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Background Vaccine allocation is a national concern especially for countries such as the Philippines that have limited resources in acquiring COVID-19 vaccines. As such, certain groups are suggested to be prioritized for vaccination to protect the most vulnerable before vaccinating others. Objective The study aims to determine an optimal and equitable allocation of COVID-19 vaccines in the Philippines that will minimize the projected number of additional COVID-19 deaths while satisfying the priority groups for immediate vaccination. Methods In this study, a linear programming model is formulated to determine an allocation of vaccines such that COVID-19 deaths are minimized while the prioritization framework set by the government is satisfied. Data used were collected up to November 2020. Total vaccine supply, vaccine effectiveness, vaccine cost, and projected deaths are analyzed. Results of the model are also compared to other allocation approaches. Results Results of the model show that a vaccine coverage of around 60–70% of the population can be enough for a community with limited supplies, and an increase in vaccine supply is beneficial if the initial coverage is less than the specified target range. Additionally, among the vaccines considered in the study, the one with 89.9% effectiveness and a 183 Philippine peso price per dose projected the lowest number of deaths. Compared with other model variations and common allocation approaches, the model has achieved both an optimal and equitable allocation. Conclusions Having a 100% coverage for vaccination with a 100% effectiveness rate of vaccine is ideal for all countries. However, some countries have limited resources. Therefore, the results of our study can be used by policymakers to determine an optimal and equitable distribution of COVID-19 vaccines for a country/community. Supplementary Information The online version contains supplementary material available at 10.1007/s40258-021-00667-z.

Parasite aggregation is a frequently occurring phenomenon where majority of the parasites accumulate in the smaller fraction of the host population while many individual hosts have low parasite load. One of the mechanisms of parasite aggregation is heterogeneity in the host-parasite interaction. Here, we aim to develop and analyze a spatiotemporal model to explain the details of this mechanism. We construct an agent-based simulation involving fish hosts that forage on zooplanktons harboring macroparasites. In this study, we restrict our simulations to a lentic ecosystem, i.e., still, closed freshwater environment. Our simulations show that (i) the initial sizes of the population of both the fish and zooplanktons have minimal effect on the aggregation of parasites; (ii) increasing the probabilities of reproduction of both fish and zooplankton lead to parasite aggregation among fish hosts; and (iii) aggregation occurs either by decreasing the size of the infection area or increasing the size of the zooplankton-free area in the lentic ecosystem. Our results can be used to provide insights and visualization of the underlying processes leading to aggregation. These can also be used to aid experimentalists in determining the statistical distribution of parasites in hosts for disease prevention and control.

The study of cooperation has been extensively studied in game theory. Especially, two-player two-strategy games have been categorized according to their equilibrium strategies and fully analysed. Recently, a grand unified game covering all types of two-player two-strategy games, i.e., the weightlifting game, was proposed. In the present study, we extend this two-player weightlifting game into an [Formula: see text]-player game. We investigate the conditions for pure strategy Nash equilibria and for Pareto optimal strategies, expressed in terms of the success probability and benefit-to-cost ratio of the weightlifting game. We also present a general characterization of [Formula: see text]-player games in terms of the proposed game. In terms of a concrete example, we present diagrams showing how the game category varies depending on the benefit-to-cost ratio. As a general rule, cooperation becomes difficult to achieve as group size increases because the success probability of weightlifting saturates towards unity. The present study provides insights into achieving behavioural cooperation in a large group by means of a cost-benefit analysis.

