Intracellular and immune-response delays effects on the interaction between tumor cells, oncolytic viruses and the immune system

Paper presented at the 4th Strathmore International Mathematics Conference (SIMC 2017), 19 - 23 June 2017, Strathmore University, Nairobi, Kenya.Background: Oncolytic viruses are used as a form of cancer treatment since they lyse the tumor cells whilst leaving normal cells largely unharmed. The oncolytic effect depends on both the viral replication ability as well as the type of immune response induced by the said replication. One major challenge to this therapy is the delays that can occur during viral replication combined with a fast immune response. Aim: We therefore aim at investigating the possible trade-offs between the tumor cells, oncolytic viruses and the immune systems with particular focus will be on the simultaneous effects of these two delays. Methods: We extend recently published mathematical models on viro therapy by taking into account the simultaneous effects of the two delays and considering various forms of virus cell infections; namely mass-action, frequency- dependent and Holing-type. We investigate the models’ stability and bifurcation behaviour and then fit them to data. Consequently, carry out numerical simulations to explore various scenarios of model treatment Results: We derived an explicit formula for the trade off between the two delays that leads to tumor eradication. One of the main findings is the occurrence of delay-induced Hopf bifurcation, indicative of tumor relapse.University of Pretoria,University of Stellenbosch, Stellenbosch, South Afric

A model of HIV infection with two viral strains and cytotoxic T-lymphocyte response under structured treatment interruptions

CITATION: Ouifki, R., Welte, A., & Pretorius, C. 2008. A model of HIV infection with two viral strains and cytotoxic T-lymphocyte response under structured treatment interruptions. South African Journal of Science, 104:216-219.The original publication is available at https://www.sajs.co.zaWe develop a model of HIV infection with two viral strains, a cytotoxic T-lymphocyte (CTL) response and structured treatment interruptions. We derive new analytical relations characterizing the dynamics between drug-sensitive and drug-resistant variants of the virus, and the strength of the CTL response.Publisher's versio

Modeling the Control of Trypanosomiasis Using Trypanocides or Insecticide-Treated Livestock

In Uganda, cattle are an important reservoir for Trypanosoma brucei rhodesiense, the causative agent of Rhodesian sleeping sickness (human African trypanosomiasis), transmitted by tsetse flies Glossina fuscipes fuscipes, which feed on cattle, humans, and wild vertebrates, particularly monitor lizards. Trypanosomiasis can be controlled by treating livestock with trypanocides or insecticide – killing parasites or vectors, respectively. Mathematical modeling of trypanosomiasis was used to compare the impact of drug- and insecticide-based interventions on R0 with varying densities of cattle, humans and wild hosts. Intervention impact changes with the number of cattle treated and the proportion of bloodmeals tsetse take from cattle. R0 was always reduced more by treating cattle with insecticide rather than trypanocides. In the absence of wild hosts, the model suggests that control of sleeping sickness (R0<1) could be achieved by treating ∼65% of cattle with trypanocides or ∼20% with insecticide. Required coverage increases as wild mammals provide increasing proportion of tsetse bloodmeals: if 60% of non-human bloodmeals are from wild hosts then all cattle have to be treated with insecticide. Conversely, it is reduced if lizards, which do not harbor trypanosomes, are important hosts and/or if insecticides are used at a scale where tsetse numbers decline

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. Williams, C. Dye, Infectious disease persistence when transmission varies seasonally, Math. Biosci. 145 (1997) 77]. We show that apart from a few exceptional parameter values, the epidemic threshold depends not only on the mean contact rate, but also on the amplitude of fluctuations

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, R0, and investigate the existence and stability of equilibria. The system is found to exhibit backward bifurcation. The implication of this occurrence is that the classical epidemiological requirement for effective eradication of malaria, R0 &lt; 1, is no longer sufficient, even though necessary. Secondly, by using optimal control theory we derive the conditions under which it is optimal to eradicate the disease and examine the impact of a possible combined vaccination and treatment strategy on the disease transmission. When eradication is impossible, we derive the necessary conditions for optimal control of the disease using Pontryagin's Maximum Principle. The results obtained from the numerical simulations of the model show that a possible vaccination combined with effective treatment regime would reduce the spread of the disease appreciably. Crown Copyright © 2011.Article in Pres

A general model for mortality in adult tsetse (Glossina spp.)

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A Treatise of Biological Models

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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. The impact of antiretroviral therapy on the incidence of HIV is unclear and depends on the extent to which it reduces sexual transmission. However, our analysis suggests that it will greatly reduce the TB notification rate

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

The original publication is available at http://www.plosone.orgWe 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. This is in contrast with earlier methods for estimating incidence from prevalence data, which work with aggregated data, and the aggregated effect of demographic and epidemiological rates over the time interval between prevalence surveys. Numerical simulation of HIV epidemics, under the presumption of known excess mortality due to infection, shows improved control of bias and variance, compared to previous methods. Our analysis motivates for a) effort to be applied to obtain accurate estimates of excess mortality rates as a function of age and time among HIV infected individuals and b) use of individual level rather than aggregated data in order to estimate HIV incidence rates at times between two prevalence surveys.Publisher's versio

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. We used the model to describe both the growth dynamics in our experiments of firefly luciferase-expressing Hep3B tumor xenografts and the effects of the immune response during the MSCs-based virotherapy. We further employed it to explore the conceptual clinical feasibility, particularly, in evaluating the relative significance of potential immune promotive/suppressive mechanisms induced by MSCs loaded with oncolytic viruses. We were able to delineate conditions which may significantly contribute to the success or failure of MSC-based virotherapy as well as generate new hypotheses. In fact, one of the most impactful outcomes shown by this investigation, not inferred from the experiments alone, was the initially counter-intuitive fact that using tumor-promoting MSCs as carriers is not only helpful but necessary in achieving tumor control. Considering the fact that it is still currently a controversial debate whether MSCs exert a pro- or anti-tumor action, mathematical models such as this one help to quantitatively predict the consequences of using MSCs for delivering virotherapeutic agents in vivo. Taken together, our results show that MSC-mediated systemic delivery of oncolytic viruses is a promising strategy for achieving synergistic anti-tumor efficacy with improved safety profiles