Quantitative Biology

Management performance of five alternative stock assessment methods was evaluated by using them to set harvest levels targeting multi-species maximum yield in a multi-species flatfish fishery, including single-species and hierarchical multi-species models, and methods that pooled data across species and spatial strata, with catch outcomes of each method under three data scenarios compared to catch under an omniscient manager simulation. Operating models included technical interactions between species intended to produce choke effects often observed in output controlled multi-species fisheries. Hierarchical multi-species models outperformed all other methods under data-poor and data-moderate scenarios, and outperformed single-species models under the data-rich scenario. Hierarchical models were least sensitive to prior precision, sometimes improving in performance when prior precision was reduced. Choke effects were found to both positive and negative effects, sometimes leading to underfishing of non-choke species, but at other times preventing overfishing of non-choke species. We highlight the importance of including technical interactions in multi-species assessment models and management objectives, how choke species can indicate mismatches between management objectives and system dynamics, and recommend hierarchical multi-species models for multi-species fishery management systems.

Amid the ongoing COVID-19 pandemic, public health authorities and the general population are striving to achieve a balance between safety and normalcy. Ever changing conditions call for the development of theory and simulation tools to finely describe multiple strata of society while supporting the evaluation of "what-if" scenarios. Particularly important is to assess the effectiveness of potential testing approaches and vaccination strategies. Here, an agent-based modeling platform is proposed to simulate the spreading of COVID-19 in small towns and cities, with a single-individual resolution. The platform is validated on real data from New Rochelle, NY -- one of the first outbreaks registered in the United States. Supported by expert knowledge and informed by reported data, the model incorporates detailed elements of the spreading within a statistically realistic population. Along with pertinent functionality such as testing, treatment, and vaccination options, the model accounts for the burden of other illnesses with symptoms similar to COVID-19. Unique to the model is the possibility to explore different testing approaches -- in hospitals or drive-through facilities -- and vaccination strategies that could prioritize vulnerable groups. Decision making by public authorities could benefit from the model, for its fine-grain resolution, open-source nature, and wide range of features.

We investigated daily COVID-19 cases and death in the 337 lower tier local authority regions in England and Wales to better understand how the disease propagated over a 10-month period. Population density scaling models revealed residual variance and skewness to be sensitive indicators of the dynamics of propagation. Lockdowns and schools reopening triggered increased variance indicative of outbreaks with local impact and country scale heterogeneity. University reopening and December holidays triggered reduced variance indicative of country scale homogenisation which reached a minimum after New Year. Homogeneous propagation was associated with better correspondence with normally distributed residuals while heterogeneous propagation was more consistent with skewed models. Skewness varied from strongly negative to strongly positive revealing an unappreciated feature of community propagation. Hot spots and super-spreading events are well understood descriptors of regional disease dynamics that would be expected to be associated with positively skewed distributions. Positively skewed behaviour was observed; however, negative skewness indicative of cold-spots and super-isolation dominated for approximately 4 months during the period of study. In contrast, death metrics showed near constant behaviour in scaling, variance, and skewness metrics over the full period with rural regions preferentially affected, an observation consistent with regional age demographics in England and Wales.

Using the classical Susceptible-Infected-Recovered epidemiological model, an analytical formula is derived for the number of beds occupied by Covid-19 patients. The analytical curve is fitted to data in Belgium, France, New York City and Switzerland, with a correlation coefficient exceeding 98.8%, suggesting that finer models are unnecessary with such macroscopic data. The fitting is used to extract estimates of the doubling time in the ascending phase of the epidemic, the mean recovery time and, for those who require medical intervention, the mean hospitalization time. Large variations can be observed among different outbreaks.

Contact Tracing (CT) is one of the measures taken by government and health officials to mitigate the spread of the novel coronavirus. In this paper, we investigate its efficacy by developing a compartmental model for assessing its impact on mitigating the spread of the virus. We describe the impact on the reproduction number R 0 of COVID-19. In particular, we discuss the importance and relevance of parameters of the model such as the number of reported cases, effectiveness of tracking and monitoring policy, and the transmission rates to contact tracing. We describe the terms "perfect tracking", "perfect monitoring" and "perfect reporting" to indicate that traced contacts will be tracked while incubating, tracked contacts are efficiently monitored so that they do not cause secondary infections, and all infected persons are reported, respectively. We consider three special scenarios: (1) perfect monitoring and perfect tracking of contacts of a reported case, (2) perfect reporting of cases and perfect monitoring of tracked reported cases and (3) perfect reporting and perfect tracking of contacts of reported cases. Furthermore, we gave a lower bound on the proportion of contacts to be traced to ensure that the effective reproduction, R c , is below one and describe R c in terms of observable quantities such as the proportion of reported and traced cases. Model simulations using the COVID-19 data obtained from John Hopkins University for some selected states in the US suggest that even late intervention of CT may reasonably reduce the transmission of COVID-19 and reduce peak hospitalizations and deaths.