Background Responses of subnational government units are crucial in the containment of the spread of pathogens in a country. To mitigate the impact of the COVID-19 pandemic, the Philippine national government through its Inter-Agency Task Force on Emerging Infectious Diseases outlined different quarantine measures wherein each level has a corresponding degree of rigidity from keeping only the essential businesses open to allowing all establishments to operate at a certain capacity. Other measures also involve prohibiting individuals at a certain age bracket from going outside of their homes. The local government units (LGUs)–municipalities and provinces–can adopt any of these measures depending on the extent of the pandemic in their locality. The purpose is to keep the number of infections and mortality at bay while minimizing the economic impact of the pandemic. Some LGUs have demonstrated a remarkable response to the COVID-19 pandemic. The purpose of this study is to identify notable non-pharmaceutical interventions of these outlying LGUs in the country using quantitative methods. Methods Data were taken from public databases such as Philippine Department of Health, Philippine Statistics Authority Census, and Google Community Mobility Reports. These are normalized using Z-transform. For each locality, infection and mortality data (dataset Y) were compared to the economic, health, and demographic data (dataset X) using Euclidean metric d=(x−y)2, where x∈X and y∈Y. If a data pair (x,y) exceeds, by two standard deviations, the mean of the Euclidean metric values between the sets X and Y, the pair is assumed to be a ‘good’ outlier. Results Our results showed that cluster of cities and provinces in Central Luzon (Region III), CALABARZON (Region IV-A), the National Capital Region (NCR), and Central Visayas (Region VII) are the ‘good’ outliers with respect to factors such as working population, population density, ICU beds, doctors on quarantine, number of frontliners and gross regional domestic product. Among metropolitan cities, Davao was a ‘good’ outlier with respect to demographic factors. Conclusions Strict border control, early implementation of lockdowns, establishment of quarantine facilities, effective communication to the public, and monitoring efforts were the defining factors that helped these LGUs curtail the harm that was brought by the pandemic. If these policies are to be standardized, it would help any country’s preparedness for future health emergencies.

In response to the need to derive empirical data on the status of pollinators, we have developed a protocol to assess the pollinator population in managed and natural ecosystems, especially in Asia where there is no harmonized initiative for pollination research. This protocol is helpful in assessing organic and non-organic farming since pollinator persistence can be an indicator of good and sustainable practices. The three important steps in the protocol are planning, implementation of the survey, and computation of indices. In the planning step, experts rank and classify the pollinator hotspots in various ecosystem types based on the seasonality and likelihood of having high number of flowers and pollinators. Two-stage sampling and mapping of each hotspots are designed. The number of sample hotspots is computed according to sampling precision and confidence levels assigned per class per ecosystem type. In each sample hotspot, sample survey sites are randomly selected according to the agreed sampling precision and confidence levels. In the second step, for orchard or agroecosystem, a grid map with 100 m2 divisions is surveyed. For natural vegetation, survey sites are randomly selected according to the location of pollinator nesting sites. All sampling surveys are conducted during the blooming period of the plants, with consideration of the peak of anthesis, because this is the period when the pollinators are actively foraging, the pollen viability is high, and the nectar secretion is at its peak. Moreover, a template is created to compute for diversity measures and our proposed pollination matching measures (P-to-P ratio and index).

Mathematical models of production and consumption are useful in devising policies for sustainable management of renewable resources. Analysis of simple but not too naive models of resource dynamics can provide initial or supplementary insights in formulating comprehensive policies. In these models, density-dependence of resources, nonlinearities in consumption schemes, and uncertainties in parameters are essential to be considered to account for the temporal complex dynamics of the resource. Here, we study minimal ordinary differential equation models which are compartmentalized into production and consumption functions. We propose density-dependent production functions with Allee and crowding effects, and nonlinear consumption functions that are hyperbolic and sigmoidal. We identify scenarios where our results differ from the existing classical logistic models with linear consumption scheme, and determine quantitative conditions leading to sustainable consumption. Our results propose conditions in which consumption efforts will not cause eventual depletion of the resource under specific assumptions. Furthermore, we analyze how delay and stochasticity affect the derived sustainability conditions. Our results can be used as initial input in formulating strategies to properly manage renewable resources, especially in the absence of models requiring extensive data availability.

The development of cooperation in human societies is a major unsolved problem in biological and social sciences. Extensive studies in game theory have shown that cooperative behaviour can evolve only under very limited conditions or with additional complexities, such as spatial structure. Non-trivial two-person games are categorized into three types of games, namely, the prisoner's dilemma game, the chicken game and the stag hunt game. Recently, the weight-lifting game has been shown to cover all five games depending on the success probability of weight lifting, which include the above three games and two trivial cases (all cooperation and all defection; conventionally not distinguished as separate classes). Here, we introduce the concept of the environmental value of a society. Cultural development and deterioration are represented by changes in this probability. We discuss cultural evolution in human societies and the biological communities of living systems.

