A previously published mathematical model, governing tumour growth with mixed immunotherapy and chemotherapy treatments, is modified and studied. The search time, which is assumed to be neglectable in the previously published model, is incorporated into the functional response for tumour-cell lysis by effector cells. The model exhibits bistability where a tumour-cell population threshold exists. A tumour with an initial cell population below the threshold can be controlled by the immune system and remains microscopic and asymptomatic called cancer without disease while that above the threshold grows to lethal size. Bifurcation analysis shows that (a) the chemotherapy-induced damage may cause a microscopic tumour, which would never grow to become lethal if untreated, to grow to lethal size, (b) applying chemotherapy alone requires a large dosage to be successful,
Keywords: 34D20; 34H20; 37M25; 92B05; Competition model; bifurcation analysis; cancer; dynamical system; numerical simulation.
(c) immunotherapy is ineffective, and (d) a combination of chemotherapy and immunotherapy can produce a synergistic effect on the outcome of a treatment.