Leon Arriola - Academia.edu (original) (raw)

Papers by Leon Arriola

Standard mathematical models of epidemiological dynamics are often constructed using ordinary dif... more Standard mathematical models of epidemiological dynamics are often constructed using ordinary differential equations (ODEs). These macroscopic deterministic models yield predictable results which assist researchers to make informed recommendations about public policy decisions. These ODE models are based on heuristic assumptions such as competition, decay, growth, homogeneous/preferential mixing, etc. This research takes a quantum viewpoint of a SI (susceptible and infected) model. The two basic assumptions are fission and successful infection transmission. The quantum approach predicts the same macroscopic behavior as the standard ODE model. However, the quantum approach also predicts that once an infection is introduced into a susceptible population, there is no disease free state. This suggests that the stochastic nature of this quantum model introduces a natural reservoir for the infection.

A quantum/stochastic mechanics formal framework is created in order to describe how the probabili... more A quantum/stochastic mechanics formal framework is created in order to describe how the probabilities of having exactly n single species objects evolve in time. This quantum viewpoint, yields the standard macroscopic ordinary di↵erential equations (ODE) such as the decay, growth and logistic models, etc.. In multiple interactions within a single species, unexpected e↵ects such as quantum tunneling occurs in the probabilities of population. These tunneling e↵ects gives specific predictions of the uncertainty in the population at the macroscopic level. This framework depicts emerging behaviors that are not seen in the current macroscopic epidemiological models such as ordinary/partial di↵erential equation ODE/PDEs.

Modeling an Anthrax Plume: Prioritizing the Delivery of Antibiotics After an Anthrax Bioterrorism... more Modeling an Anthrax Plume: Prioritizing the Delivery of Antibiotics After an Anthrax Bioterrorism Event. Anthrax is a potentially fatal pathogen and could be used as a biological weapon with devastating consequences. In the case of a hypothetical anthrax attack on Maricopa County, the current governmental response plan is inadequate. The standard plume model predicts an unrealistically high number of infections because it assumes that anthrax spores are uniformly distributed over a large area and that all who breathe the spores get infected. It is impossible to deliver the requisite number of antibiotics under that model before the infections progress to an untreatable stage. We develop a fine-grained plume model with GIS data. The model is based on the scalar transport equation and in-host modeling and assumes a drone attack. We obtain the diffusion and advection coefficients of the plume of anthrax spores and use the resultant concentrations along with census data to build a susceptibility model. This model predicts which areas will be the hardest hit and, therefore, what quantity of antibiotics should be delivered based on population density. Wind conditions play a significant role in shaping the plume. We conclude that state and local governments should modify their simplistic Gaussian plume models in order to better serve the people in harm's way.

New Developments in Difference Equations and Applications, 2017

Biochemical and histological studies for nephrotic syndrome were performed in Buffalo/Mna (B/Mna)... more Biochemical and histological studies for nephrotic syndrome were performed in Buffalo/Mna (B/Mna) rats which spontaneously develop thymoma. These rats showed a steroid-resistant nephrotic syndrome characterized by proteinuria, hypoalbuminernia, hyperlipidemia, and slight edema from their early ages, and light microscopical features of focal and segmental glomerular sclerosis in their advanced ages. The proteinuria was ascribed to a remarkable increase in albumin excretion (albuminuria). A continuous rise in urinary protein was observed from 10 to 20 weeks of age and the peak was maintained thereafter. This period almost coincides with the early stage of thymic abnormality as weight change before it is recognized as thymoma.

Mathematical Population Studies, 2021

Stripe rust, also known as yellow rust, is a disease caused by the fungus Puccinia striiformis th... more Stripe rust, also known as yellow rust, is a disease caused by the fungus Puccinia striiformis that affects host crops, primarily barley and wheat. It is the most prevalent strain of wheat rust within North America, and can account for a significant amount of yield loss within a harvest. In order to estimate the dynamic yield loss of a wheat crop infected by stripe rust undergoing fungicide application, a single-host, single-pathogen compartmental model is introduced using a system of nonlinear ordinary differential equations. Two fungicidal effects are considered: preventative and anti-sporulant, which reduce susceptibility and inhibit the further spread of an infection, respectively. The stability conditions associated with the disease-free and endemic equilibria are identified. Numerical simulations are then used to examine the time-dependent behavior of fungicide efficacy and approximate yield loss. Finally, sensitivity indices are calculated to study the impact of fungicide eff...

