A probabilistic model of pre-erythrocytic malaria vaccine combination in mice

Malaria remains one the world's most deadly infectious diseases, with almost half a million deaths and over 150 million clinical cases each year. An effective vaccine would contribute enormously to malaria control and will almost certainly be required for eventual eradication of the disease. However, the leading malaria vaccine candidate, RTS,S, shows only 30-50% efficacy under field conditions, making it less cost-effective than long-lasting insecticide treated bed nets. Other subunit malaria vaccine candidates, including TRAP-based vaccines, show no better protective efficacy. This has led to increased interest in combining subunit malaria vaccines as a means of enhancing protective efficacy. Mathematical models of the effect of combining such vaccines on protective efficacy can help inform optimal vaccine strategies and decision-making at all stages of the clinical process. So far, however, no such model has been developed for pre-clinical murine studies, the stage at which all candidate antigens and combinations begin evaluation. To address this gap, this paper develops a mathematical model of vaccine combination adapted to murine malaria studies. The model is based on simple probabilistic assumptions which put the model on a firmer theoretical footing than previous clinical models, which rather than deriving a relationship between immune responses and protective efficacy posit the relationship to be either exponential or Hill curves. Data from pre-clinical murine malaria studies are used to derive values for unknowns in the model which in turn allows simulations of vaccine combination efficacy and suggests optimal strategies to pursue. Finally, the ability of the model to shed light on fundamental biological variables of murine malaria such as the blood stage growth rate and sporozoite infectivity is explored.