Tumour cells behave differently than normal cells in the body. They grow and
divide in an uncontrolled manner (actively proliferating) and fail to respond to signal.
However, there are cells that become inactive and reside in quiescent phase (G0). These
cells are known as quiescence cells that are less sensitive to drug treatments (radiotherapy
and chemotherapy) than actively proliferation cells. This paper proposes a new mathe-
matical model that describes the interaction of tumour growth and immune response by
considering tumour population that is divided into three different phases namely inter-
phase, mitosis and G0. The model consists of a system of delay differential equations
where the delay, represents the time for tumour cell to reside interphase before entering
mitosis phase. Stability analysis of the equilibrium points of the system was performed
to determine the dynamics behaviour of system. Result showed that the tumour popu-
lation depends on number of tumour cells that enter active (interphase and mitosis) and
G0phases. This study is important for treatment planning since tumour cell can resist
treatment when they refuge in a quiescent state.
The discovery of new antimalarial drugs from medicinal plants is urgently neededdue to the development of multidrug-resistant Plasmodium falciparum. Therefore, Piper sarmentosum(kaduk), a commonly used as a herbal medicine to treat malarial symptoms was screened for antimalarial as well as toxicological activities of their methanol and water leaves extracts. The inhibitory concentration (IC50) of P. sarmentosum methanol and water extracts against a chloroquine-sensitive strain (3D7) of P. falciparumwas determined by using a malarial SYBR Green I-based fluorescence (MSF) assay. The lethal concentration (LC50) of the plant extracts was evaluated by using a brine shrimp lethality test (BSLT). The presence of heavy metal contents in the crude extract was alsodetected by using an atomic absorption spectrometry (AAS). Both methanol and water extracts showed an inactive antimalarial activity with an IC50value of 138.8 ± 0.122 μg/mL and 229.7 ± 0.125 μg/mL, respectively. The water extract was considered non-toxic (LC50= 2741.7 3.16 ppm), while the methanol extract was toxic (LC50= 894.94 0.018 ppm). The heavy metals such as plumbum (Pb), zinc (Zn), cadmium (Cd) and chromium (Cr) were identified in the crude extract but they were below the safety limits recommended except for arsenic (As). Further investigations are required to determine the toxicological profiles of P. sarmentosum extracts on mammalian models.