Qualitative Analysis and Optimal Control of a Two-Strain Dengue Model with its Co-infections
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Qualitative Analysis and Optimal Control of a Two-Strain Dengue Model with its Co-infections Jayanta Kumar Ghosh1 · Uttam Ghosh2
· Susmita Sarkar2
Accepted: 26 September 2020 © Springer Nature India Private Limited 2020
Abstract This paper describes a co-infected two-strain Dengue model with bilinear infection rate. Three efforts, namely awareness efforts to protect human from mosquitoes bites, treatment efforts for infected human and mosquitoes killing efforts are considered to eradicate the infections. The treatment reproduction number R0 of the model is derived, which provides whether Dengue can persist or not. The existence and the stability analysis of different equilibrium points have been investigated. Sotomayor theorem is employed to prove the existence of transcritical bifurcation of the model. The sensitivity analysis has been performed to identify the most effective parameter for controlling the Dengue infection. The model is also used as an optimal control problem as all the three efforts are considered as time dependent functions. The Pontryagin’s maximum principle has been used to characterize the optimal control. Numerical results show the positive impacts for implementing three controls to reduce the Dengue infections. Finally efficiency analysis is carried out, which shows that awareness efforts to protect human from mosquitoes bites along with treatment is more effective than the mosquitoes killing efforts along with treatment. Keywords Optimal control · Efficiency analysis · Strain · Co-infections Mathematics Subject Classification 37N25 · 34C23 · 49J15 · 92D30
Introduction Mathematical modelling of different vector borne diseases is an important area of research [1–3]. The spreading of vector borne diseases has been occurring due to interaction of the hosts with the vectors. Dengue is a viral vector borne (mosquito-borne) infectious disease that is transmitted to human through the bites of the Aedes aegypti and Aedes albopictus female mosquitoes. According to the World Health Organisation (WHO), over 2.5 billion people of the world are now living at risk for Dengue disease which is usually found in
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Uttam Ghosh [email protected]
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Boalia Junior High School, Nadia, West Bengal, India
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Department of Applied Mathematics, University of Calcutta, Kolkata, India 0123456789().: V,-vol
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Int. J. Appl. Comput. Math
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tropical and subtropical regions around the world [4–6]. In recent decades, Dengue infection has been made a global public health threat because of its high morbidity and mortality. The infection of Dengue is caused by the Dengue virus (DENV). DENV, a positive-stranded RNA virus, have mainly four strains denoted by DENV-1, DENV-2, DENV-3 and DENV-4. These four strains have different interactions with the antibodies in human blood serum. DENV is co-circulated through all the four strains. An individual, who was affected by any Dengue strain, has lifetime immunity with respect to that particular strain, but not the other strains i.e. the in
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