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University of Utah
"Mathematical modeling of regulatory T cell mechanisms in experimental autoimmune encephalomyelitis"
The study of T cell mediation of the adaptive immune response during multiple sclerosis (MS) can lead to development of treatments and therapies for this demyelinating disease. A prominent mouse model for MS is experimental autoimmune encephalomyelitis (EAE). EAE is mediated by populations of CD4+ T cells: regulatory T cells (Tregs), which prevent the immune system from attacking self proteins, and other effector T cells (Teffs) that are activated against myelin oligodendrocyte glycoprotein. The disease can result in either relapsing remitting or constant symptoms which can be either mild, medium, or severe for extended periods of time. These differences in severity are influenced by the numbers of precursor T cells, and by the initial dose of antigen in the system. We have developed an ODE model of Treg and Teff populations over time that incorporates immune regulatory mechanisms in order to make testable predictions about EAE disease course. This model exhibits three stable steady states (a state with all cell populations near 0, an intermediate state, and a high Teff state) for realistic parameter values, and biologically plausible initial conditions lie in the basins of attraction for all three stable steady states. Thus this model can explain biologically observed disease outcomes, and mathematical analysis can provide specific, biologically testable predictions about the cause of each outcome.
University of Tennessee, Knoxville
"A Mathematical Framework to Augment the Q-MARSH Score in the Diagnosis of Celiac Disease"
This work provides a mathematical framework to better understand the effects of immune activation on gut health. This mathematical model uses a system of ordinary differential equations to track changes in villus and crypt cell densities as well as intraepithelial lymphocytes to better understand the dynamics of small intestinal destruction. The model will be used to investigate and analyze various theories behind the progression of celiac disease by focusing on understanding the dynamics of the small intestine in situations mirroring healthy function, celiac disease, and refractory celiac disease. By doing so, we can assist in further quantifying and augmenting diagnostic measures and investigate potential therapies to mitigate the negative effects of celiac disease.
"Evaluating the role of memory B and T cells during secondary dengue infection"
Dengue viruses (DENV) are transmitted by Aedes mosquito bite that causes mild dengue fever (DF) or dengue severe (DS). There are more than 50 million DF cases each year. There are four serotypes of dengue virus, DENV1 - DENV4, which has only 20%-35% divergence to each other. The cross-reactive immune response contributes to increased disease severity following heterologous infections. In general, primary infections result in either asymptomatic or mild DF disease. Secondary infections with different serotypes are either cleared or can induce dengue severe. Mechanisms responsible for the severity of secondary dengue infections are not entirely understood. One of them is the cross-reactive antibodies can enhance the disease, which is called antibody-dependent enhancement (ADE). ADE is explained as follows. When a person is first infected with one dengue strain, the host produces neutralizing antibodies specific against this strain. After the primary infection is eliminated, due to the immunological memory plasma cells produce specific antibodies for the first dengue strain, which persist in the body. If this person is secondly infected with a different dengue strain, antibodies from the primary infection bind the second virus but do not neutralize it. Besides that, macrophages recruited to clear the immune complex; they internalize this non-neutralized virus and become infected in the process of clearance. There is evidence that Fc receptors, which are proteins on the surface of some cells like macrophages and monocytes that bind to the antigen-antibody complex, might facilitate viral entry in cells and increase dengue viral replication. We propose a mathematical model composed of seven non-linear differential equations to describe the ADE phenomenon in secondary dengue infection, considering that partial cross-immunity takes place due to primary dengue infection. We consider that the immune system has not yet performed a complete response against the secondary infection. During this time, the circulating antibodies against the primary virus can facilitate heterologous secondary infection. Here we consider target cells - macrophages, a specific antibody against the primary infection, memory B cells, memory T cells, the formation of the immune complex, and dengue virus. We focus on the role of memory B and T cells during the secondary dengue infection. It is possible to determine the basic reproduction number parameter, R0, and B and T cell cloning during the secondary dengue infection. In the impossibility of cloning these cells, we find that if R0<1, there will be no possibility of ADE's appearance. However, when we introduced the possibility of memory B cell cloning, we saw that an infectious state could arise even when the basal reproduction number is less than one. Analogously, when we analyzed only the effect of memory T cell cloning, we saw that ADE's emergence is not possible. These cells only act to decrease viral concentration.
