Immune response to a malaria infection: properties of a mathematical model

We establish some properties of a within host mathematical model of malaria proposed by Recker et al which includes the role of the immune system during the infection. The model accounts for the antigenic variation exhibited by the malaria parasite (P. falciparum). We show that the model can exhibit a wide variety of dynamical behaviors. We provide criteria for global stability, competitive exclusion, and persistence. We also demonstrate that the disease equilibrium can be destabilized by non-symmetric cross-reactive responses.

💡 Research Summary

The paper conducts a rigorous mathematical investigation of a within‑host malaria model originally proposed by Recker et al., which explicitly incorporates antigenic variation of Plasmodium falciparum and the host’s immune response. The model consists of a system of ordinary differential equations for (n) parasite clones (x_i(t)) and their corresponding immune effectors (y_i(t)). Each clone grows logistically with intrinsic rate (r_i) and carrying capacity (K_i), and is suppressed by both a self‑immune term (\beta_i x_i y_i) and cross‑immune terms (\beta_{ij} x_i y_j). The cross‑immune coefficients are organized in a matrix (C=