The number of COVID-19 cases is continuously increasing in different countries (as of March 2020) including the Philippines. It is estimated that the basic reproductive number of COVID-19 is around 1.5 to 4. The basic reproductive number characterizes the average number of persons that a primary case can directly infect in a population full of susceptible individuals. However, there can be superspreaders that can infect more than this estimated basic reproductive number. In this study, we formulate a conceptual mathematical model on the transmission dynamics of COVID-19 between the frontliners and the general public. We assume that the general public has a reproductive number between 1.5 to 4, and frontliners (e.g. healthcare workers, customer service and retail personnel, food service crews, and transport or delivery workers) have a higher reproduction number. Our simulations show that both the frontliners and the general public should be protected or resilient against the disease. Protecting only the frontliners will not result in flattening the epidemic curve. Protecting only the general public may flatten the epidemic curve but the infection risk faced by the frontliners is still high, which may eventually affect their work. Our simple model does not consider all factors involved in COVID-19 transmission in a community, but the insights from our model results remind us of the importance of community effort in controlling the transmission of the disease. All in all, the take-home message is that everyone in the community, whether a frontliner or not, should be protected or should implement preventive measures to avoid being infected.

Vaccine allocation is a national concern especially for countries such as the Philippines that have limited resources in acquiring COVID-19 vaccines. As such, certain groups are suggested to be prioritized for vaccination to protect the most vulnerable before vaccinating others. Our model suggests an allocation of vaccines such that COVID-19 deaths are minimized while the prioritization framework is satisfied. Results of the model show that a vaccine coverage of at least 50 to 70% of the population can be enough for a community with limited supplies, and an increase in vaccine supply is beneficial if initial coverage is less than the specified target range. Also, among the vaccines considered in the study, the one with 89.9% effectiveness and has a 183 Philippine peso (Php) price per dose projected the least number of deaths. Compared to other model variations and common allocation approaches, the model has achieved both an optimal and equitable allocation. This will be helpful for policymakers in determining a vaccine distribution for a resource-constrained community.

We formulate an agent-based model and a compartmental model (SEIR) that simulate the spread of a respiratory infectious disease between two neighboring cities. We consider preventive measures such as implementation of social distancing and lockdown in a city, as well as the effect of protective gears or practices. The chance of travelling to another city and within the city during lockdown, and initial percentage of exposed and infected individuals on both cities influence the increase in the number of newly-infected individuals on both models. Our simulations show that (i) increase in exposed individuals results in increase in number of new infections, hence the need for increased testing-isolation efforts; (ii) protection level of 75-100% effectiveness impedes disease transmission; (iii) travelling within city or to other city can be an option given that strict preventive measures (e.g., non-pharmaceutical interventions) are observed; and (iv) the ideal set-up for neighboring cities is to implement lockdown when there is high risk of disease local transmission while individuals observe social distancing, maximizing protective measures, and isolating those that are exposed. The results of the agent-based and compartmental models show similar qualitative dynamics; the differences are due to different spatio-temporal heterogeneity and stochasticity. These models can aid decision makers in designing infectious disease-related policies to protect individuals while continuing population movement.

Mass transportation is one of the areas that are badly hit by respiratory infectious disease outbreaks due to moderate to high exposure risk to pathogens brought about by the interaction among commuters. Here, we formulate agent-based models that simulate the spread of a respiratory infectious disease in a train wagon in the Manila Light Rail Transit System, and in a 49-seater public utility bus. We consider preventive measures such as implementation of social distancing, and limitation of interaction or movement among the commuters to investigate how these measures will inhibit disease transmission. We also consider the effect of protective gears and practices, crowd density, and prevalence of disease in the community on the possible number of newly-infected individuals. Our simulations show that (i) individuals must have protection with more than 90% effectiveness to inhibit transmission of the disease; (ii) social or physical distancing by more than 1m distance reduces the risk of being infected; (iii) minimizing movement or interaction with other passengers reduces the risk of transmission by 50%; (iv) passenger capacity should be less than 10-50% of the maximum seating capacity to reduce the number of infections depending on the level of imposed social distancing and passenger interaction; (v) vehicles with greater number of occupied seating capacity generate higher number of infections but vehicles with smaller dimensions have faster disease transmissions; and (vi) ideal set-up for a 24-seater train wagon (49-seater bus) is to allow a maximum of 12 (24) passengers, with little to no interaction among passengers, with social distancing of more than 1m distance apart, and each person has a protection with 90% effectiveness as much as possible. These results can aid policy makers in determining optimal strategies to minimize infections while maintaining transportation services during pandemics or disease outbreaks.