Standard epidemic models based on compartmental differential equations are investigated under continuous parameter change as external forcing. We show that seasonal modulation of the contact parameter superimposed a monotonic decay needs a different description than that of the standard chaotic dynamics. The concept of snapshot attractors and their natural probability distribution has been adopted from the field of the latest climate-change-research to show the importance of transient effect and ensemble interpretation of disease spread. After presenting the extended bifurcation diagram of measles, the temporal change of the phase space structure is investigated. By defining statistical measures over the ensemble, we can interpret the internal variability of the epidemic as the onset of complex dynamics even for those values of contact parameter where regular behavior is expected. We argue that anomalous outbreaks of infectious class cannot die out until transient chaos is presented for various parameters. More important, that this fact becomes visible by using of ensemble approach rather than single trajectory representation. These findings are applicable generally in nonlinear dynamical systems such as standard epidemic models regardless of parameter values.

This is a pedagogical paper on estimating the number of people that can be infected by one infectious person during an epidemic outbreak, known as the reproduction number. Knowing the number is crucial for developing policy responses. There are generally two types of such a number, i.e., basic and effective (or instantaneous). While basic reproduction number is the average expected number of cases directly generated by one case in a population where all individuals are susceptible, effective reproduction number is the number of cases generated in the current state of a population. In this paper, we exploit the deterministic susceptible-infected-removed (SIR) model to estimate them through three different numerical approximations. We apply the methods to the pandemic COVID-19 in Italy to provide insights into the spread of the disease in the country. We see that the effect of the national lockdown in slowing down the disease exponential growth appeared about two weeks after the implementation date. We also discuss available improvements to the simple (and naive) methods that have been made by researchers in the field. Authors of this paper are members of the SimcovID (Simulasi dan Pemodelan COVID-19 Indonesia) collaboration.

We proposed a three-species food chain model with hunting co-operation among the middle predator. In this model, third species prey on the middle species and the middle prey on the first species. The hunting cooperation among the middle predator affects interestingly on the numbers of both the predators and the prey. We examined the linear stability of the model theoretically and numerically. We conducted the two-parameter numerical analysis to check the long-term behavior and the change in the number of species with respect to hunting co-operation. Our findings supported the postulates from the two species food chain model with hunting co-operation.

Traditionally, the identification of parameters in the formulation and solution of inverse problems considers that models, variables and mathematical parameters are free of uncertainties. This aspect simplifies the estimation process, but does not consider the influence of relatively small changes in the design variables in terms of the objective function. In this work, the SIDR (Susceptible, Infected, Dead and Recovered) model is used to simulate the dynamic behavior of the novel coronavirus disease (COVID-19), and its parameters are estimated by formulating a robust inverse problem, that is, considering the sensitivity of design variables. For this purpose, a robust multi-objective optimization problem is formulated, considering the minimization of uncertainties associated to the estimation process and the maximization of the robustness parameter. To solve this problem, the Multi-objective Stochastic Fractal Search algorithm is associated with the Effective Mean concept for the evaluation of robustness. The results obtained considering real data of the epidemic in China demonstrate that the evaluation of the sensitivity of the design variables can provide more reliable results.

We demonstrate the ability of statistical data assimilation to identify the measurements required for accurate state and parameter estimation in an epidemiological model for the novel coronavirus disease COVID-19. Our context is an effort to inform policy regarding social behavior, to mitigate strain on hospital capacity. The model unknowns are taken to be: the time-varying transmission rate, the fraction of exposed cases that require hospitalization, and the time-varying detection probabilities of new asymptomatic and symptomatic cases. In simulations, we obtain accurate estimates of undetected (that is, unmeasured) infectious populations, by measuring the detected cases together with the recovered and dead - and without assumed knowledge of the detection rates. Given a noiseless measurement of the recovered population, excellent estimates of all quantities are obtained using a temporal baseline of 101 days, with the exception of the time-varying transmission rate at times prior to the implementation of social distancing. With low noise added to the recovered population, accurate state estimates require a lengthening of the temporal baseline of measurements. Estimates of all parameters are sensitive to the contamination, highlighting the need for accurate and uniform methods of reporting. The aim of this paper is to exemplify the power of SDA to determine what properties of measurements will yield estimates of unknown parameters to a desired precision, in a model with the complexity required to capture important features of the COVID-19 pandemic.