Critical observation of WHO recommended multidrug therapy on the disease leprosy through mathematical study

Leprosy is a skin disease and it is characterized by a disorder of the peripheral nervous system which occurs due to the infection of Schwann cells. In this research article, we have formulated a four-dimensional ODE-based mathematical model which consists of the densities of healthy Schwann cells, infected Schwann cells, M. leprae bacteria, and the concentration of multidrug therapy (MDT). This work primarily aims on exploring the dynamical changes and interrelations of the system cell populations during the disease progression. Also, evaluating a critical value of the drug efficacy rate of MDT remains our key focus in this article so that a safe drug dose regimen for leprosy can be framed more effectively and realistically. We have examined the stability scenario of different equilibria and the occurrence of Hopf-bifurcation for the densities of our system cell populations with respect to the drug efficacy rate of MDT to gain insight on the precise impact of the efficiency rate on both the infected Schwann cell and the bacterial populations. Also, a necessary transversality condition for the occurrence of the bifurcation has been established. Our analytical and numerical investigations in this research work precisely explores that the process of demyelination, nerve regeneration, and infection of the healthy Schwann cells are the three most crucial factors in the leprosy pathogenesis and to control the M. leprae-induced infection of Schwann cells successfully, a more flexible version of MDT regime with efficacy rate varying in the range η∈(0.025,0.059) for 100-120 days in PB cases and 300 days in MB cases obtained in this research article should be applied. All of our analytical outcomes have been verified through numerical simulations and compared with some existing clinical findings.

The influence of vaccination on the control of JE with a standard incidence rate of mosquitoes, pigs and humans

In this article, a nonlinear mathematical model used for the impact of vaccination on the control of infectious disease, Japanese encephalitis with a standard incidence rate of mosquitoes, pigs and humans has been planned and analyzed. During the modeling process, it is expected that the disease spreads only due to get in touch with the susceptible and infected class only. It is also assumed that due to the effect of vaccination, the total human population forms a separate class and avoids contact with the infection. The dynamical behaviors of the system have been explored by using the stability theory of differential equations and numerical simulations. The local and global stability of the system for both equilibrium states under certain conditions has been studied. We have set up a threshold condition in the language of the vaccine-induced reproduction number R ( α 1 ) , which is fewer than unity, the disease dies in the absence of the infected population, otherwise, the infection remains in the population. Furthermore, it is found that vaccine coverage has a substantial effect on the basic reproduction number. Also, by continuous efforts and effectiveness of vaccine coverage, the disease can be eradicated. It is also found a more sensitive parameter for the transmission of Japanese encephalitis virus by using sensitivity analysis. In addition, numerical results are used to investigate the effect of some parameters happening the control of JE infection, for justification of analytical results.

How can HPV-induced cervical cancer be controlled by a combination of drug therapy? A mathematical study

This paper deals with a control strategy through impulsive drug treatment to study the effect of Chemotherapy and CTL activator drug to eradicate the cervical cancer. CTL kills the HPV infected cells and helps to prevent cervical cancer. Dendritic cell (DC) plays a crucial role in this disease dynamics in enhancing the activity of CTL. To explore these effects, we have formulated a mathematical model consisting of six compartments to describe the interactions between HPV and three classes of cervical cells (susceptible, infected, cancerous), with DC and CTL. Calculating the basic reproduction ratio, we find that there exists a disease-free equilibrium point and an endemic equilibrium point. In our study, we have shown that though DC enhances the activity of CTL, it is not sufficient to eradicate the disease totally. How we could restrict the cancer development by using double drug in an impulsive way with particular drug doses is being reflected in the results. To illustrate our results, numerical simulations are also presented.