IntroductionAs of early December 2019, COVID-19, a disease induced by SARS-COV-2, has started spreading, originated in Wuhan, China, and now on, have infected more than 2 million individuals throughout the world.PurposeThis study aimed to nowcast the COVID-19 outbreak throughout Iran and to forecast the trends of the disease spreading in the upcoming month.MethodsThe cumulative incidence and fatality data were extracted from official reports of the National Ministry of Health and Medical Educations of Iran. To formulate the outbreak dynamics, six phenomenological models, as well as a modified mechanistic Susciptible-Exposed-Infectious-Recovered (SEIR) model, were implemented. The models were calibrated with the integrated data, and trends of the epidemic in Iran was then forecasted for the next month.ResultsThe final outbreak size calculated by the best fitted phenomenological models was estimated to be in the range of 68,486 to 118,923 cases; however, the calibrated SEIR model estimated that the outbreak would rage again, starting from April 26. Moreover, projected by the mechanistic model, approximately half of the infections have undergone undetected.ConclusionAlthough the advanced phenomenological models perfectly fitted the data, they are incapable of applying behavioral aspects of the outbreak and hence, are not reliable enough for authorities’ decision adoptions. In contrast, the mechanistic SEIR model alarms that the COVID-19 outbreak in Iran may peak for the second time, consequent to lifting the control measures. This implies that the government may implement a more granular decision making to control the outbreak.

Testing is crucial for early detection, isolation, and treatment of coronavirus disease (COVID-19)-infected individuals. However, in resource-constrained countries such as the Philippines, test kits have limited availability. As of 12 April 2020, there are 11 testing centers in the country that have been accredited by the Department of Health (DOH) to conduct testing. In this paper, we determine the optimal percentage allocation of COVID-19 test kits among accredited testing centers in the Philippines that gives an equitable chance to all infected individuals to be tested. Heterogeneity in testing accessibility, population density of municipalities, and the capacity of testing facilities are included in the model. Our results showed that the range of optimal allocation per testing center are: Research Institute for Tropical Medicine (4.17% −6.34%), San Lazaro Hospital (14.65% −24.03%), University of the Philippines-National Institutes of Health (16.25% −44.80%), Lung Center of the Philippines (15.8% −26.40%), Baguio General Hospital Medical Center (0.58% −0.76%), The Medical City, Pasig City (5.96% −25.51%), St. Luke’s Medical Center, Quezon City (1.09% −6.70%), Bicol Public Health Laboratory (0.06% −0.08%), Western Visayas Medical Center (0.71% −4.52%), Vicente Sotto Memorial Medical Center (1.02% −2.61%), and Southern Philippines Medical Center (≈0.01%). If there will be changes in the number of testing centers, our model can still be used to modify the test kit allocation. Our results can serve as a guide to the authorities in distributing the COVID-19 test kits. These can also be used to determine the capacity of testing centers and the effects of increasing its number. The model can also be used for proposing additional number and location of new testing centers.

The number of confirmed COVID-19 cases admitted in hospitals is continuously increasing in the Philippines. Frontline health care workers are faced with imminent risks of getting infected. In this study, we formulate a theoretical model to calculate the risk of being infected in health care facilities considering the following factors: the average number of encounters with a suspected COVID-19 patient per hour; interaction time for each encounter; work shift duration or exposure time; crowd density, which may depend on the amount of space available in a given location; and availability and effectiveness of protective gears and facilities provided for the frontline health care workers. Based on the simulation results, a set of risk assessment criteria is proposed to classify risks as ‘low’, ‘moderate’, or ‘high’. We recommend the following: (i) decrease the rate of patient encounter per frontline health care worker, e.g., maximum of three encounters per hour in a 12-hour work shift duration; (ii) decrease the interaction time between the frontline health care worker and the patients, e.g., less than 40 minutes for the whole day; (iii) increase the clean and safe space for social distancing, e.g., maximum of 10% crowd density, and if possible, implement compartmentalization of patients; and/or (iv) provide effective protective gears and facilities, e.g., 95% effective, that the frontline health care workers can use during their shift. Moreover, the formulated model can be used for other similar scenarios, such as identifying infection risk in public transportation, school classroom settings, offices, and mass gatherings.

Insects are the most diverse organisms on earth consisting of more than 900 thousand species. However, only few of them are considered agricultural pests. Life history traits such as high fecundity, fast population growth, and high dispersal ability have been used to characterize agricultural pest insects. However, many other non-pest insects also share these traits, which indicates that there has not been a decisive condition characterizing agricultural pest insects. Agricultural habitats are risky and ephemeral to pests because of pest control and harvesting. The usual arithmetic mean fitness cannot be used to measure the persistence of these pests, because the maximal mean fitness is achieved only when they exhibit no dispersal, but that leads to immediate extinction. Using a geometric mean fitness model, we propose a quantitative measure of long-term reproductive success for agricultural pest insects. By using this approach, we can evaluate the trade-off between long-distance dispersal and high reproduction correctly and estimate the condition for the long-term persistence of pest insects in agricultural habitats. We discuss some general perspectives of pest control from the proposed characterization.

