Dengue infection modeling and its optimal control analysis in East Java, Indonesia

Abstract

In this study, we present a mathematical model of dengue fever transmission with hospitalization to describe the dynamics of the infection. We estimated the basic reproduction number for the infected cases in East Java Province for the year 2018 is  0 ≈ 1.1138. The parameters of the dengue model are estimated by using the confirmed notified cases of East Java province, Indonesia for the year 2018. We formulated the model for dengue with hospitalization and present its dynamics in details. Initially, we present the basic mathematical results and then show briefly the stability results for the model. Further, we formulate an optimal control problem with control functions and obtain the optimal control characterization. The optimal control problem is solved numerically and the results comprised of controls system for different strategies. The controls such as prevention and insecticide could use the best role in the disease eradication from the community. Our results suggest that the prevention of humans from the mosquitoes and the insecticide spray on mosquitoes can significantly reduce the infection of dengue fever and may reduce further spread of infection in the community.

Local and Global Stability Analysis of Dengue Disease with Vaccination and Optimal Control

“…where m 1 , m 2 , C 1 , C 2 , D 1 , D 2 > 0, and ψ > 1. Therefore, there exists an optimal control for the system of Equations ( 33)- (36) satisfying the Pontryagin's minimum principle [25][26][27][28][29]51,52]. Theorem 6.…”

“…The stability analysis of two equilibrium points is carried out and a simulation is given for different parameter settings and to simulate the succession of two epidemics with variable human populations [24]. Khan and Fatmawati [25] described changes in dengue infection from basic reproductive values which defines a model with hospitalization and presents the changes in detail. The results suggest that spraying insecticides on mosquitoes can significantly reduce dengue infection.…”

Optimal Control in a Mathematical Model of Smoking

“…Thus, the following Hamiltonian function is obtained: 𝐻 = (𝑆(𝑡) − 𝑄 𝑃 (𝑡) + The PMP method was used to obtain the adjoint variables [17][18][19][20][21][22][23]. ) , 1)…”

Analysis and optimal control of a Huanglongbing mathematical model with resistant vector

“…In particular, a comparative analysis to understand the costs of different intervention strategies is important for decision makers who are often faced with the resource allocation challenges. In view of this, the application of optimal control theory can serve as a useful tool for assessing the effectiveness of various policies and interventions relative to the cost of implementing them ( Alzahrani et al., 2021 ; Khan & Fatmawatic, 2021 ; Okosun et al., 2013 ). Based on these considerations, in this paper, we formulate a compartmental model to investigate HLB transmission dynamics with resistant ACP in a single orchard of citrus trees.…”