The role of immune cells in resistance to oncolytic viral therapy.

Resistance to treatment poses a major challenge for cancer therapy, and oncoviral treatment encounters the issue of viral resistance as well. In this investigation, we introduce deterministic differential equation models to explore the effect of resistance on oncolytic viral therapy. Specifically, we classify tumor cells into resistant, sensitive, or infected with respect to oncolytic viruses for our analysis.

Effects of prey refuge and predator cooperation on a predator-prey system.

We develop and investigate a discrete-time predator-prey model with cooperative hunting among predators and a spatial prey refuge. The system can exhibit two positive equilibria if the magnitude of cooperation is large and the maximal reproduction number of predators is less than one. In such a scenario, the predator population may exhibit a strong Allee effect, and therefore the predator may survive if its density is above the threshold.

Exploring the Interactions of Oncolytic Viral Therapy and Immunotherapy of Anti-CTLA-4 for Malignant Melanoma Mice Model.

Oncolytic ability to direct target and lyse tumor cells makes oncolytic virus therapy (OVT) a promising approach to treating cancer. Despite its therapeutic potential to stimulate anti-tumor immune responses, it also has immunosuppressive effects. The efficacy of OVTs as monotherapies can be enhanced by appropriate adjuvant therapy such as anti-CTLA-4.

Bistability in a model of tumor-immune system interactions with an oncolytic viral therapy.

A mathematical model of tumor-immune system interactions with an oncolytic virus therapy for which the immune system plays a twofold role against cancer cells is derived. The immune cells can kill cancer cells but can also eliminate viruses from the therapy. In addition, immune cells can either be stimulated to proliferate or be impaired to reduce their growth by tumor cells.

The effect of demographic and environmental variability on disease outbreak for a dengue model with a seasonally varying vector population.

Seasonal changes in temperature, humidity, and rainfall affect vector survival and emergence of mosquitoes and thus impact the dynamics of vector-borne disease outbreaks. Recent studies of deterministic and stochastic epidemic models with periodic environments have shown that the average basic reproduction number is not sufficient to predict an outbreak. We extend these studies to time-nonhomogeneous stochastic dengue models with demographic variability wherein the adult vectors emerge from the larval stage vary periodically.

Modeling Pancreatic Cancer Dynamics with Immunotherapy.

We develop a mathematical model of pancreatic cancer that includes pancreatic cancer cells, pancreatic stellate cells, effector cells and tumor-promoting and tumor-suppressing cytokines to investigate the effects of immunotherapies on patient survival. The model is first validated using the survival data of two clinical trials. Local sensitivity analysis of the parameters indicates there exists a critical activation rate of pro-tumor cytokines beyond which the cancer can be eradicated if four adoptive transfers of immune cells are applied.

Cooperative hunting in a discrete predator-prey system II.

We investigate a discrete-time predator-prey system with cooperative hunting in the predators proposed by Chow et al. by determining local stability of the interior steady states analytically in certain parameter regimes. The system can have either zero, one or two interior steady states.

Discrete-time host-parasitoid models with pest control.

We propose a simple discrete-time host-parasitoid model to investigate the impact of external input of parasitoids upon the host-parasitoid interactions. It is proved that the input of the external parasitoids can eventually eliminate the host population if it is above a threshold and it also decreases the host population level in the unique interior equilibrium. It can simplify the host-parasitoid dynamics when the host population practices contest competition.

Cannibalism in discrete-time predator-prey systems.

In this study, we propose and investigate a two-stage population model with cannibalism. It is shown that cannibalism can destabilize and lower the magnitude of the interior steady state. However, it is proved that cannibalism has no effect on the persistence of the population.

Dynamics of an age-structured population with Allee effects and harvesting.

We propose a discrete-time, age-structured population model to study the impact of Allee effects and harvesting. It is assumed that survival probabilities from one age class to the next are constants and fertility rate is a function of weighted total population size. Global extinction is certain if the maximal growth rate of the population is less than one.

Discrete host-parasitoid models with Allee effects and age structure in the host.

We study a stage-structured single species population model with Allee effects. The asymptotic dynamics of the model depend on the maximal growth rate of the population as well as on its initial population size. We also investigate two models of host-parasitoid interaction with stage-structure and Allee effects in the host.

Dynamics of discrete-time larch budmoth population models.

The larch budmoth (LBM) population in the Swiss Alps is well known for its periodic outbreaks and regular oscillations over several centuries. The ecological mechanisms that drive these oscillations, however, have not been unambiguously identified, although a number of hypotheses have been proposed. In this article, we investigate several LBM resulting from these different ecological hypotheses.

Continuous-time predator-prey models with parasites.

We study a deterministic continuous-time predator-prey model with parasites, where the prey population is the intermediate host for the parasites. It is assumed that the parasites can affect the behavior of the predator-prey interaction due to infection. The asymptotic dynamics of the system are investigated.

Plankton-toxin interaction with a variable input nutrient.

A simple model of phytoplankton-zooplankton interaction with a periodic input nutrient is presented. The model is then used to study a nutrient-plankton interaction with a toxic substance that inhibits the growth rate of plankton populations. The effects of the toxin upon the existence, magnitude, and stability of the periodic solutions are discussed.

A three-stage discrete-time population model: continuous versus seasonal reproduction.

We consider a three-stage discrete-time population model with density-dependent survivorship and time-dependent reproduction. We provide stability analysis for two types of birth mechanisms: continuous and seasonal. We show that when birth is continuous there exists a unique globally stable interior equilibrium provided that the inherent net reproductive number is greater than unity.

Mathematical epidemiology of hiv/aids in cuba during the period 1986-2000.

We study a stage-structured single species population model with Allee effects. The asymptotic dynamics of the model depend on the maximal growth rate of the population as well as on its initial population size. We also investigate two models of host-parasitoid interaction with stage-structure and Allee effects in the host.