Malaria is a plasmodium parasite-caused serious and deadly infection transmitted by the bite of a female Anopheles mosquito that carries the infection. This study is intended to explore the optimal combinations of three time-dependent control intervention strategies, including personal protective measures \(u_{1}(t)\) , improved treatment capability \(u_{2}(t)\) , and mosquito breeding site destruction \(u_{3}(t)\) to pull down the infection. To achieve this aim, we extend the autonomous malaria mathematical model proposed in [34] into an optimal control model by introducing these three time-evolution controls. We first considered constant controls to compute the basic reproductive number \(\mathcal {R}_{0}\) through the method of next-generation matrix. We fitted the autonomous model with the help of Ethiopian malaria incidence data from 2000 to 2022 years. To determine the most sensitive parameters, we calculated the forward sensitivity indexes of \(\mathcal {R}_{0}\) with respect to model parameters. Further, we analytically derived the relative impact \(\mathcal {R}_{0}\) along with each constant control. We applied Pontryagin’s Minimum Principle to derive the necessary conditions for an optimal control model. To locate the most cost-effective intervention strategy, we computed ACER and ICER. The numerical simulation of the optimality system is displayed in the Python Gekko optimization package, which supports analytical results. Findings from the numerical results indicate that malaria can be well controlled by implementing any of the proposed strategies. However, the realization of these strategies is hindered in resource-limited settings. Thus, we comprehend the cost-effectiveness analysis to determine economically viable approach. The finding from the cost-effectiveness analysis reveals that implementing the optimal combination of improved treatment capability and destruction of mosquito breeding sites is economically best strategy to control malaria transmission than the remaining combinations.
