Threshold dynamics and regional optimal control of a malaria model with spatial heterogeneity and ivermectin therapy

The recent experimental results illustrate that adding ivermectin to artemisinin-based combination therapy can target malaria parasite and its vector, which may be a new treatment option. In this paper, we present a new malaria transmission model, which incorporates spatial heterogeneity, general incidence rate and treatment plan with ivermectin. The basic reproduction number R0 is introduced as a threshold parameter to determine whether malaria will eventually die out or not. Further, we propose and analyze the regional optimal control problem to minimize mosquito population, exposed and infectious humans as well as cost. Numerically, we investigate the transmission and control of malaria in The Gambia. Results show that the treatment plans with ivermectin and without ivermectin have the same contribution to R0, but have different effects on the epidemic level of malaria. This conclusion also holds for different incidence rates with some assumptions. Moreover, by comparing the cost and benefit of different strategies, the most cost-effective strategy is found.