Fractional Modeling of Cancer with Mixed Therapies

BACKGROUND

Cancer is the biggest cause of mortality globally, with approximately 10 million fatalities expected by 2020, or about one in every six deaths. Breast, lung, colon, rectum, and prostate cancers are the most prevalent types of cancer.

METHODS

In this work, fractional modeling is presented which describes the dynamics of cancer treatment with mixed therapies (immunotherapy and chemotherapy). Mathematical models of cancer treatment are important to understand the dynamical behavior of the disease. Fractional models are studied considering immunotherapy and chemotherapy to control cancer growth at the level of cell populations. The models consist of the system of fractional differential equations (FDEs). Fractional term is defined by Caputo fractional derivative. The models are solved numerically by using Adams-Bashforth-Moulton method.

RESULTS

For all fractional models the reasonable range of fractional order is between β = 0.6 and β = 0.9. The equilibrium points and stability analysis are presented. Moreover, positivity and boundedness of the solution are proved. Furthermore, a graphical representation of cancerous cells, immunotherapy and chemotherapy is presented to understand the behaviour of cancer treatment.

CONCLUSIONS

At the end, a curve fitting procedure is presented which may help medical practitioners to treat cancer patients.

Effects of different acetylsalicylic acid doses on body organs, histopathology, and serum biochemical parameters in broiler birds

The poultry industry suffers from various diseases or stresses. In poultry, apart from being antipyretic, acetylsalicylic acid (ASA) is widely used to cope with different issues including heat stress, and respiratory and digestive orders. This study evaluated the beneficial and toxic effects of ASA at different dose levels in broiler birds. To evaluate these toxic and beneficial effects it is necessary to examine the physical and serum biochemical parameters as well as the histopathological changes with tissue sections taken from broiler birds under experimental trial. This study was conducted on 60 one-day-old broiler chicks purchased from a local market in Faisalabad. Chicks were reared for the first 14 days under similar conditions. On the 15th day, birds were randomly divided into 4 groups (1-4) with 15 birds in each group. Group 4 was kept as control, while groups 1, 2, and 3 were treated with ASA at the dose of 300, 600, and 1200 mg/L of drinking water for 21 days. There were 3 samplings performed at 21, 28, and 35 days post-treatment. The live body weight and carcass weight were noted on each sampling. All the visceral organs were recorded for gross pathological changes. The serum samples were collected for biochemical evaluation. Histopathology of all the visceral organs was performed to observe the microscopic changes. A significant (P<0.05) increase in live body weight at a 300mg/L dose was noted after the first 2 samplings. A significant (P<0.05) increase in the relative organ weight was recorded at 1200 mg/L. The groups treated with ASA 600 and 1200 mg/L showed increased (P<0.05) AST, ALT, and creatinine levels from that of the control group. The group treated with 1200 mg/L of ASA showed increased (P<0.05) urea, serum total protein, and albumin level in all the samplings. Histopathological changes revealed swollen hepatocytes, increased sinusoidal spaces in the liver, congestion and abnormal glomerular spaces in the kidney, congestion and alveolar disruption in the lungs, and generation of villi and cellular degeneration in the intestine in a high-dose group. The study concluded that ASA at a low dose can be used for a long time in broilers and has a growth promontory role, while high-level doses cause hepatorenal toxicity.