In silico experimental modeling of cancer involves combining findings from biological literature with computer-based models of biological systems in order to conduct investigations of hypotheses entirely in the computer laboratory. In this paper, we discuss the use of in silico modeling as a precursor to traditional clinical and laboratory research, allowing researchers to refine their experimental programs with an aim to reducing costs and increasing research efficiency. We explain the methodology of in silico experimental trials before providing an example of in silico modeling from the biomathematical literature with a view to promoting more widespread use and understanding of this research strategy.

In this paper, a modified Leslie–Gower predator-prey model with Beddington–DeAngelis functional response and double Allee effect in the growth rate of a predator population is proposed. In order to consider memory effect on the proposed model, we employ the Caputo fractional-order derivative. We investigate the dynamic behaviors of the proposed model for both strong and weak Allee effect cases. The existence, uniqueness, non-negativity, and boundedness of the solution are discussed. Then, we determine the existing condition and local stability analysis of all possible equilibrium points. Necessary conditions for the existence of the Hopf bifurcation driven by the order of the fractional derivative are also determined analytically. Furthermore, by choosing a suitable Lyapunov function, we derive the sufficient conditions to ensure the global asymptotic stability for the predator extinction point for the strong Allee effect case as well as for the prey extinction point and the interior point for the weak Allee effect case. Finally, numerical simulations are shown to confirm the theoretical results and can explore more dynamical behaviors of the system, such as the bi-stability and forward bifurcation.

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This paper deals with a construction and an analysis of harvested predator-prey model with ratio-dependent response function and prey refuge. The harvesting is applied on both of predator and prey because they have a commercial value, while the prey refuge is applied in accordance with the fact that prey has a refuge instinct enabling to reduce the possibility of prey catching rate. According to the analysis, there are four equilibrium points which are stable under certain conditions, namely the prey extinction, the predator extinction, and two coexistence points. Finally, numerical solutions are presented not only to illustrate each equilibrium points but also to illustrate the effects of prey refuge.

In this paper we study the dynamics of predator-prey model with allelopathic effect on prey. We find that the model has four equilibrium points that are extinction of prey equilibrium, the extinction of predator equilibrium, the extinction of both predator and prey, and the coexistence equilibrium. It is shown that the extinction of predator equilibrium and the extinction of both predator and prey equilibrium are unstable, while the extinction of prey equilibrium is conditionally stable. The coexistence equilibrium is unconditionally stable. The analytical results are confirmed by numerical simulations.

A predator-prey model with disease in both populations is proposed to illustrate the possibility of disease transmission between prey and predator through contact and predation. We used saturated incidence rate which takes behavioural changes of healthy population into consideration when disease spreads around them. The existence of eight non-negative equilibrium points is analysed and their local stability has been investigated. Numerical simulations are given to illustrate analytic results.

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In this paper, the dynamics of a fractional-order Leslie-Gower model with Allee effect in predator is investigated. Firstly, we determine the existing condition and local stability of all possible equilibrium points. The model has four equilibrium points, namely both prey and predator extinction point, the prey extinction point, the predator extinction point, and the interior point. Furthermore, we also show the dynamic changing around the interior point due to the changing of the order of the fractional derivative, namely the Hopf bifurcation. In the end, some numerical simulations are demonstrated to illustrate the dynamics of the model. Here we show numerically the local stability, the occurrence of Hopf bifurcation, and the impact of the Allee effect to the prey and predator densities.