Effect of partial immunity on transmission dynamics of dengue disease with optimal control

Abstract

Dengue fever is one of the most dangerous vector‐borne diseases in the world in terms of death and economic cost. Hence, the modeling of dengue fever is of great significance to understand the dynamics of dengue. In this paper, we extend dengue disease transmission models by including transmit vaccinated class, in which a portion of recovered individual loses immunity and moves to the susceptibles with limited immunity and hence a less transmission probability. We obtain the threshold dynamics governed by the basic reproduction number R0; it is shown that the disease‐free equilibrium is locally asymptotically stable if R0 ≤ 1, and the system is uniformly persistence if R0 > 1. We do sensitivity analysis in order to identify the key factors that greatly affect the dengue infection, and the partial rank correlation coefficient (PRCC) values for R0 shows that the bitting rate is the most effective in lowering dengue new infections, and moreover, control of mosquito size plays an essential role in reducing equilibrium level of dengue infection. Hence, the public are highly suggested to control population size of mosquitoes and to use mosquito nets. By formulating the control objective, associated with the low infection and costs, we propose an optimal control question. By the application of optimal control theory, we analyze the existence of optimal control and obtain necessary conditions for optimal controls. Numerical simulations are carried out to show the effectiveness of control strategies; these simulations recommended that control measures such as protection from mosquito bites and mosquito eradication strategies effectively control and eradicate the dengue infections during the whole epidemic.

Optimal vaccination strategy for dengue transmission in Kupang city, Indonesia

“…This approach is rather conventional and has been frequently used in the epidemiological modelling including dengue modelling [11,13,26 approach to investigate the effects of vector control and vaccination on dengue transmission dynamics. They used quadratic terms in the control variables as to represent the nonlinear cost [23], which has been also used in the other work for the similar reason to investigate the dengue transmission dynamics in the presence of controls [11,13,26,15,23,39,40,12].…”

“…In optimal control approach, we use quadratic terms in the control variables to capture the nonlinear cost in the implementation of controls. This approach is rather conventional and has been frequently used in the epidemiological modelling including dengue modelling [11] , [13] , [26] , [15] , [23] , [39] , [40] , [12] . Rawson et al implemented optimal control approach to investigate the effects of vector control and vaccination on dengue transmission dynamics.…”

Fractional Dynamics of HIV with Source Term for the Supply of New CD4+ T-Cells Depending on the Viral Load via Caputo–Fabrizio Derivative

“…Several biological phenomena and processes can be formulating in the language of mathematics in the framework of ordinary differential equations, fractional differential equations, impulsive differential equations, stochastic differential equations, delay differential equations, etc. [ 2 , 3 , 4 , 5 , 6 ]. Different assumptions, laws, axioms governing these processes are used in the formulation of these mathematical models to show the intricate dynamics of biological phenomena.…”

Modified Modelling for Heat Like Equations within Caputo Operator

“…FPDEs are the key mathematical methods used to model many physical processes in various branches of applied science, such as physics, engineering, or other sciences. Modeling in the form of FPDEs appears in several engineering and science applications, including microelectronics, chemistry, biology, thermodynamics, chemical kinetics and other physical processes [15][16][17][18][19][20][21][22][23][24][25][26]. Different analytical and numerical methods to solve these forms of FPDEs have been published in the literature.…”