Optimal Control Analysis of Malaria Infection in Children Under Five Years and Pregnant women under the Influence of Temperature

Malaria remains a notable global public health problem, affecting particularly children under five years and pregnant women in areas where temperatures are conducive for transmission. A mathematical model was developed to analyze and assess the impact of three controls which are treatment of infected individuals, long-lasting insecticide nets (LLINs), and spraying of insecticides. Due to the nature of data collected, the analysis started with the model with treatment. The next-generation matrix approach was utilized to compute the effective reproduction number (Re) which is essential for comprehending the disease transmission pattern. The numerical analysis for the model with treatment shows that treatment of individuals with malaria is an effective method to manage the disease. The optimal control theory was employed to ascertain the optimal strategy in controlling malaria infection. The cases when controls are applied independently or in combination of two or three were considered. For the case when one control was applied, it was found out that treatment of infectious humans was more successful than spraying insecticides or utilizing LLINs. When controls are used in combination, the use of Long Lasting Insecticide Nets (LLINs) with treatment has revealed to be the most optimal strategy. However employing all three controls did not significantly outperform the combination of Long Lasting Insecticide Nets (LLINs) and treatment. Therefore to manage malaria transmission, the study suggests utilization of Long Lasting Insecticide Nets (LLINs) in combination with treatment of infected individuals.