"Stochastic time-inhomogeneous HIV dynamics following treatment suspension"
Antiretroviral therapy (ART) effectively controls HIV infection, suppressing HIV viral loads. Typically suspension of therapy is rapidly followed by rebound of viral loads to high, pre-therapy levels. However, recent studies suggest that approximately 10% of study participants undergoing ART treatment interruption show viral rebound only months or years after interruption, while some may be controlling infection permanently. We will first define what we mean by viral rebound and describe model-supported hypotheses of HIV viral rebound and control. We will then describe our branching process model to gain broad insight into these post-treatment dynamics. Specifically we provide theory that explains both short- and long-term viral rebounds, and post-treatment control, via a branching process with time-inhomogeneous rates, validated with data from Li et al. (2016). We will discuss the associated biological interpretation and implications. Finally, treatment interruption clinical trials are used to test efficacy of drug or other interventions to delay or prevent viral rebound; we will show how our modeling can be used to guide and inform such clinical trials.
Josephine Naa Ayeley Tetteh
Frankfurt Institute of Advanced Studies
"Switching strategy for mitigation against bacterial resistance"
The control of drug resistant infections has become difficult as there are little to no new drugs being discovered. Using control engineering approaches, we develop strategies aimed at minimizing the appearance of drug-resistant pathogens within the host. With a mathematical model based on a two-strain bacterial population, a switching strategy can be found to ensure the stability of the eradication equilibrium based on the use of a Lyapunov function. Our numerical simulations support the use of this switching strategy for mitigation against bacterial resistance.
Utrecht University, Theoretical Biology & Bioinformatics
"A theoretical model for the natural course of HIV infection in infants"
HIV infection in young children differs markedly from that in adults: (i) children have higher viral loads (VL), (ii) their set point VL is not much lower than the peak VL, and (iii) children tend to progress faster towards AIDS. We use classic simple ODE models for HIV infection to study which differences between adults and children can explain these observations. We test whether (1) increased viral replication rates, (2) increased target cell population, (3) increased production of target cell population, and/or (4) delayed/weakened immune responses in children can explain the data. Whenever possible, we feed the model with parameter estimates from untreated paediatric data available from datasets within the EPIICAL project (https://www.epiical.org/). This data allowed us to reject hypothesis (1): the viral replication rate seems to be decreased in infants compared to adults. Thus, a mathematical model might help to get a better understanding of paediatric HIV infections and provides a foundation to simulate current cure and prevention strategies.
Juliano Ferrari Gianlupi
"Multiscale spatiotemporal modeling of acute primary viral infection and immune response in epithelial tissues"
Simulations of tissue-specific effects of primary acute viral infections like COVID-19 are essential for understanding differences in disease outcomes and optimizing therapeutic interventions. We present a multiscale model and simulation of an epithelial tissue infected by a virus, a simplified cellular immune response and viral and immune-induced tissue damage. The model exhibits basic patterns of infection dynamics: widespread infection, slowed infection, recurrence, containment and clearance. Inhibition of viral internalization and faster immune-cell recruitment promote containment of infection. Fast viral internalization and slower immune response lead to uncontrolled spread of infection. Because antiviral drugs can have side effects at high doses and show reduced clinical effectiveness when given later during the course of infection, we studied the effects on infection progression of both treatment potency (which combines drug effectiveness and dosage) and time-of-first treatment after infection. Simulation of a drug which reduces the replication rate of viral RNA shows that even a low potency therapy greatly decreases the total tissue damage and virus burden when given near the beginning of infection. However, even a high potency therapy rapidly loses effectiveness when given later near the time of peak viral load in the untreated case. Many combinations of dosage and treatment time lead to stochastic outcomes, with some simulation replicas showing clearance or control of the virus (treatment success), while others show rapid infection of all epithelial cells in the simulated tissue subregion (treatment failure). This switch between a regime of consistent treatment success and failure occurs as the time of treatment increases. However, stochastic variations in viral spread mean that high potency treatments at late times are occasionally effective. The model is open-source and modular, allowing rapid development and extension of its components by groups working in parallel. We're extending the model through already calibrated ODE models to have more biological meaningful behaviors. ODE models can be calibrated in a straightforward manner, however they don't contain information about space which is meaningful. As ODE based models are not spatial they need to be spatialized in some manner for our use, we've developed a method to generate spatial models from ODE models and have the spatial model recover the ODE predicted population behaviors. While the spatialized model shows differences, we recuperate the overall ODE model behavior, and we are exploring how spatiality itself causes those differences. With this work we will bring forth more ways in which ODE models can be useful, e.g., having their overall behavior inform and predict how the COVID infection spreads through the lungs.