Standard heuristic mathematical models of population dynamics are often constructed using ordinar... more Standard heuristic mathematical models of population dynamics are often constructed using ordinary differential equations (ODEs). These deterministic models yield pre-dictable results which allow researchers to make informed recommendations on public policy. A common immigration, natural death, and fission ODE model is derived from a quantum mechanics view. This macroscopic ODE predicts that there is only one stable equilibrium point . We therefore presume that as t → ∞, the expected value should be . The quantum framework presented here yields the same standard ODE model, however with very unexpected quantum results, namely . The obvious questions are: why isn’t , why are the probabilities ≈ 0.37, and where is the missing probability of 0.26? The answer lies in quantum tunneling of probabilities. The goal of this paper is to study these tunneling effects that give specific predictions of the uncertainty in the population at the macroscopic level. These quantum effects open the poss...

Open Journal of Ecology, 2012

The purpose of this study is to analyze the population dynamics of loggerhead sea turtles (Carett... more The purpose of this study is to analyze the population dynamics of loggerhead sea turtles (Caretta caretta) affected by localized oil spills. Methods include development of a spatial, stageclassified matrix model parameterized for the following primary loggerhead populations: Gulf of Mexico, western North Atlantic Ocean, and Florida peninsula. Oil spills are simulated deterministically in each population's nesting region, with 1) oil-induced mortality ranging from 25% to 100% and 2) stage classes affected either proportionally or equally. A transient sensitivity analysis was performed to determine the parameters most influential to the population growth rate. Results suggest that increased protection and understanding of young sea turtles found in the Sargasso Sea is essential to the survival of the species. In addition, findings provide insights into the population dynamics of the Atlantic loggerhead turtles and identify conservation measures appropriate in each oil spill case.

... dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions... more ... dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions –Riley, Fraser. 5, Gershengorn HB, Blower SM. Could widespread use of combination antiretroviral therapy eradicate HIV epidemics? Lancet Infect Dis – JX. 2, PW, Castillo-Garsow MA ...

Chagas' disease, caused by certain strains of the parasite Trypanosoma cTUzi, is a vector-bor... more Chagas' disease, caused by certain strains of the parasite Trypanosoma cTUzi, is a vector-borne disease, previously thought to be transmitted solely through the· fecal matter of the triatomine vectors after feeding on the mammalian host. However, this mode of transmission is inefficient in the vectors, Triatoma Sanguisuga a subspecies of the reduviid family, prevalent in the Southeastern United States, due to the significant delay between feeding and defecation times. The prevalence in this region, 40-60% thus necessitates an alternative explanation. The hosts in the sylvatic cycle of this region, including opossums, raccoons, and armadillos, to name ~ few, are known to consume the vectors, although this is a traditionally inefficient way of transmitting the parasite. Recently, vector behavior has been observed to be modified during infection, termed differential behavior, such as feeding more frequently and wandering into broad daylight. The extent to which this affects the disease dynamics warrants investigation and could explain the persistence of T. Gruzi in the sylvatic cycle of this region. To include both modes of transmission, a deterministic model of the disease dynamics has been developed, incorporating both vector-host and predator-prey dynamics. This model is studied to examine how the differential behavior affects the disease dynamics, threshold of infection, and the current endemic equilibrium which is presently the case. Numerical simulations are carried out to verify the theoretical results. We have shown that elevation of consumption of the vector decreases infection levels and could possibly drive the vector population to extinction. Vectors increased vulnerability to predation increases consumption of infected vectors, which decreases prevalence levels but only slightly affects the total population size. Also, increased feeding frequency of the vectors boosts infection levels significantly, and could explain the high prevalence of T. Gruzi in the southeastern United States.

Prion diseases are lethal neurodegenerative disorders such as mad cow disease in bovines, chronic... more Prion diseases are lethal neurodegenerative disorders such as mad cow disease in bovines, chronic wasting disease in cervids, and Creutzfeldt-Jakob disease in humans. They are caused when the prion protein PrPC misfolds into PrPSc, which is capable of inducing further misfolding in healthy PrPC proteins. Recent in vivo experiments show that pharmacological chaperones can temporarily prevent this conversion by binding to PrPC molecules, and thus constitute a possible treatment. A second strategic approach uses interferons to decrease the concentration of PrPSc. In order to study the quantitative effects of these treatments on prion proliferation, we develop a model using a non-linear system of ordinary differential equations. By evaluating their efficacy and potency, we find that interferons act at lower doses and achieve greater prion decay rates. However, there are benefits in combining them with pharmacological chaperones in a two-fold therapy. This research is crucial to guide fu...