The epigenetic landscape illustrates how cells differentiate into different types through the control of gene regulatory networks. Numerous studies have investigated epigenetic gene regulation but there are limited studies on how the epigenetic landscape and the presence of pathogens influence the evolution of host traits. Here we formulate a multistable decision-switch model involving many possible phenotypes with the antagonistic influence of parasitism. As expected, pathogens can drive dominant (common) phenotypes to become inferior, such as through negative frequency-dependent selection. Furthermore, novel predictions of our model show that parasitism can steer the dynamics of phenotype specification from multistable equilibrium convergence to oscillations. This oscillatory behavior could explain pathogen-mediated epimutations and excessive phenotypic plasticity. The Red Queen dynamics also occur in certain parameter space of the model, which demonstrates winnerless cyclic phenotype-switching in hosts and in pathogens. The results of our simulations elucidate how epigenetic landscape is associated with the phenotypic fitness landscape and how parasitism facilitates non-genetic phenotypic diversity.

SummaryMathematical models provide insights for the design and optimization of strategies to control disease epidemics and evolution of pesticide resistance in crops. Here, we present a simple mathematical model to investigate the population dynamics of non-Bt resistant and Bt resistant cornborers in a field with refuge. In the presence of refuge, it is expected that the population of Bt resistant pests will decline due to the dilution effect (non-Bt resistant cornborers mate with Bt resistant pests). We have found that increasing the refuge size can be effective in reducing Bt resistant pests as long as there exists a relatively huge population of non-Bt resistant cornborers at the start of the simulation. This implies that refuge is useless in inhibiting the evolution of cornborers if a sufficient initial population of non-Bt resistant cornborers is absent.

1.Overview and PurposeWe present ABM-IRM, an agent-based modeling approach to insect resistance management. ABM-IRM is one of the agent-based models that we have developed to simulate the insect resistance of Asian Corn Borer (ACB) to BT corn. The model was implemented using NetLogo, an agent-based programming environment (Wilensky, 1999). We created our model using simple rules to find emergent patterns (Wilensky and Rand, 2015) based on refuge types and pyramid BT events that may aid in controlling the resistance of ACB to BT Corn. Following how the Overview, Design concepts, and Details (ODD) protocol was used in presenting a related ABM paper as guide (Anderson and Dragićević, 2015), the following sections are organized as follows: Section 2 covers the typologies of the agents, Section 3 discusses the process overview, and Section 4 highlights our results and emergent patterns.

Parasite aggregation, a recurring pattern in macroparasite infections, is considered one of the “laws” of parasite ecology. Few hosts have a large number of parasites while most hosts have a low number of parasites. Phenomenological models of host-parasite systems thus use the negative-binomial distribution. However, to infer the mechanisms of aggregation, a mechanistic model that does not make any a priori assumptions is essential. Here we formulate a mechanistic model of parasite aggregation in hosts without assuming a negative-binomial distribution. Our results show that a simple model of parasite accumulation still results in an aggregated pattern, as shown by the derived mean and variance of the parasite distribution. By incorporating the derived statistics in host-parasite interactions, we can predict how aggregation affects the population dynamics of the hosts and parasites through time. Thus, our results can directly be applied to observed data as well as can inform the designing of statistical sampling procedures. Overall, we have shown how a plausible mechanistic process can result in the often observed phenomenon of parasite aggregation occurring in numerous ecological scenarios, thus providing a basis for a “law” of ecology.

Competition and cooperation play an important role in society. It drives the species to survive and it enables to balance and maintain the biodiversity in communities. These concepts are important in many fields, such as in ethology, economics, ecology, and evolutionary theory. In this paper, we develop a mathematical model that describes the dynamics of the population of a species that simultaneously interact with a competitor and/or with a cooperator. This modeling study uses a Hill-type function rather than the classical Lotka-Volterra equations. Numerical simulations are done on this model. Heat maps are used to describe different cases by varying the competition coefficient δ and cooperation coefficient γ. Our model has demonstrated not just coexistence but also exclusion or extinction of the population of species. This means that even if competition and cooperation are done simultaneously by a species, it is not a guarantee that they will always survive in the long run. It depends on how much the strength of competition and cooperation they exerted towards its co-competitor or co-cooperator. Moreover, cooperating species are most likely to survive as compared to the competing species. This modeling study enables us to look possibly for ways to control δ and γ, and consequently, control populations in our ecosystem. This will be useful not only for biologists and ecologists but also for researchers who are interested in studying the competitive and cooperative interactions of species in societies.