Masud M A
Pusan National University, Pusan, South Korea
"Title to be determined."
Dengue is one of the most prevalent vector-borne diseases with no medical treatment for cure. Sometimes, dengue infection develops hemorrhagic shock which is life-threatening and urges emergency medical support. At this stage, the infusion of intravenous fluid of an adequate amount is a must for the survival of the patient. However, unsystematic fluid infusion may lead to fluid overload and bring adverse outcomes. With an aim to quantify required amount of fluid infusion I extend minimal within-host dengue model to incorporate plasma dynamics as well as the intravenous fluid infusion. I experimented type I and type II functional response to model the impact of cytokines on plasma leakage, where Type II model showed better fit with published data. Optimal control theory has been used to establish the existence of a time-dependent optimal fluid infusion strategy. The forward-backward sweep method was used to solve the model numerically and deduce the optimal fluid infusion rate. The optimal strategy recommends fluid infusion initiation at a slower rate, which should be kept increasing for about 24 hours. Then the rate should be decreased gradually. The infusion requires about 4000 ml to 5000 ml within an interval of 2 to 3 days. Delay of a few hours in fluid support after initiation of leakage could be compensated. But a delay of more than one day could be life-threatening.
University of Tennessee, Knoxville
"A minority of liver-resident CD8 T cells searching for Plasmodium-infected hepatocytes demonstrate difficult-to-detect attraction"
Malaria is a disease caused by parasites from genus Plasmodium that causes over 200 million infections and kills over 400,000 people every year. A critical step of malaria infection is when mosquito-injected sporozoites travel to the liver and form liver stages. Several malaria vaccine candidates induce high levels of Plasmodium-specific CD8 T cells which are able to eliminate all liver stages, thus providing sterilizing immunity against the disease. However, how CD8 T cells locate the site of infection is not well understood. We generated and analyzed data from intravital microscopy experiments in mice in which movement of T cells relative to the liver stage was recorded in several different settings. To detect attraction of T cells towards the infection site, we developed a novel metric based on the Von Mises-Fisher (VMF) distribution, which is more powerful than previously used metrics. We found that the majority (85-95%) of Plasmodium-specific CD8 T cells and T cells of irrelevant specificity did not display attraction towards the parasite when the parasite was not found by T cells, which was consistent with the random search for infection. In contrast, when some T cells located the parasite and formed a cluster, a minority of other T cells did display strong attraction towards the infection. Interestingly, the speed of T cell movement (and small turning angles) correlated with the bias of T cell movement towards the infection site (while many other parameters do not), suggesting that a deeper understanding of what determines the speed of T cell movement in the liver may help with improving T cell vaccine efficacy. Stochastic simulations suggested that a small movement bias towards the parasite dramatically reduces the number of CD8 T cells needed for the complete elimination of all malaria liver stages, and yet, to detect such attraction by individual cells requires extremely long imaging experiments which may not be currently feasible. Our developed methodology can be allied to detect weak attraction of moving agents in other conditions.
Hosted by eSMB2020 Follow
Virtual conference of the Society for Mathematical Biology, 2020.