Journal of Applied Mathematics

Research Article

Optimal Control of a Spatio-Temporal Model for Malaria: Synergy Treatment and Prevention

Table 1

Parameters for the model described in any patch 𝑖 , 𝑖 = 1 , … , 𝑛 .
Parameters and biological description 
Ξ› 2 𝑖 : recruitment into the susceptible human Ξ› 2 𝑖 > 0
𝛼 2 𝑖 : rate of progression from the infectious human class to the semi-immune class 𝛼 2 𝑖 > 0
𝜌 2 𝑖 : rate of progression from the infectious human class to the susceptible human class 𝜌 2 𝑖 > 0
𝛽 2 𝑖 : rate of progression from the semi-immune class to the susceptible human class 𝛽 2 𝑖 > 0
𝛾 2 𝑖 : disease-induced death rate 𝛾 2 𝑖 β‰₯ 0
πœ‡ 2 𝑖 : naturally induced death rate of the human population πœ‡ 2 𝑖 > 0
πœ‡ 2 𝑖 βˆ’ 1 : naturally induced death rate of the mosquitoes πœ‡ 2 𝑖 βˆ’ 1 > 0
Ξ› 2 𝑖 βˆ’ 1 : recruitment into susceptible mosquitoes class Ξ› 2 𝑖 βˆ’ 1 > 0
 𝜎 2 𝑖 , 2 𝑖 βˆ’ 1 : probability of transmission of the infection from a semi-immune human to
    a susceptible mosquito		  𝜎 2 𝑖 , 2 𝑖 βˆ’ 1 > 0
𝜎 2 𝑖 βˆ’ 1 , 2 𝑖 : probability of transmission of infection from an infectious mosquito to
   a susceptible human		 𝜎 2 𝑖 βˆ’ 1 , 2 𝑖 ∈ [ 0 ; 1 ]
𝜎 2 𝑖 , 2 𝑖 βˆ’ 1 : probability of transmission of infection from an infectious human to
    a susceptible mosquito		 𝜎 2 𝑖 , 2 𝑖 βˆ’ 1 ∈ [ 0 ; 1 ]
Μƒ π‘Ž 2 𝑖 : maximum number of mosquito bites a human can receive per time unit Μƒ π‘Ž 2 𝑖 β‰₯ 0
Μƒ π‘Ž 2 𝑖 βˆ’ 1 : number of time one mosquito would β€œwant to” bite humans per time unit Μƒ π‘Ž 2 𝑖 βˆ’ 1 β‰₯ 0