Long noncoding RNAs (lncRNAs) are transcripts longer than 200 nucleotides that are not translated into proteins. They have recently gained widespread attention due to the finding that tens of thousands of lncRNAs reside in the human genome, and due to an increasing number of lncRNAs that are found to be associated with disease. Some lncRNAs, including disease-associated ones, play different roles in regulating the cell cycle. Mathematical models of the cell cycle have been useful in better understanding this biological system, such as how it could be robust to some perturbations and how the cell cycle checkpoints could act as a switch. Here, we discuss mathematical modeling techniques for studying lncRNA regulation of the mammalian cell cycle. We present examples on how modeling via network analysis and differential equations can provide novel predictions toward understanding cell cycle regulation in response to perturbations such as DNA damage.

Long noncoding RNAs (lncRNAs) are transcripts longer than 200 nucleotides that are not translated into proteins. They have recently gained widespread attention due to the finding that tens of thousands of lncRNAs reside in the human genome, and due to an increasing number of lncRNAs that are found to be associated with disease. Some lncRNAs, including disease-associated ones, play different roles in regulating the cell cycle. Mathematical models of the cell cycle have been useful in better understanding this biological system, such as how it could be robust to some perturbations and how the cell cycle checkpoints could act as a switch. Here, we discuss mathematical modeling techniques for studying lncRNA regulation of the mammalian cell cycle. We present examples on how modeling via network analysis and differential equations can provide novel predictions toward understanding cell cycle regulation in response to perturbations such as DNA damage.

Currently, there is limited data on the suitability of estuaries in Cagayan province, Philippines for aquaculture. In this brief report, we discuss the overall assessment score of Buguey estuary in the municipality of Buguey, Cagayan as potential spot for the culture of green mussel ( Perna viridis ), locally known in the Philippines as "tahong". The score is mainly based on salinity and water temperature. We also present the condition of dissolved oxygen and pH levels in the estuary but these factors do not have major effect on mussel growth compared to salinity and water temperature. The reference ideal values for a suitable culture site are 27 to 35 psu for salinity; 27 to 30°C for water temperature; >5 mg/L for dissolved oxygen; and 7.7 to 8.4 for pH. Based on this reference values, areas in Buguey estuary have acceptable possibility of success for green mussel culture, which is qualitatively equivalent to having "good" suitability. This translates to a production estimate of 81% to 90% of cultured mussels will have a marketable size. However, these ratings may vary due to competition with existing oyster farming, water depth of the chosen site (since several areas in Buguey estuary are shallow), and other factors.

Concurrent decision-making model (CDM) of interaction networks with more than two antagonistic components represents various biological systems, such as gene interaction, species competition and mental cognition. The CDM model assumes sigmoid kinetics where every component stimulates itself but concurrently represses the others. Here we prove generic mathematical properties (e.g., location and stability of steady states) of n -dimensional CDM with either symmetric or asymmetric reciprocal antagonism between components. Significant modifications in parameter values serve as biological regulators for inducing steady state switching by driving a temporal state to escape an undesirable equilibrium. Increasing the maximal growth rate and decreasing the decay rate can expand the basin of attraction of a steady state that contains the desired dominant component. Perpetually adding an external stimulus could shut down multi-stability of the system which increases the robustness of the system against stochastic noise. We further show that asymmetric interaction forming a repressilator-type network generates oscillatory behavior.

Philippines as an archipelago and tropical country, which is situated near the Pacific ocean, faces uncertain rainfall intensities. This makes environmental, agricultural and economic systems affected by precipitation difficult to manage. Time series analysis of Philippine rainfall pattern has been previously done, but there is no study investigating its probability distribution. Modeling the Philippine rainfall using probability distributions is essential, especially in managing risks and designing insurance products. Here, daily and cumulative rainfall data (January 1961 - August 2016) from 28 PAGASA weather stations are fitted to probability distributions. Moreover, the fitted distributions are examined for invariance under subsets of the rainfall data set. We observe that the Gamma distribution is a suitable fit for the daily up to the ten-day cumulative rainfall data. Our results can be used in agriculture, especially in forecasting claims in weather index-based insurance.

