Role of farming awareness in crop pest management - A mathematical model.

Control of pest attack is an important aspect in agriculture to obtain healthy crop as well as high yield. Farming awareness is also equally important in pest management. Awareness campaign are made for making people aware of damages due to the pest and protect the crop from pests which ultimately leads to high crop yield. In this article, a mathematical model is proposed to study the effect of awareness among the people in crop pest management using plant biomass, pest and aware population. Pest population is divided into two compartments: susceptible pest and infected pest. We assume that the growth of awareness level is assumed to be proportional to the density of healthy pest in the crop field. Global source such as radio, TV etc. can increase the level of awareness. It is further assumed that aware people will adopt biological control methods like integrated pest management. Susceptible pests are made infected by this process as infected pest are less harmful to crop. Moreover, there may be some time delay in measuring the healthy pests in the crop field i.e. some delay may take place in taking necessary steps while controlling the pest attack. Thus we developed the model incorporating time delay into the system. The existence and the stability criteria of the equilibria are obtained in terms of the basic reproduction number. The Hopf-bifurcation analysis has been done at the endemic equilibrium considering time delay as the bifurcation parameter. Numerical simulations are carried out to justify the analytical results.

Global Dynamics of SARS-CoV-2 Infection with Antibody Response and the Impact of Impulsive Drug Therapy.

Mathematical modeling is crucial to investigating tthe ongoing coronavirus disease 2019 (COVID-19) pandemic. The primary target area of the SARS-CoV-2 virus is epithelial cells in the human lower respiratory tract. During this viral infection, infected cells can activate innate and adaptive immune responses to viral infection. Immune response in COVID-19 infection can lead to longer recovery time and more severe secondary complications. We formulate a micro-level mathematical model by incorporating a saturation term for SARS-CoV-2-infected epithelial cell loss reliant on infected cell levels. Forward and backward bifurcation between disease-free and endemic equilibrium points have been analyzed. Global stability of both disease-free and endemic equilibrium is provided. We have seen that the disease-free equilibrium is globally stable for R0<1, and endemic equilibrium exists and is globally stable for R0>1. Impulsive application of drug dosing has been applied for the treatment of COVID-19 patients. Additionally, the dynamics of the impulsive system are discussed when a patient takes drug holidays. Numerical simulations support the analytical findings and the dynamical regimes in the systems.

Effect of DAA therapy in hepatitis C treatment - an impulsive control approach.

In this article, we have presented a mathematical model to study the dynamics of hepatitis C virus (HCV) disease considering three populations namely the uninfected liver cells, infected liver cells, and HCV with the aim to control the disease. The model possesses two equilibria namely the disease-free steady state and the endemically infected state. There exists a threshold condition (basic reproduction number) that determines the stability of the disease-free equilibrium and the number of the endemic states. We have further introduced impulsive periodic therapy using DAA into the system and studied the efficacy of the DAA therapy for hepatitis C infected patients in terms of a threshold condition. Finally, impulse periodic dosing with varied rate and time interval is adopted for cost effective disease control for finding the proper dose and dosing interval for the control of HCV disease.

Farming awareness based optimum interventions for crop pest control.

We develop a mathematical model, based on a system of ordinary differential equations, to the upshot of farming alertness in crop pest administration, bearing in mind plant biomass, pest, and level of control. Main qualitative analysis of the proposed mathematical model, akin to both pest-free and coexistence equilibrium points and stability analysis, is investigated. We show that all solutions of the model are positive and bounded with initial conditions in a certain significant set. The local stability of pest-free and coexistence equilibria is shown using the Routh-Hurwitz criterion. Moreover, we prove that when a threshold value is less than one, then the pest-free equilibrium is locally asymptotically stable. To get optimum interventions for crop pests, that is, to decrease the number of pests in the crop field, we apply optimal control theory and find the corresponding optimal controls. We establish existence of optimal controls and characterize them using Pontryagin's minimum principle. Finally, we make use of numerical simulations to illustrate the theoretical analysis of the proposed model, with and without control measures.

SARS-CoV-2 infection with lytic and non-lytic immune responses: A fractional order optimal control theoretical study.

In this research article, we establish a fractional-order mathematical model to explore the infections of the coronavirus disease (COVID-19) caused by the novel SARS-CoV-2 virus. We introduce a set of fractional differential equations taking uninfected epithelial cells, infected epithelial cells, SARS-CoV-2 virus, and CTL response cell accounting for the lytic and non-lytic effects of immune responses. We also include the effect of a commonly used antiviral drug in COVID-19 treatment in an optimal control-theoretic approach. The stability of the equilibria of the fractional ordered system using qualitative theory. Numerical simulations are presented using an iterative scheme in Matlab in support of the analytical results.

Dynamics of a delayed plant disease model with Beddington-DeAngelis disease transmission.

In the present research, we study a mathematical model for vector-borne plant disease with the plant resistance to disease and vector crowding effect and propose using Beddington-DeAngelis type disease transmission and incubation delay. Existence and stability of the equilibria have been studied using basic reproduction number ($ \mathcal{R}_0 $). The region of stability of the different equilibria is presented and the impact of important parameters has been discussed. The results obtained suggest that disease transmission depends on the plant resistance and incubation delay. The delay and resistance rate can stabilise the system and plant epidemic can be avoided increasing plant resistance and incubation period.