Optimal control of treatment in a mathematical model of chronic myelogenous leukemia

Nanda, Seema; Moore, Helen M.; Lenhart, Suzanne

doi:10.1016/j.mbs.2007.05.003

Cited by 98 publications

(70 citation statements)

References 30 publications

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“…The use of optimal control in the context of the VEPART method would allow a more general optimal protocol to be identified, where "optimal" could be defined in many ways; for instance, one could seek to minimize tumor volume at an endpoint, minimize tumor volume over a time horizon, minimize drug concentration, minimize toxicity, minimize some weighted average the above, etc. (37)(38)(39)(40)(41)(42)(43)(44)(45). Further, this optimization can be performed subject to various types of constraints; for instance, toxicity could be introduced as a constraint on the amount of drug that can be administered (37,46).…”

Section: Discussionmentioning

confidence: 99%

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Evaluating optimal therapy robustness by virtual expansion of a sample population, with a case study in cancer immunotherapy

Barish

Ochs

Sontag

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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Cancer is a highly heterogeneous disease, exhibiting spatial and temporal variations that pose challenges for designing robust therapies. Here, we propose the VEPART (Virtual Expansion of Populations for Analyzing Robustness of Therapies) technique as a platform that integrates experimental data, mathematical modeling, and statistical analyses for identifying robust optimal treatment protocols. VEPART begins with time course experimental data for a sample population, and a mathematical model fit to aggregate data from that sample population. Using nonparametric statistics, the sample population is amplified and used to create a large number of virtual populations. At the final step of VEPART, robustness is assessed by identifying and analyzing the optimal therapy (perhaps restricted to a set of clinically realizable protocols) across each virtual population. As proof of concept, we have applied the VEPART method to study the robustness of treatment response in a mouse model of melanoma subject to treatment with immunostimulatory oncolytic viruses and dendritic cell vaccines. Our analysis (i) showed that every scheduling variant of the experimentally used treatment protocol is fragile (nonrobust) and (ii) discovered an alternative region of dosing space (lower oncolytic virus dose, higher dendritic cell dose) for which a robust optimal protocol exists.robust therapies | cancer treatment | mathematical modeling | virotherapy | immunotherapy H eterogeneity is a defining feature of cancer (1, 2). Interpatient heterogeneity manifests clinically in variable disease progression and treatment response between patients with the same diagnosis, whereas intrapatient heterogeneity describes variations that exist between tumor cells in a single patient. Intrapatient heterogeneity can be broken down further into intratumor heterogeneity, intrametastatic heterogeneity, intermetastatic heterogeneity, and temporal heterogeneity (2, 3). Intratumor heterogeneity is evident through the presence of multiple genetic subclones within a primary tumor (2), which have even been shown to exist in spatially distinct regions of the primary tumor (4). Intrametastatic heterogeneity is similar to intratumor heterogeneity, but describes heterogeneity within a single metastatic lesion instead of within the primary tumor (2). Intermetastatic heterogeneity, on the other hand, describes variations in subclones between different metastases in the same patient (2). Finally, temporal heterogeneity is defined as changes that take place in the tumor over time, whether they are a result of genomic instability, natural selection, non-Darwinian evolution, or selective pressures imposed by treatment (4-6). Note that, in each case, heterogeneity need not be genetic but may also be epigenetic, phenotypic, or microenvironmental (2, 7, 8).For decades, cancer patients have been treated using standard of care, meaning they receive the best known treatment that has been deemed as efficacious and safe in epidemiological studies (9). However, in the face of such int...

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Section: Discussionmentioning

confidence: 99%

“…49), and, when the model is too complex to obtain an analytic expression, approximation techniques can be used (see, for instance, ref. 43). When the optimal solution is computationally intractable, heuristic optimization algorithms, including genetic algorithm and simulated annealing can be used, as done in refs.…”

Section: Discussionmentioning

confidence: 99%

Evaluating optimal therapy robustness by virtual expansion of a sample population, with a case study in cancer immunotherapy

Barish

Ochs

Sontag

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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“…For Q ≡ 0 the variable P is bounded above by P ss and therefore the compact setP 0 is positively invariant under Equations (9) and (11). The dynamical system has the following trivial equilibrium solutions in the boundary ofP 0 : (0, 0), (P * , 0) with P * = P ss exp − δ P r P < P ss and (0, E * ) with E * given by…”

Section: Lemmamentioning

confidence: 99%

“…In 2004, Moore and Li [10] published a model of CML dynamics, which accounts for the actions of naive and effector T-cells separately. In [11], this model was analyzed as an optimal control problem. The model presented here first appeared in [12] and models the immune system effects with one compartment, and separates the CML cells into quiescent and proliferating classes.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Systems Properties of a Mathematical Model for the Treatment of CML

Ledzewicz

Moore

2016

Applied Sciences

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A mathematical model for the treatment of chronic myeloid leukemia (CML) through a combination of tyrosine kinase inhibitors and immunomodulatory therapies is analyzed as a dynamical system for the case of constant drug concentrations. Equilibria and their stability are determined and it is shown that, depending on the parameter values, the model exhibits a variety of behaviors which resemble the chronic, accelerated and blast phases typical of the disease. This work provides qualitative insights into the system which should be useful for understanding the interaction between CML and the therapies considered here.

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“…It was also used in a malaria model with genetically modified mosquitoes but without human population [17]. For other applications of optimal control to modelling of infectious diseases [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Global stability analysis and control of leptospirosis

2016

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Abstract:The aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination, treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters' case is analyzed, also calculate the basic reproduction number and investigate the existence and stability of equilibria. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved when the basic reproduction number is less than unity. The model is found to exhibit the existence of multiple endemic equilibria. Furthermore, to assess the relative impact of each of the constant control parameters measures the sensitivity index of the basic reproductive number to the model's parameters are calculated. In the time-dependent constant control case, Pontryagin's Maximum Principle is used to derive necessary conditions for the optimal control of the disease. The cost-effectiveness analysis is carried out by first of all using ANOVA to check on the mean costs. Then followed by Incremental Cost-Effectiveness Ratio (ICER) for all the possible combinations of the disease control measures. Our results revealed that the most cost-effective strategy for the control of leptospirosis is the combination of the vaccination and treatment of infective livestocks. Though the combinations of all control measures is also effective, however, this strategy is not cost-effective and so too costly. Therefore, more efforts from policy makers on vaccination and treatment of infectives livestocks regime would go a long way to combat the disease epidemic.

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Optimal control of treatment in a mathematical model of chronic myelogenous leukemia

Cited by 98 publications

References 30 publications

Evaluating optimal therapy robustness by virtual expansion of a sample population, with a case study in cancer immunotherapy

Evaluating optimal therapy robustness by virtual expansion of a sample population, with a case study in cancer immunotherapy

Dynamical Systems Properties of a Mathematical Model for the Treatment of CML

Global stability analysis and control of leptospirosis

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