Various distance metrics and their induced norms are employed in the quantitative modeling of evolutionary dynamics. Minimization of these distance metrics when applied to evolutionary optimization are hypothesized to result in different outcomes. Here, we apply the different distance metrics to the evolutionary trait dynamics brought about by the interaction between two competing species infected by parasites (exploiters). We present deterministic cases showing the distinctive selection outcomes under the Manhattan, Euclidean and Chebyshev norms. Specifically, we show how they differ in the time of convergence to the desired optima (e.g., no disease), and in the egalitarian sharing of carrying capacity between the competing species. However, when randomness is introduced to the population dynamics of parasites and to the trait dynamics of the competing species, the distinctive characteristics of the outcomes under the three norms become indistinguishable. Our results provide theoretical cases when evolutionary dynamics using different distance metrics exhibit similar outcomes.

Predator-prey systems have been studied intensively for over a hundred years. These studies have demonstrated that the dynamics of Lotka-Volterra (LV) systems are not stable, that is, exhibiting either cyclic oscillation or divergent extinction of one species. Stochastic versions of the deterministic cyclic oscillations also exhibit divergent extinction. Thus, we have no solution for asymptotic stability in predator-prey systems, unlike most natural predator-prey interactions that sometimes exhibit stable and persistent coexistence. Here, we demonstrate that adding a small immigration into the prey or predator population can stabilize the LV system. Although LV systems have been studied intensively, there is no study on the non-linear modifications that we have tested. We also checked the effect of the inclusion of non-linear interaction term to the stability of the LV system. Our results show that small immigrations invoke stable convergence in the LV system with three types of functional responses. This means that natural predator-prey populations can be stabilized by a small number of sporadic immigrants.

Farmers frequently decide where to locate the colonies of their domesticated eusocial bees, especially given the following mutually exclusive scenarios: (i) there are limited nectar and pollen sources within the vicinity of the apiary that cause competition among foragers; and (ii) there are fewer pollinators compared to the number of inflorescence that may lead to suboptimal pollination of crops. We hypothesize that optimally distributing the beehives in the apiary can help address the two scenarios stated above. In this paper, we develop quantitative models (specifically using linear programming) for addressing the two given scenarios. We formulate models involving the following factors: (i) fuzzy preference of the beekeeper; (ii) number of available colonies; (iii) unknown-but-bounded strength of colonies; (iv) probabilistic carrying capacity of the plant clusters; and (v) spatial orientation of the apiary.

Red Queen dynamics are observed in selected genotypes, whereas the rest of the genotypes remain subordinate in synchronized dynamics., Interactions between hosts and parasites have been hypothesized to cause winnerless coevolution, called Red Queen dynamics. The canonical Red Queen dynamics assume that all interacting genotypes of hosts and parasites undergo cyclic changes in abundance through negative frequency-dependent selection, which means that any genotype could become frequent at some stage. However, this prediction cannot explain why many rare genotypes stay rare in natural host-parasite systems. To investigate this, we build a mathematical model involving multihost and multiparasite genotypes. In a deterministic and controlled environment, Red Queen dynamics occur between two genotypes undergoing cyclic dominance changes, whereas the rest of the genotypes remain subordinate for long periods of time in phase-locked synchronized dynamics with low amplitude. However, introduction of stochastic noise in the model might allow the subordinate cyclic host and parasite types to replace dominant cyclic types as new players in the Red Queen dynamics. The factors that influence such evolutionary switching are interhost competition, specificity of parasitism, and degree of stochastic noise. Our model can explain, for the first time, the persistence of rare, hardly cycling genotypes in populations (for example, marine microbial communities) undergoing host-parasite coevolution.

Mathematical models in neuroscience have led to the formulation of new theories of cognition. Several models have focused on equilibrium-converging cognitive activities but human and artificial cognition are frequently dynamic. Here we present some of the models that produce dynamic behavior of cognition, specifically those that produce temporal oscillations in decision-making.

