Amar Nath Chatterjee

Effect of HAART on CTL Mediated Immune Cells: An Optimal Control Theoretic Approach

Highly active antiretroviral therapy (HAART) reduces the virus load during long term drug therapy. It is observed that during drug therapy virus load sustained in the immune system also CTL is generated due to activation of immune cells and declination of memory CTL which is actually the causal effect of suppression of virus load. Here we extended our work (Roy PK, Chatterjee AN (2010) Lecture notes in engineering and computer science: proceedings of the World Congress on engineering 2010, pp 615–620) and formulate a set of differential equations to study the effect of HAART on immune cells to a HIV infected individuals. We also incorporate in our model of an optimal control strategy during drug treatment, which reduces the infected cell population and increases the uninfected cell population. It is to be mentioned here that the control variable is used as drug dose which introduces in the diseases transmission term. Analytical and numerical study shows that optimal control process can reduces the infected cell population. An objective function is also introduced to minimize the systemic cost of chemotherapy.

Anti-viral drug treatment along with immune activator IL-2: a control-based mathematical approach for HIV infection

Recent development in antiretroviral treatment against HIV can help AIDS patients to fight against HIV. But the question that whether the disease is to be partially or totally eradicated from HIV infected individuals still remains unsolved. Usually, the most effective treatment for the disease is HAART which can only control the disease progression. But as the immune system becomes weak, the patients can not fight against other diseases. Immune cells are activated and proliferated by IL-2 after the identification of antigen. IL-2 production is impaired in HIV positive patients and intermitted administration of immune activator IL-2 together with HAART which is a more effective treatment to fight against the disease. Thus, its expediency is essential and is yet to be explored. In this article we anticipated a mathematical model of the effect of IL-2 together with RTIs therapy in HIV positive patients. Our analytical as well as numerical study shows that the optimal schedule of treatment for best result is to be obtained by systematic drug therapy. But at the last stage of treatment, the infection level raises again due to minimisation of drug dosage. Thus we study the perfect adherence of the drugs and found out if RTIs are taken with sufficient interval then for fixed interval of IL-2 therapy, certain amount of drug dosages may be able to sustain the immune system at pre-infection stage and the infected CD4+T cells are going towards extinction.

A MATHEMATICAL MODEL ON CTL MEDIATED CONTROL OF HIV INFECTION IN A LONG-TERM DRUG THERAPY

Bonhoeffer et al.1 studied the long-term dynamics of HIV drug therapy and virus load dynamics. It is well known that highly active anti retroviral therapy (HAART) can effectively control the HIV replication. It is also well known that reverse transcriptase inhibitors (RTIs) could block new infection and as a result control HIV infection. The positive feedback control on such dynamics plays an important role and CD4+T cells are not only produced from a source but also produced from existing T cells. The present investigation takes into account these factors in the original model of Bonhoeffer et al. The optimal control therapy and the effect of time delay in the positive feedback control function have been investigated. Numerical simulation of the nonlinear model has confirmed our analytical studies.

A Mathematical Approach to Control Cutaneous Leishmaniasis Through Insecticide Spraying

Leishmaniasis is one sort of the vector born diseases, which is transmitted to human or animals by sand-fly bites. Single cell parasite grounds skin infection called Cutaneous Leishmaniasis. In our current research article, we consider a simple mathematical model to analyze the disease dynamics of Cutaneous Leishmaniasis consisting susceptible and infected populations of human and vector. In this article, our focus is to reduce the vector population so that the disease may be controlled. Here we try to explore the effect of insecticide for controlling the vector population through impulsive mode. We have established the efficiency of the insecticide spraying, which contributes a greater impact on the dynamics to move the system towards disease free situation.

Human immunodeficiency virus/acquired immune deficiency syndrome: Using drug from mathematical perceptive.

Entry of acquired immune deficiency syndrome virus into the host immune cell involves the participation of various components of host and viral cell unit. These components may be categorized as attachment of the viral surface envelope protein subunit, gp120, to the CD4(+) receptor and chemokine coreceptors, CCR5 and CXCR4, present on T cell surface. The viral fusion protein, gp41, the second cleaved subunit of Env undergoes reconfiguration and the membrane fusion reaction itself. Since the CD4(+) T cell population is actively involved; the ultimate outcome of human immunodeficiency virus infection is total collapse of the host immune system. Mathematical modeling of the stages in viral membrane protein-host cell receptor-coreceptor interaction and the effect of antibody vaccine on the viral entry into the susceptible host cell has been carried out using as impulsive differential equations. We have studied the effect of antibody vaccination and determined analytically the threshold value of drug dosage and dosing interval for optimum levels of infection. We have also investigated the effect of perfect adherence of drug dose on the immune cell count in extreme cases and observed that systematic drug dosage of the immune cells leads to longer and improved lives.

Immune Cell Response to Negative Feedback Effect on HIV

Alteration in host-virus interaction dynamics during long-term infection by HIV necessitates consideration of inverse relationship between high viral load and density of CTL response leading to dis-regulation of host immunity system. Mathematical modeling introducing negative feedback control mechanism helps in establishment of threshold condition for disease eradication as well as necessary conditions for existence of different equilibria depending on values of basic reproduction ratio. Moreover, IL-2 adjuvenated HAART therapy has been found to be highly cost-effective in recovery of the immunity status in the present mathematical model using negative feedback effect. KeywordsHIV; CD4T Cells; CTL; Negative Feedback Control; HAART; IL-2

The effect of vaccination to dendritic cell and immune cell interaction in HIV disease progression

In this research paper, our main objective is to find out the meticulous role of activated dendritic cells (DCs) during the human immunodeficiency virus (HIV) infection process. DCs play a dual role by enhancing both HIV infection progression, as well as antiviral immune response. To explore the implications of these dual roles, we have formulated our mathematical model and analyzed the model by both analytical and numerical approaches. By using an impulsive differential equation, we have studied the effect of DC-based vaccination. Analytically we have determined the threshold value of drug dosage and dosing interval for optimum levels of infection. We have also investigated the effect of perfect adherence of drug dose on the immune cell count in extreme cases and observed that, systematic drug dose of the immune cells leads to its maximum level.

Reduction of HIV Infection that Includes a Delay with Cure Rate During Long Term Treatment: A Mathematical Study

Progress towards antiviral treatment of HIV infected individual has largely been improved in recent years. From amassed literature it has been observed that antiviral treatment during disease progression can develop CTL and these CTL has an immense importance to control the disease progression. During long term treatment, CD4 and CD8 mediated immune response take part in an effective role against HIV and thus virus load is abridged monotonically or else high virus load leads to have weak immunity. Here we extended our work (Roy PK, Chatterjee AN, Chattopadhyay B (2010) Lecture notes in engineering and computer science: proceedings of the World Congress on engineering 2010:533–538) and further introduced a population model representing long term dynamics of HIV infection in response to available drug therapies considering a cure rate and a discrete time delay in the disease transmission term. We studied the model in different avenue. Our studies reveal that delay in the disease transmission term competes with the killing rate of infected T-cells as well as stimulation rate of CTL. Increasing of delay in this case makes the system progressively unstable and when delay reach to its threshold value, a periodical solution arise through Hopf bifurcation. It is also been observed that increasing value of cure rate could be able to improvise towards stability of the system inspite of delay effect.