Age-Dependent Survival Rates in SIR-SI Dengue Transmission Model and Its Application Considering Human Vaccination and Wolbachia Infection in Mosquitoes

Asep K. Supriatna (), Hennie Husniah, Edy Soewono, Bapan Ghosh, Yedhi Purwanto and Elah Nurlaelah
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Asep K. Supriatna: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia
Hennie Husniah: Department of Industrial Engineering, Faculty of Engineering, Universitas Langlangbuana, Bandung 40261, Indonesia
Edy Soewono: Center for Mathematical Modeling and Simulation, Institut Technologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia
Bapan Ghosh: Differential Equations, Modeling, and Simulation Group, Department of Mathematics, Indian Institute of Technology Indore, Indore 453552, India
Yedhi Purwanto: Humanities Research Group, Institut Technologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia
Elah Nurlaelah: International Program of Science Education, Universitas Pendidikan Indonesia, Jl. Dr. Setiabudhi 229, Bandung 40154, Indonesia

Mathematics, 2022, vol. 10, issue 21, 1-22

Abstract: In this paper, an SIR-SI mathematical model in the form of a system of integral equations describing the transmission of dengue disease between human and mosquitoes is proposed and analyzed. Age-dependent functions are used to describe the survival of individuals in human and mosquito populations. The basic reproduction number is derived and its relationship to the equilibria is also explored. The results show that the existence of the positive endemic equilibrium is determined by a threshold number. This threshold number is also the same one that determines the global stability of the equilibrium. The threshold acts like the known basic reproduction number in the counterpart differential equations model and also follows the same rule for the critical level of intervention. Furthermore, as an application, the effect of wolbachia infection is explored, such as how this infection changes the resulting threshold and what the consequence of its presence is in the dynamics of the disease. In this case, the decrease of the mosquitoes’ life expectancy and biting rate are used to reflect the effect of wolbachia bacterial infection on the mosquitoes. In other words, a mosquito which is infected by wolbachia has a lower life expectancy than a normal mosquito. The results, both from mathematical analysis and numerical examples, show that the presence of wolbachia has the potential as a biological control agent to eliminate the dengue in the human population. A comparison of the wolbachia introduction into the mosquito population with the existing strategy, such as vaccination, is also presented.

Keywords: SIR-SI integral equations; Gronwall-like inequality; applied mathematics; dengue disease; wolbachia infection; biological control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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