Ischaemic Hepatitis (IH) or Hypoxic Hepatitis (HH) also known as centrilobular liver cell necrosi... more Ischaemic Hepatitis (IH) or Hypoxic Hepatitis (HH) also known as centrilobular liver cell necrosis is an acute liver injury characterized by a rapid increase in serum aminotransferase. The liver injury typically results from another underlying medical conditions like cardiac failure, respiratory failure and septic shock in which the liver becomes damaged due to deprivation of either blood or oxygen. IH is a potentially lethal condition which is often preventable if diagnosed properly. Unfortunately, mechanism that causes IH are often not well understood, making it difficult to diagnose or accurately quantify the patterns of related biomakers. In most cases, currently the only way to determine a case of IH (i.e., to diagnose it) is to rule out all other possible conditions for other liver injuries. A better understanding of the liver’s response to IH is necessary to aid in its diagnosis, measurement and improve outcomes. The goal of this study, is to identify mechanisms that can alte...

Proceedings of the Fourth International Conference on Difference Equations, 2000

Journal of Difference Equations and Applications, 1998

... 1 I Hf(x) =- and Hf(y) =- @(x) NY) Furthermore, since H isa global first integral, this impli... more ... 1 I Hf(x) =- and Hf(y) =- @(x) NY) Furthermore, since H isa global first integral, this implies H1(x) = H' (y) f' (x). (10) Substituting Eqs. (9) into Eq. (10) gives ... Page 8. 530 LM ARRIOLA Proof Consider the following calculation: Proof' Taking a Taylor scries of Eq. ...

severe acute respiratory syndrome (SARS) outbreak was based on rapid diagnosis coupled with effec... more severe acute respiratory syndrome (SARS) outbreak was based on rapid diagnosis coupled with effective patient isolation. We used uncertainty and sensitivity analysis of the basic reproductive number R 0 to assess the role that model parameters play in outbreak control. The transmission rate and isolation effectiveness have the largest fractional effect on R 0 . We estimated the distribution of the reproductive number R 0 under perfect isolation conditions. The distribution lies in the interquartile range 0.19-1.08, with a median of 0.49. Even though the median of R 0 is <1, we found that 25% of our R 0 distribution lies at R 0 > 1, even with perfect isolation. This implies the need to simultaneously apply more than one method of control.

Standard mathematical models of epidemiological dynamics are often constructed using ordinary dif... more Standard mathematical models of epidemiological dynamics are often constructed using ordinary differential equations (ODEs). These macroscopic deterministic models yield predictable results which assist researchers to make informed recommendations about public policy decisions. These ODE models are based on heuristic assumptions such as competition, decay, growth, homogeneous/preferential mixing, etc. This research takes a quantum viewpoint of a SI (susceptible and infected) model. The two basic assumptions are fission and successful infection transmission. The quantum approach predicts the same macroscopic behavior as the standard ODE model. However, the quantum approach also predicts that once an infection is introduced into a susceptible population, there is no disease free state. This suggests that the stochastic nature of this quantum model introduces a natural reservoir for the infection.

A quantum/stochastic mechanics formal framework is created in order to describe how the probabili... more A quantum/stochastic mechanics formal framework is created in order to describe how the probabilities of having exactly n single species objects evolve in time. This quantum viewpoint, yields the standard macroscopic ordinary di↵erential equations (ODE) such as the decay, growth and logistic models, etc.. In multiple interactions within a single species, unexpected e↵ects such as quantum tunneling occurs in the probabilities of population. These tunneling e↵ects gives specific predictions of the uncertainty in the population at the macroscopic level. This framework depicts emerging behaviors that are not seen in the current macroscopic epidemiological models such as ordinary/partial di↵erential equation ODE/PDEs.

Modeling an Anthrax Plume: Prioritizing the Delivery of Antibiotics After an Anthrax Bioterrorism... more Modeling an Anthrax Plume: Prioritizing the Delivery of Antibiotics After an Anthrax Bioterrorism Event. Anthrax is a potentially fatal pathogen and could be used as a biological weapon with devastating consequences. In the case of a hypothetical anthrax attack on Maricopa County, the current governmental response plan is inadequate. The standard plume model predicts an unrealistically high number of infections because it assumes that anthrax spores are uniformly distributed over a large area and that all who breathe the spores get infected. It is impossible to deliver the requisite number of antibiotics under that model before the infections progress to an untreatable stage. We develop a fine-grained plume model with GIS data. The model is based on the scalar transport equation and in-host modeling and assumes a drone attack. We obtain the diffusion and advection coefficients of the plume of anthrax spores and use the resultant concentrations along with census data to build a susceptibility model. This model predicts which areas will be the hardest hit and, therefore, what quantity of antibiotics should be delivered based on population density. Wind conditions play a significant role in shaping the plume. We conclude that state and local governments should modify their simplistic Gaussian plume models in order to better serve the people in harm's way.

