinary differential equations, and other two models are based on fractional order differential equations. The proposed models are validated using published monthly dengue incidence data from two provinces of Venezuela during the period 1999-2002. We estimate several parameters of these models like the order of the fractional derivatives (in case of two fractional order systems), the biting rate of mosquito, two probabilities of infection, mosquito recruitment and mortality rates, etc., from the data. The basic reproduction number, R0, for the ODE system is estimated using the data. For two fractional order systems, an upper bound for, R0, is derived and its value is obtained using the published data. The force of infection, and the effective reproduction number, R(t), for the three models are estimated using the data. Sensitivity analysis of the mosquito memory parameter with some important responses is worked out. We use Akaike Information Criterion (AIC) to identify the best model among the three proposed models. It is observed that the model with memory in both the host, and the vector population provides a better agreement with epidemic data. Finally, we provide a control strategy for the vector-borne disease, dengue, using the memory of the host, and the vector.

AB - In the present investigation, three mathematical models on a common single strain mosquito-transmitted diseases are considered. The first one is based on ordinary differential equations, and other two models are based on fractional order differential equations. The proposed models are validated using published monthly dengue incidence data from two provinces of Venezuela during the period 1999-2002. We estimate several parameters of these models like the order of the fractional derivatives (in case of two fractional order systems), the biting rate of mosquito, two probabilities of infection, mosquito recruitment and mortality rates, etc., from the data. The basic reproduction number, R0, for the ODE system is estimated using the data. For two fractional order systems, an upper bound for, R0, is derived and its value is obtained using the published data. The force of infection, and the effective reproduction number, R(t), for the three models are estimated using the data. Sensitivity analysis of the mosquito memory parameter with some important responses is worked out. We use Akaike Information Criterion (AIC) to identify the best model among the three proposed models. It is observed that the model with memory in both the host, and the vector population provides a better agreement with epidemic data. Finally, we provide a control strategy for the vector-borne disease, dengue, using the memory of the host, and the vector.

KW - Fractional order differential equations

KW - Mathematical model

KW - Parameter estimation

KW - Reproduction number

KW - Single strain mosquito-transmitted diseases

UR - http://www.scopus.com/inward/record.url?scp=84961288982&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961288982&partnerID=8YFLogxK

U2 - 10.1016/j.mbs.2015.01.009

DO - 10.1016/j.mbs.2015.01.009

M3 - Article

VL - 263

SP - 18

EP - 36

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

ER -