Background: The genetic control strategies of vector borne diseases includes the replacement of a vector population by disease-refractory mosquitoes and the release of mosquitoes with a gene to control the vector's reproduction rates. Wolbachia are common intracellular bacteria that are found in arthropods and nematodes. Wolbachia infected male mosquitos have been used in different experimental trials around the world to suppress the target population of Aedes aegypti and this genetic control strategy has proved to be a promising alternative to other treatment strategies. Due to certain limitations, the successful application of this strategy is still awaited. Methods: Mathematical frame work for Wolbachia induced genetic control strategy has been developed in this article. With the aid of Artificial Intelligence (Al) tools, accurate parametric values are depicted. For the first time, the model is well synchronized with the experimental findings. The model is comprised of the generalized varying coefficient and multiple mating rates between infected and uninfected compartments of Aedes aegypti dengue to forecast the disease control. Results: Two mathematical models are developed in this article to demonstrate different mating rates of the genetic control strategy. The important parameters and time varying coefficients are well demonstrated with the aid of numerical computations. The resulting thresholds and forecasting may prove to be a useful tool for future experimental studies. Conclusions: From our analysis, we have concluded that the genetic control strategy is a promising technique and the role of Wolbachia infected male mosquitos, in genetic control strategies, can be better interpreted in an inexpensive manner with the aid of a theoretical model.

Calcitonin, a potent hypocalcemic hormone, plays a vital role in inhibiting osteoclastic activities and suppressing bone removal. The physiological characteristics of calcitonin have long been discussed, along a few recommending calcitonin as a vestigial hormone. The basis for this article is to discuss the role of low and high levels of calcitonin in normal and osteoprotic bone turnover. The effect of calcitonin on the receptor activator of nuclear factor kappa-ligand and osteoclasts has been demonstrated using numerical simulations. This behavior recommends that treatment of osteoporosis via calcitonin does not provide the required upshots. For effectiveness calcitonin must be advised along with a combined therapy like aspirin which agrees with the experimental results available in the literature.

The dynamics of the osteoporotic bone turnover is studied in this paper with the aid of stability analysis of the associated mathematical model. Osteoporosis, which is a common bone disorder, is studied in this papper in detail with an emphasis on the relative threshold values. We examine the expository signaling among the bone cells named osteoclast and osteoblast. Main functioning of osteoblasts is bone formation, whereas osteoclasts are bone removal cells. Mathematical framework for osteoporotic bone turnover comprising of the communication between osteoclasts and osteoblasts has been presented to exhibit the conditions for stability in bone turnover. The percentage ratios of the population of osteoblasts/osteoclasts have been determined via numerical simulations. The remedial upshots of targeting osteoporotic cells participating in such process are examined. From our analysis we have conclude that the role of external agents in treating the diseased bone can be better interpreted with the aid of a theoretical model.

Background: Osteoporosis is a chronic metabolic disease characterized by an imbalance of bone resorption and formation, leading to bone fragility and increased susceptibility to fracture. Parathyroid hormone is approved therapy for the treatment of osteoporosis.

Methods: The intermittent therapy of parathyroid hormone requires accurate administration. Meta-analysis is conducted to draw a clear picture of the impact of intermittent therapy and dose rates relative to time, on the osteoporotic patients. A novel mathematical model is presented in this article synchronised with the parametric values, depicted from meta-analysis.

Findings: Results obtained from the mathematical model are in close agreement with the results obtained from the clinical trials. The model can be used to forecast the drug potency and dosage rates, to control the vicious cycle of osteoporosis.

Interpretations: The intermittent administration of parathyroid hormone, rather than the continuous administration, is more effective, furthermore it is also concluded that a mathematical model, linked with the extensive literature of clinical trials, using meta-analysis can help in drug administration and future clinical studies of drug development.