Fahad Al Basir

Fractional-order model of the disease Psoriasis: A control based mathematical approach

Autoimmune diseases are generated through irregular immune response of the human body. Psoriasis is one type of autoimmune chronic skin diseases that is differentiated by T-Cells mediated hyper-proliferation of epidermal Keratinocytes. Dendritic Cells and CD8+ T-Cells have a significant role for the occurrence of this disease. In this paper, the authors have developed a mathematical model of Psoriasis involving CD4+ T-Cells, Dendritic Cells, CD8+ T-Cells and Keratinocyte cell populations using the fractional differential equations with the effect of Cytokine release to observe the impact of memory on the cell-biological system. Using fractional calculus, the authors try to explore the suppressed memory, associated with the cell-biological system and to locate the position of Keratinocyte cell population as fractional derivative possess non-local property. Thus, the dynamics of Psoriasis can be predicted in a better way using fractional differential equations rather than its corresponding integer order model. Finally, the authors introduce drug into the system to obstruct the interaction between CD4+ T-Cells and Keratinocytes to restrict the disease Psoriasis. The authors derive the Euler-Lagrange conditions for the optimality of the drug induced system. Numerical simulations are made through Matlab by developing iterative schemes.

Effect of Glycerol Kinetics and Mass Transfer During Enzymatic Biodiesel Production from Jatropha Oil

Enzymatic transesterification for biodiesel production from Jatropha curcas oil has gained favorable attention due to high selectivity and mild reaction conditions. Beside this, mass transfer limitation is a barrier for maximum biodiesel yield. Stirring and enzyme regulates the mass transfer in transesterification of Jatropha oil. Moreover, the effects of enzyme and stirring have been considered by many researchers but the effect of glycerol was neglected while studying mass transfer kinetics. In this article, the aim is to study the mass transfer resistance due to immiscibility of alcohol and oil as well as to reduce glycerol inhibition to increase enzyme activity by formulating a mathematical model. Optimal control approach has been applied on mixing intensity to avoid mass transfer limitations in both the phases which minimizes the glycerol effect and gives cost effective production of biodiesel. Simulation results of the model system are in a good agreement with experimental results available in the literature.

The generalization of an n-patch model for Leishmaniasis

Leishmaniasis is a vector borne disease, which is caused by a protozoan parasite. Infected female sandflies \textit{(Phlebotomine sp.)} are responsible for such disease transmission. People can carry some species of Leishmania for long periods and the incubation period for Leishmaniasis may be few weeks or several months. Migration depends on host immunological status also. Leishmaniasis is endemic globally in ninety eight countries. Spread of the disease is intensely dependent on migration of the disease among human and vector between various regions or countries. Here, we formulate an

Effects of Temperature and Stirring on Mass Transfer to Maximize Biodiesel Production from Jatropha curcas Oil: A Mathematical Study

n

Effect of mass transfer kinetics for maximum production of biodiesel from Jatropha Curcas oil: A mathematical approach

-patch mathematical model (such patches can be some states, regions or countries) considering each patch have susceptible, infected human as well as susceptible and infected vector population. We have derived basic reproduction ratio for each patch as well as the general basic reproduction ratio for the system and shown that there exists a disease-free equilibrium that is locally asymptotically stable. Further, we study the system analytically and numerically when the migration between each patch of individual class of humans and vector effects the spreading of the disease. We also established the results taking into account for different number of patches for

Studies on biodiesel production from Jatropha Curcas oil using chemical and biochemical methods – A mathematical approach

n=2

Effects of awareness program for controlling mosaic disease in Jatropha curcas plantations

. Our result reveals that the movement of human and vector from each patch to another patch plays an important role for spreading of the disease. https://doi.org/10.28919/cmbn/3361

Effect of awareness programs in controlling the disease HIV/AIDS: an optimal control theoretic approach

Biodiesel, the most promising renewable and alternative energy, is produced through transesterification of vegetable oils. One of the most cost effective sources of biodiesel is Jatropha curcas oil. Transesterification of Jatropha oil depends significantly on reaction parameters such as reaction time, temperature, molar ratio, catalyst amount, and stirrer speed. Among these parameters temperature and stirring have noteworthy effect on mass transfer. In this research article, we have shown the simultaneous effect of temperature and stirring on mass transfer by considering a mathematical model. The optimal profiles of temperature and stirring are determined as a combined parameter, for which maximum biodiesel can be obtained. Further, we have shown that this pair exists and is unique for the optimality of the system.