New Developments in Difference Equations and Applications, 2017

Biochemical and histological studies for nephrotic syndrome were performed in Buffalo/Mna (B/Mna)... more Biochemical and histological studies for nephrotic syndrome were performed in Buffalo/Mna (B/Mna) rats which spontaneously develop thymoma. These rats showed a steroid-resistant nephrotic syndrome characterized by proteinuria, hypoalbuminernia, hyperlipidemia, and slight edema from their early ages, and light microscopical features of focal and segmental glomerular sclerosis in their advanced ages. The proteinuria was ascribed to a remarkable increase in albumin excretion (albuminuria). A continuous rise in urinary protein was observed from 10 to 20 weeks of age and the peak was maintained thereafter. This period almost coincides with the early stage of thymic abnormality as weight change before it is recognized as thymoma.

Mathematical Population Studies, 2021

Stripe rust, also known as yellow rust, is a disease caused by the fungus Puccinia striiformis th... more Stripe rust, also known as yellow rust, is a disease caused by the fungus Puccinia striiformis that affects host crops, primarily barley and wheat. It is the most prevalent strain of wheat rust within North America, and can account for a significant amount of yield loss within a harvest. In order to estimate the dynamic yield loss of a wheat crop infected by stripe rust undergoing fungicide application, a single-host, single-pathogen compartmental model is introduced using a system of nonlinear ordinary differential equations. Two fungicidal effects are considered: preventative and anti-sporulant, which reduce susceptibility and inhibit the further spread of an infection, respectively. The stability conditions associated with the disease-free and endemic equilibria are identified. Numerical simulations are then used to examine the time-dependent behavior of fungicide efficacy and approximate yield loss. Finally, sensitivity indices are calculated to study the impact of fungicide eff...

Standard heuristic mathematical models of population dynamics are often constructed using ordinar... more Standard heuristic mathematical models of population dynamics are often constructed using ordinary differential equations (ODEs). These deterministic models yield pre-dictable results which allow researchers to make informed recommendations on public policy. A common immigration, natural death, and fission ODE model is derived from a quantum mechanics view. This macroscopic ODE predicts that there is only one stable equilibrium point . We therefore presume that as t → ∞, the expected value should be . The quantum framework presented here yields the same standard ODE model, however with very unexpected quantum results, namely . The obvious questions are: why isn’t , why are the probabilities ≈ 0.37, and where is the missing probability of 0.26? The answer lies in quantum tunneling of probabilities. The goal of this paper is to study these tunneling effects that give specific predictions of the uncertainty in the population at the macroscopic level. These quantum effects open the poss...

Open Journal of Ecology, 2012

The purpose of this study is to analyze the population dynamics of loggerhead sea turtles (Carett... more The purpose of this study is to analyze the population dynamics of loggerhead sea turtles (Caretta caretta) affected by localized oil spills. Methods include development of a spatial, stageclassified matrix model parameterized for the following primary loggerhead populations: Gulf of Mexico, western North Atlantic Ocean, and Florida peninsula. Oil spills are simulated deterministically in each population's nesting region, with 1) oil-induced mortality ranging from 25% to 100% and 2) stage classes affected either proportionally or equally. A transient sensitivity analysis was performed to determine the parameters most influential to the population growth rate. Results suggest that increased protection and understanding of young sea turtles found in the Sargasso Sea is essential to the survival of the species. In addition, findings provide insights into the population dynamics of the Atlantic loggerhead turtles and identify conservation measures appropriate in each oil spill case.

... dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions... more ... dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions –Riley, Fraser. 5, Gershengorn HB, Blower SM. Could widespread use of combination antiretroviral therapy eradicate HIV epidemics? Lancet Infect Dis – JX. 2, PW, Castillo-Garsow MA ...

