A Role of Effector CD T Cells Against Circulating Tumor Cells Cloaked with Platelets: Insights from a Mathematical Model.

Cancer metastasis accounts for a majority of cancer-related deaths worldwide. Metastasis occurs when the primary tumor sheds cells into the blood and lymphatic circulation, thereby becoming circulating tumor cells (CTCs) that transverse through the circulatory system, extravasate the circulation and establish a secondary distant tumor. Accumulating evidence suggests that circulating effector CD T cells are able to recognize and attack arrested or extravasating CTCs, but this important antitumoral effect remains largely undefined.

A combination therapy of oncolytic viruses and chimeric antigen receptor T cells: a mathematical model proof-of-concept.

Combining chimeric antigen receptor T (CAR-T) cells with oncolytic viruses (OVs) has recently emerged as a promising treatment approach in preclinical studies that aim to alleviate some of the barriers faced by CAR-T cell therapy. In this study, we address by means of mathematical modeling the main question of whether a single dose or multiple sequential doses of CAR-T cells during the OVs therapy can have a synergetic effect on tumor reduction. To that end, we propose an ordinary differential equations-based model with virus-induced synergism to investigate potential effects of different regimes that could result in efficacious combination therapy against tumor cell populations.

Mathematical model for the estrogen paradox in breast cancer treatment.

Estrogen is known to stimulate the growth of breast cancer, but is also effective in treating the disease. This is referred to as the"estrogen paradox". Furthermore, short-term treatment with estrogen can successfully eliminate breast cancer, whereas long-term treatment can cause cancer recurrence.

Natural Killer Cells Recruitment in Oncolytic Virotherapy: A Mathematical Model.

In this paper, we investigate how natural killer (NK) cell recruitment to the tumor microenvironment (TME) affects oncolytic virotherapy. NK cells play a major role against viral infections. They are, however, known to induce early viral clearance of oncolytic viruses, which hinders the overall efficacy of oncolytic virotherapy.

Mesenchymal stem cells used as carrier cells of oncolytic adenovirus results in enhanced oncolytic virotherapy.

Mesenchymal stem cells (MSCs) loaded with oncolytic viruses are presently being investigated as a new modality of advanced/metastatic tumors treatment and enhancement of virotherapy. MSCs can, however, either promote or suppress tumor growth. To address the critical question of how MSCs loaded with oncolytic viruses affect virotherapy outcomes and tumor growth patterns in a tumor microenvironment, we developed and analyzed an integrated mathematical-experimental model.

Assessing the role of human mobility on malaria transmission.

South Sudan accounts for a large proportion of all annual malaria cases in Africa. In recent years, the country has witnessed an unprecedented number of people on the move, refugees, internally displaced people, people who have returned to their counties or areas of origin, stateless people and other populations of concern, posing challenges to malaria control. Thus, one can claim that human mobility is one of the contributing factors to the resurgence of malaria.

Assessing the role of climate factors on malaria transmission dynamics in South Sudan.

Malaria is endemic in South Sudan and it is one of the most severe diseases in the war-torn nation. There has been much concern about whether the severity of its transmission might depend upon climatic conditions that are related to the reproduction of the single-cell parasite attaching to female mosquitoes, especially in high altitude areas. The country experiences two different climatic conditions; namely one tropical and the other hot and semi-arid.

On a three-stage structured model for the dynamics of malaria transmission with human treatment, adult vector demographics and one aquatic stage.

A modelling framework that describes the dynamics of populations of the female Anopheles sp mosquitoes is used to develop and analyse a deterministic ordinary differential equation model for dynamics and transmission of malaria amongst humans and varying mosquito populations. The framework includes a characterization of the gonotrophic cycle of the female mosquito. The epidemiological model also captures a novel feature whereby treated human's blood can become mosquitocidal to the questing mosquitoes upon the successful ingestion of the treated human's blood.

Enhancement of chemotherapy using oncolytic virotherapy: Mathematical and optimal control analysis.

Oncolytic virotherapy has been emerging as a promising novel cancer treatment which may be further combined with the existing therapeutic modalities to enhance their effects. To investigate how virotherapy could enhance chemotherapy, we propose an ODE based mathematical model describing the interactions between tumour cells, the immune response, and a treatment combination with chemotherapy and oncolytic viruses. Stability analysis of the model with constant chemotherapy treatment rates shows that without any form of treatment, a tumour would grow to its maximum size.

Mathematical modeling of bone marrow - peripheral blood dynamics in the disease state based on current emerging paradigms, part II.

The cancer stem cell hypothesis has gained currency in recent times but concerns remain about its scientific foundations because of significant gaps that exist between research findings and comprehensive knowledge about cancer stem cells (CSCs). In this light, a mathematical model that considers hematopoietic dynamics in the diseased state of the bone marrow and peripheral blood is proposed and used to address findings about CSCs. The ensuing model, resulting from a modification and refinement of a recent model, develops out of the position that mathematical models of CSC development, that are few at this time, are needed to provide insightful underpinnings for biomedical findings about CSCs as the CSC idea gains traction.

Modelling the effect of bednet coverage on malaria transmission in South Sudan.

