The Dynamics of Malaria in the Blood and the Role of Acquired Immunity: A Mathematical Modeling Approach

Malaria poses a significant health challenge, particularly in tropical and subtropical regions. In this study, a mathematical model for the dynamics of malaria in the blood is formulated and analyzed to explore the role of acquired immunity. To achieve this objective, we analyze the model when there is no acquired immunity and when there is acquired immunity. The basic and the immune-acquired reproduction numbers, R0 and R01 are computed, and global sensitivity analysis is employed to assess the impact of acquired immunity. In the absence of acquired immunity, malaria persists when the basic reproduction number, R0, exceeds unity. The basic reproduction number R0 is positively influenced by the number of free merozoites from ruptured schizonts. Thus, when there is no acquired immunity, malaria parasites are continuously produced, leading to uncontrolled increase of R0. The analysis shows that in the absence of acquired immunity, malaria parasites can infect the entire population of uninfected red blood cells in approximately 10 days. This indicates that individuals with no prior exposure to malaria may develop clinical symptoms sooner than those who have previously experienced the disease and developed acquired immunity. In the presence of acquired immunity, the immune-acquired reproduction number R01 decreases when recruitment of immune cells from the bone marrow increases and increases when immune cells suffer natural death. This highlights the crucial role played by acquired immunity. Numerical results show that, in the presence of acquired immunity, malaria parasites can infect the entire population of uninfected red blood cells after approximately 14 days. This implies that following malaria infection, individuals with acquired immunity develop clinical symptoms after a longer period compared to individuals without acquired immunity. These findings highlight the crucial role of acquired immunity in controlling malaria infection in the blood.