Chagas' disease, caused by certain strains of the parasite Trypanosoma cTUzi, is a vector-bor... more Chagas' disease, caused by certain strains of the parasite Trypanosoma cTUzi, is a vector-borne disease, previously thought to be transmitted solely through the· fecal matter of the triatomine vectors after feeding on the mammalian host. However, this mode of transmission is inefficient in the vectors, Triatoma Sanguisuga a subspecies of the reduviid family, prevalent in the Southeastern United States, due to the significant delay between feeding and defecation times. The prevalence in this region, 40-60% thus necessitates an alternative explanation. The hosts in the sylvatic cycle of this region, including opossums, raccoons, and armadillos, to name ~ few, are known to consume the vectors, although this is a traditionally inefficient way of transmitting the parasite. Recently, vector behavior has been observed to be modified during infection, termed differential behavior, such as feeding more frequently and wandering into broad daylight. The extent to which this affects the disease dynamics warrants investigation and could explain the persistence of T. Gruzi in the sylvatic cycle of this region. To include both modes of transmission, a deterministic model of the disease dynamics has been developed, incorporating both vector-host and predator-prey dynamics. This model is studied to examine how the differential behavior affects the disease dynamics, threshold of infection, and the current endemic equilibrium which is presently the case. Numerical simulations are carried out to verify the theoretical results. We have shown that elevation of consumption of the vector decreases infection levels and could possibly drive the vector population to extinction. Vectors increased vulnerability to predation increases consumption of infected vectors, which decreases prevalence levels but only slightly affects the total population size. Also, increased feeding frequency of the vectors boosts infection levels significantly, and could explain the high prevalence of T. Gruzi in the southeastern United States.

Prion diseases are lethal neurodegenerative disorders such as mad cow disease in bovines, chronic... more Prion diseases are lethal neurodegenerative disorders such as mad cow disease in bovines, chronic wasting disease in cervids, and Creutzfeldt-Jakob disease in humans. They are caused when the prion protein PrPC misfolds into PrPSc, which is capable of inducing further misfolding in healthy PrPC proteins. Recent in vivo experiments show that pharmacological chaperones can temporarily prevent this conversion by binding to PrPC molecules, and thus constitute a possible treatment. A second strategic approach uses interferons to decrease the concentration of PrPSc. In order to study the quantitative effects of these treatments on prion proliferation, we develop a model using a non-linear system of ordinary differential equations. By evaluating their efficacy and potency, we find that interferons act at lower doses and achieve greater prion decay rates. However, there are benefits in combining them with pharmacological chaperones in a two-fold therapy. This research is crucial to guide fu...

Ischaemic Hepatitis (IH) or Hypoxic Hepatitis (HH) also known as centrilobular liver cell necrosi... more Ischaemic Hepatitis (IH) or Hypoxic Hepatitis (HH) also known as centrilobular liver cell necrosis is an acute liver injury characterized by a rapid increase in serum aminotransferase. The liver injury typically results from another underlying medical conditions like cardiac failure, respiratory failure and septic shock in which the liver becomes damaged due to deprivation of either blood or oxygen. IH is a potentially lethal condition which is often preventable if diagnosed properly. Unfortunately, mechanism that causes IH are often not well understood, making it difficult to diagnose or accurately quantify the patterns of related biomakers. In most cases, currently the only way to determine a case of IH (i.e., to diagnose it) is to rule out all other possible conditions for other liver injuries. A better understanding of the liver’s response to IH is necessary to aid in its diagnosis, measurement and improve outcomes. The goal of this study, is to identify mechanisms that can alte...

Proceedings of the Fourth International Conference on Difference Equations, 2000

Journal of Difference Equations and Applications, 1998

... 1 I Hf(x) =- and Hf(y) =- @(x) NY) Furthermore, since H isa global first integral, this impli... more ... 1 I Hf(x) =- and Hf(y) =- @(x) NY) Furthermore, since H isa global first integral, this implies H1(x) = H' (y) f' (x). (10) Substituting Eqs. (9) into Eq. (10) gives ... Page 8. 530 LM ARRIOLA Proof Consider the following calculation: Proof' Taking a Taylor scries of Eq. ...

severe acute respiratory syndrome (SARS) outbreak was based on rapid diagnosis coupled with effec... more severe acute respiratory syndrome (SARS) outbreak was based on rapid diagnosis coupled with effective patient isolation. We used uncertainty and sensitivity analysis of the basic reproductive number R 0 to assess the role that model parameters play in outbreak control. The transmission rate and isolation effectiveness have the largest fractional effect on R 0 . We estimated the distribution of the reproductive number R 0 under perfect isolation conditions. The distribution lies in the interquartile range 0.19-1.08, with a median of 0.49. Even though the median of R 0 is <1, we found that 25% of our R 0 distribution lies at R 0 > 1, even with perfect isolation. This implies the need to simultaneously apply more than one method of control.