A chemotherapy model for cancer treatment is studied, where the chemotherapy agent and cells are assumed to follow a predator-prey type relation. The time delays from the instant that the chemotherapy agent is injected to the instant that the treatment is effective are taken into account and dynamics of systems with or without delays are compared. First basic properties of solutions including existence and uniqueness, boundedness and positiveness are discussed. Then conditions on model parameters are established for different outcomes of the treatment. Numerical simulations are provided to illustrate theoretical results.2010 Mathematics Subject Classification. Primary: 34D23, 34K20; Secondary: 92B05, 93D05.
A nonautonomous mathematical model of chemotherapy cancer treatment with time-dependent infusion concentration of the chemotherapy agent is developed and studied. In particular, a mutual inhibition type model is adopted to describe the interactions between the chemotherapy agent and cells, in which the chemotherapy agent is modeled as the prey being consumed by both cancer and normal cells, thereby reducing the population of both. Properties of solutions and detailed dynamics of the nonautonomous system are investigated, and conditions under which the treatment is successful or unsuccessful are established. It can be shown both theoretically and numerically that with the same amount of chemotherapy agent infused during the same period of time, a treatment with variable infusion may over perform a treatment with constant infusion.
The time required to identify and confirm risk factors for new diseases and to design an appropriate treatment strategy is one of the most significant obstacles medical professionals face. Traditionally, this approach entails several clinical studies that may last several years, during which time strict preventative measures must be in place to contain the epidemic and limit the number of fatalities. Analytical tools may be used to direct and accelerate this process. This study introduces a six-state compartmental model to explain and assess the impact of age demographics by designing a dynamic, explainable analytics model of the SARS-CoV-2 coronavirus. An age-stratified mathematical model taking the form of a deterministic system of ordinary differential equations divides the population into different age groups to better understand and assess the impact of age on mortality. It also provides a more accurate and effective interpretation of the disease evolution, specifically in terms of the cumulative numbers of infected cases and deaths. The proposed Kermack-Mckendrick model is incorporated into a non-linear least-squares optimization curve-fitting problem whose optimized parameters are numerically obtained using the Levenberg-Marquard algorithm. The curve-fitting model’s efficiency is proved by testing the age-stratified model’s performance on three U.S. states: Connecticut, North Dakota, and South Dakota. Our results confirm that splitting the population into different age groups leads to better fitting and forecasting results overall as compared to those achieved by the traditional method, i.e., without age groups. By using comprehensive models that account for age, gender, and ethnicity, regional public health authorities may be able to avoid future epidemics from inflicting more fatalities and establish a public health policy that reduces the burden on the elderly population.
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