Most terrestrial plant communities exhibit relatively high species diversity and many competitive species are ubiquitous. Many theoretical studies have been carried out to investigate the coexistence of a few competitive species and in most cases they suggest competitive exclusion. Theoretical studies have revealed that coexistence of even three or four species can be extremely difficult. It has been suggested that the coexistence of many species has been achieved by the fine differences in suitable microhabitats for each species, attributing to niche-separation. So far there is no explicit demonstration of such a coexistence in mathematical and simulation studies. Here we built a simple lattice Lotka-Volterra model of competition by incorporating the minute differences of suitable microhabitats for many species. By applying the site variations in species-specific settlement rates of a seedling, we achieved the coexistence of more than 10 species. This result indicates that competition between many species is avoided by the spatial variations in species-specific microhabitats. Our results demonstrate that coexistence of many species becomes possible by the minute differences in microhabitats. This mechanism should be applicable to many vegetation types, such as temperate forests and grasslands.

Modern biology will never be the same without mathematical and computational tools. Using mind map with “epigenetics” as the root, we discuss the current advancement in the field of biomathematics for modeling cell-fate specification. In the discussions, we also present possible directions for future research.

The well-known Waddington?s epigenetic landscape of cell-fate determination is not static but varies because of the dynamic gene regulation during development. However, existing mathematical models with few state variables and fixed parameters are inadequate in characterizing the temporal transformation of the landscape. Here we simulate a decision-switch model of gene regulation with more than two state variables and with time-varying repression among regulatory factors. We are able to demonstrate multi-lineage differentiation at different timescales that portrays the branching canals in Waddington?s illustration. We also present a repressilator-type system that activates suppressed genes via sustained oscillations in a flattened landscape, hence providing an alternative scheme for cellular reprogramming. The time-dependent parameters governed by gradient-based dynamics regulate cell differentiation, dedifferentiation and transdifferentiation. Our prediction integrates the theories of branching and structural oscillations in cell-fate determination, which reveals key temporal patterns of cell differentiation and associated diseases, such as cancer. Keywords: gene regulatory network, stem cells, pluripotency, synthetic biology, multistability, attractor Note: This paper has been accepted for publication in Progress in Biophysics and Molecular Biology (Elsevier). DOI of the peer-reviewed manuscript: 10.1016/j.pbiomolbio.2015.01.006

Concurrent decision-making model (CDM) of interaction networks involving more than two antagonistic components can represent various biological systems, such as gene interaction, species competition and mental perception. The model assumes sigmoid kinetics where every component stimulates itself but concurrently represses the others. Here we prove general dynamical properties of the CDM (e.g., location and stability of steady states) for any dimension of the state space even if the reciprocal antagonism between two components is asymmetric. Significant modifications in parameter values serve as biological regulators for inducing steady state switching by leading a temporal state to escape an undesired equilibrium. Increasing the maximal growth rate and decreasing the decay rate expand the basin of attraction of a steady state with the desired dominant component. Perpetually adding an external stimulus can shut down multi-stability of the system that increases the robustness of the system against stochastic noise. We further show that asymmetric interaction that forms a repressilator-type network generates oscillatory behavior.

In this paper, we examine a nonlinear concurrent decision-making model (CDM) of interaction networks that involve more than two antagonistic components (e.g., proteins, species, communities, mental choices). The model assumes sigmoid kinetics where every component stimulates itself but represses all others. We are able to prove general dynamical properties of the CDM (e.g., location and stability of steady states) for any dimension of the state space even if the reciprocal antagonism between two components is asymmetric. There are cases where asymmetric interaction generates oscillatory behavior. Some parameters can serve as biological regulators for inducing steady state switching by leading a temporal state to escape an undesired equilibrium. Increasing the maximal growth rate and decreasing the decay rate can expand the basin of attraction of a steady state with the desired component having the dominant value. We further show that perpetually adding an external stimulus can shutdown multi-stability of the system that increases the robustness of the system against stochastic noise.

In a host-parasite system, the constitutive interaction among the species, regulated by the growth rates and functional response, may induce populations to approach equilibrium or sometimes to exhibit simple cycles or peculiar oscillations, such as chaos. A large carrying capacity coupled with appropriate parasitism effectiveness frequently drives long-term apparent oscillatory dynamics in population size. We name these oscillations due to the structure of the constitutive interaction among species as ecological. On the other hand, there are also exceptional cases when the evolving quantitative traits of the hosts and parasites induce oscillating population size, which we call as evolutionary. This oscillatory behavior is dependent on the speed of evolutionary adaptation and degree of evolutionary trade-off. A moderate level of negative trade-off is essential for the existence of oscillations. Evolutionary oscillations due to the host-parasite coevolution (known as the Red Queen) can be observed beyond the ecological oscillations, especially when there are more than two competing species involved.