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

Figure 1

A conceptual mathematical model for malaria transmission involving human hosts and vector mosquitoes in each patch 𝑖,𝑖=1,…,𝑛. The dotted arrow shows the direction of the transmission from humans to mosquitoes (through infectious humans to susceptible mosquitoes) or from mosquitoes to humans (through infectious mosquitoes to susceptible humans); 𝑢_2𝑖 and 𝑣_2𝑖 represent the prevention and treatment control over time, respectively. Φ_2𝑖=(1−𝑢_2𝑖)Φ_2𝑖 and Φ_2𝑖−1=(1−𝑢_2𝑖)Φ_2𝑖−1 represent the force of infection from mosquitoes to humans and from humans to mosquitoes, respectively, where Φ_2𝑖 and Φ_2𝑖−1 are defined in (2.2). The other parameters are described in Table 1.