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The complement system is a powerful mechanism of innate immunity poised to eliminate foreign cells and pathogens. It is an intricate network of >35 proteins, which, once activated, leads to the tagging of the surface to be eliminated, produces potent chemoattractants to recruit immune cells, and inserts cytotoxic pores into nearby lipid surfaces. Although it can be triggered via different pathways, its net output is largely based on the direct or indirect activation of the alternative pathway. Complement dysregulation or deficiencies may cause severe pathologies, such as paroxysmal nocturnal hemoglobinuria (PNH), where a lack of complement control proteins leads to hemolysis and life-threatening anemia. The complexity of the system poses a challenge for the interpretation of experimental data and the design of effective pharmacological therapies. To address this issue, we developed a mathematical model of the alternative complement pathway building on previous modelling efforts. The model links complement activation to the hemolytic activity of the terminal alternative pathway, providing an accurate description of pathway activity as observed in vitro and in vivo, in health and disease. Through adjustment of the parameters describing experimental conditions, the model was capable of reproducing the results of an array of standard assays used in complement research. To demonstrate its clinical applicability, we compared model predictions with clinical observations of the recovery of hematological biomarkers in PNH patients treated with the complement inhibiting anti-C5 antibody eculizumab. In conclusion, the model can enhance the understanding of complement biology and its role in disease pathogenesis, help identifying promising targets for pharmacological intervention, and predict the outcome of complement-targeting pharmacological interventions. Author summary: The complement system as a part of the innate immunity builds a first line of defense of the body against foreign and altered host structures, such as pathogens and damaged cells. In contrast to the adaptive immune system, which takes days to weeks to mount a response, the complement system can react within seconds to minutes and therefore enables the body to quickly react to infections. Dysregulation of the system, however, has been identified as a major driver or significant contributor to several pathologies, ranging from the pathologic lysis of body's own erythrocytes to the progressive loss of eyesight. The pathway's highly diverse and interconnected architecture makes it difficult to identify promising points of therapeutic intervention and to predict clinical study outcomes. Building on previous modelling efforts, in this work we developed a mathematical model of the alternative pathway of the complement system that can explain experimental observations acquired over more than 50 years of complement research. These include results acquired in the laboratory as well as in patients. We envision that this work can be used to support the development of novel treatments for complement-mediated diseases at several key points such as target selection or design of clinical studies. [ABSTRACT FROM AUTHOR]