A campaign for malaria control, using Long Lasting Insecticide Nets (LLINs) was launched in South Sudan in 2009. The success of such a campaign often depends upon adequate available resources and reliable surveillance data which help officials understand existing infections. An optimal allocation of resources for malaria control at a sub-national scale is therefore paramount to the success of efforts to reduce malaria prevalence.

Oncolytic potency and reduced virus tumor-specificity in oncolytic virotherapy. A mathematical modelling approach.

In the present paper, we address by means of mathematical modeling the following main question: How can oncolytic virus infection of some normal cells in the vicinity of tumor cells enhance oncolytic virotherapy? We formulate a mathematical model describing the interactions between the oncolytic virus, the tumor cells, the normal cells, and the antitumoral and antiviral immune responses. The model consists of a system of delay differential equations with one (discrete) delay. We derive the model's basic reproductive number within tumor and normal cell populations and use their ratio as a metric for virus tumor-specificity.

Mathematical model of tumor-immune surveillance.

We present a novel mathematical model involving various immune cell populations and tumor cell populations. The model describes how tumor cells evolve and survive the brief encounter with the immune system mediated by natural killer (NK) cells and the activated CD8(+) cytotoxic T lymphocytes (CTLs). The model is composed of ordinary differential equations describing the interactions between these important immune lymphocytes and various tumor cell populations.

Mathematical modeling of bone marrow--peripheral blood dynamics in the disease state based on current emerging paradigms, part I.

Stemming from current emerging paradigms related to the cancer stem cell hypothesis, an existing mathematical model is expanded and used to study cell interaction dynamics in the bone marrow and peripheral blood. The proposed mathematical model is described by a system of nonlinear differential equations with delay, to quantify the dynamics in abnormal hematopoiesis. The steady states of the model are analytically and numerically obtained.

Modelling the long-term impacts on affected children of adult HIV: benefits, challenges and a possible approach.

We outline the benefits, challenges and possible approaches to developing mathematical models that could be used to estimate the magnitude of negative consequences of adult HIV infection for children. Adult HIV infection can lead to numerous negative consequences for dependent children, including depression, anxiety, withdrawal from school and early sexual debut, among others. For advocacy and planning purposes, it is important to highlight and consider as many of these as possible.

Modelling the use of insecticide-treated cattle to control tsetse and Trypanosoma brucei rhodesiense in a multi-host population.

We present a mathematical model for the transmission of Trypanosoma brucei rhodesiense by tsetse vectors to a multi-host population. To control tsetse and T. b.

Optimal control strategies and cost-effectiveness analysis of a malaria model.

The aim of this paper is to investigate the effectiveness and cost-effectiveness of three malaria preventive measures (use of treated bednets, spray of insecticides and a possible treatment of infective humans that blocks transmission to mosquitoes). For this, we consider a mathematical model for the transmission dynamics of the disease that includes these measures. We first consider the constant control parameters' case, we calculate the basic reproduction number and investigate the existence and stability of equilibria; the model is found to exhibit backward bifurcation.

A general HIV incidence inference scheme based on likelihood of individual level data and a population renewal equation.

We derive a new method to estimate the age specific incidence of an infection with a differential mortality, using individual level infection status data from successive surveys. The method consists of a) an SI-type model to express the incidence rate in terms of the prevalence and its derivatives as well as the difference in mortality rate, and b) a maximum likelihood approach to estimate the prevalence and its derivatives. Estimates can in principle be obtained for any chosen age and time, and no particular assumptions are made about the epidemiological or demographic context.

Modeling the control of trypanosomiasis using trypanocides or insecticide-treated livestock.

Background: In Uganda, Rhodesian sleeping sickness, caused by Trypanosoma brucei rhodesiense, and animal trypanosomiasis caused by T. vivax and T. congolense, are being controlled by treating cattle with trypanocides and/or insecticides.

Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity.

We derive and analyse a deterministic model for the transmission of malaria disease with mass action form of infection. Firstly, we calculate the basic reproduction number, R(0), and investigate the existence and stability of equilibria. The system is found to exhibit backward bifurcation.

Stability analysis of a model for HIV infection with RTI and three intracellular delays.

We consider a model of HIV-1 infection with a reverse transcriptase inhibitor (RTI) therapy and three delays: the first delay is defined as the time from the virus entry into the target cell to the reverse transcriptase step, the second delay represents the time from the virus entry to the production of new viruses and the third delay corresponds to the time necessary for a newly produced virus to become infectious. We analyse the stability of the steady states and determine a threshold value for the first delay at which the system exhibits a Hopf bifurcation. This might explain the clinically observed transient elevated viremia called viral blips.

Modeling the joint epidemics of TB and HIV in a South African township.

We present a simple mathematical model with six compartments for the interaction between HIV and TB epidemics. Using data from a township near Cape Town, South Africa, where the prevalence of HIV is above 20% and where the TB notification rate is close to 2,000 per 100,000 per year, we estimate some of the model parameters and study how various control measures might change the course of these epidemics. Condom promotion, increased TB detection and TB preventive therapy have a clear positive effect.

Growth rate and basic reproduction number for population models with a simple periodic factor.

For continuous-time population models with a periodic factor which is sinusoidal, both the growth rate and the basic reproduction number are shown to be the largest roots of simple equations involving continued fractions. As an example, we reconsider an SEIS model with a fixed latent period, an exponentially distributed infectious period and a sinusoidal contact rate studied in Williams and Dye [B.G.