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

N1 - Funding Information:
Tridip Sardar is supported by the research fellowship from Council of Scientific and Industrial Research (CSIR), Government of India. Funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Publisher Copyright:
© 2015 Elsevier Inc.

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

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U2 - 10.1016/j.mbs.2015.01.009

DO - 10.1016/j.mbs.2015.01.009

M3 - Article

C2 - 25645185

AN - SCOPUS:84961288982

SN - 0025-5564

VL - 263

SP - 18

EP - 36

JO - Mathematical Biosciences

JF - Mathematical Biosciences

ER -