Spatio-temporal solutions of a diffusive directed dynamics model with harvesting.

The study considers a directed dynamics reaction-diffusion competition model to study the density of evolution for a single species population with harvesting effect in a heterogeneous environment, where all functions are spatially distributed in time series. The dispersal dynamics describe the growth of the species, which is distributed according to the resource function with no-flux boundary conditions. The analysis investigates the existence, positivity, persistence, and stability of solutions for both time-periodic and spatial functions. The carrying capacity and the distribution function are either arbitrary or proportional. It is observed that if harvesting exceeds the growth rate, then eventually, the population drops down to extinction. Several numerical examples are considered to support the theoretical results. Supplementary Information: The online version contains supplementary material available at 10.1007/s12190-022-01742-x.

Mathematical Study of a Resource-Based Diffusion Model with Gilpin-Ayala Growth and Harvesting.

This paper focuses on a Gilpin-Ayala growth model with spatial diffusion and Neumann boundary condition to study single species population distribution. In our heterogeneous model, we assume that the diffusive spread of population is proportional to the gradient of population per unit resource, rather than the population density itself. We investigate global well-posedness of the mathematical model, determine conditions on harvesting rate for which non-trivial equilibrium states exist and examine their global stability. We also determine conditions on harvesting that leads to species extinction through global stability of the trivial solution. Additionally, for time periodic growth, resource, capacity and harvesting functions, we prove existence of time-periodic states with the same period. We also present numerical results on the nature of nonzero equilibrium states and their dependence on resource and capacity functions as well as on Gilpin-Ayala parameter [Formula: see text]. We conclude enhanced effects of diffusion for small [Formula: see text] which in particular disallows existence of nontrivial states even in some cases when intrinsic growth rate exceeds harvesting at some locations in space for which a logistic model allows for a nonzero equilibrium density.

Evolution of dispersal and the analysis of a resource flourished population model with harvesting.

This study explores a spatially distributed harvesting model that signifies the outcome of the competition of two species in a heterogeneous environment. The model is controlled by reaction-diffusion equations with resource-based diffusion strategies. Two different situations are maintained by the harvesting effects: when the harvesting rates are independent in space and do not exceed the intrinsic growth rate; and when they are proportional to the time-independent intrinsic growth rate. In particular, the competition between both species differs only by their corresponding migration strategy and harvesting intensity. We have computed the main results for the global existence of solutions that represent either coexistence or competitive exclusion of two competing species depending on the harvesting levels and different imposed diffusion strategies. We also established some estimates on harvesting efforts for which coexistence is apparent. Also, some numerical results are exhibited in one and two spatial dimensions, which shed some light on the ecological implementation of the model.

Understanding the relationship between stay-at-home measures and vaccine shortages: a conventional, heterogeneous, and fractional dynamic approach.

In light of the global prevalence of a highly contagious respiratory disease, this study presents a novel approach to address the pressing and unanticipated issues by introducing a modified vaccination and lockdown-centered epidemic model. The rapid spread of the disease is attributed to viral transmissibility, the emergence of new strains (variants), lack of immunization, and human unawareness. This study aims to provide policymakers with crucial insights for making informed decisions regarding lockdown strategies, vaccine availability, and other control measures. The research adopts three types of models: deterministic, heterogeneous, and fractional-order dynamics, on both theoretical and numerical approaches. The heterogeneous network considers varying connectivity and interaction patterns among individuals, while the ABC fractional-order derivatives analyze the impact of integer-order control in different semi-groups. An extensive theoretical analysis is conducted to validate the proposed model. A comprehensive numerical investigation encompasses deterministic, stochastic, and ABC fractional-order derivatives, considering the combined effects of an effective vaccination program and non-pharmaceutical interventions, such as lockdowns and shutdowns. The findings of this research are expected to be valuable for policymakers in different countries, helping them implement dynamic strategies to control and eradicate the epidemic effectively.

Seasonal Variability and Stochastic Branching Process in Malaria Outbreak Probability.

BACKGROUND: Malaria is the world's most fatal and challenging parasitic disease, caused by the Plasmodium parasite, which is transmitted to humans by the bites of infected female mosquitoes. Bangladesh is the most vulnerable region to spread malaria because of its geographic position. In this paper, we have considered the dynamics of vector-host models and observed the stochastic behavior. This study elaborates on the seasonal variability and calculates the probability of disease outbreaks. METHODS: We present a model for malaria disease transmission and develop its corresponding continuous-time Markov chain (CTMC) representation. The proposed vector-host models illustrate the malaria transmission model along with sensitivity analysis. The deterministic model with CTMC curves is depicted to show the randomness in real scenarios. Sequentially, we expand these studies to a time-varying stochastic vector-host model that incorporates seasonal variability. Phase plane analysis is conducted to explore the characteristics of the disease, examine interactions among various compartments, and evaluate the impact of key parameters. The branching process approximation is developed for the corresponding vector-host model to calculate the probability outbreak. Numerous numerical results are accomplished to observe the analytical investigation. RESULTS: Seasonality and contact patterns affect the dynamics of disease outbreaks. The numerical illustration provides that the probability of a disease outbreak depends on the infected host or vector. Additionally, periodic transmission rates have a great influence on the probability outbreak. The basic reproduction number (R0) is derived, which is the main justification for studying the dynamical behavior of epidemic models. CONCLUSIONS: Seasonal variability significantly impacts malaria transmission, and the probability of disease outbreaks is influenced by time and the initial number of infected individuals. Moreover, the branching process approximation is applicable when the population size is large enough and the basic reproduction number is less than 1. In the future, such analysis can help decision-makers understand the impact of various parameters and their stochastic behavior in the vector-host model to prevent such types of disease outbreaks.

Downscaling epidemiological time series data for improving forecasting accuracy: An algorithmic approach.

Data scarcity and discontinuity are common occurrences in the healthcare and epidemiological dataset and often is needed to form an educative decision and forecast the upcoming scenario. Often to avoid these problems, these data are processed as monthly/yearly aggregate where the prevalent forecasting tools like Autoregressive Integrated Moving Average (ARIMA), Seasonal Autoregressive Integrated Moving Average (SARIMA), and TBATS often fail to provide satisfactory results. Artificial data synthesis methods have been proven to be a powerful tool for tackling these challenges. The paper aims to propose a novel algorithm named Stochastic Bayesian Downscaling (SBD) algorithm based on the Bayesian approach that can regenerate downscaled time series of varying time lengths from aggregated data, preserving most of the statistical characteristics and the aggregated sum of the original data. The paper presents two epidemiological time series case studies of Bangladesh (Dengue, Covid-19) to showcase the workflow of the algorithm. The case studies illustrate that the synthesized data agrees with the original data regarding its statistical properties, trend, seasonality, and residuals. In the case of forecasting performance, using the last 12 years data of Dengue infection data in Bangladesh, we were able to decrease error terms up to 72.76% using synthetic data over actual aggregated data.

Interplay of harvesting and the growth rate for spatially diversified populations and the testing of a decoupled scheme.

The loss and degradation of habitat, Allee effects, climate change, deforestation, hunting-overfishing and human disturbances are alarming and significant threats to the extinction of many species in ecology. When populations compete for natural resources, food supply and habitat, survival to extinction and various other issues are visible. This paper investigates the competition of two species in a heterogeneous environment that are subject to the effect of harvesting. The most realistic harvesting case is connected with the intrinsic growth rate, and the harvesting functions are developed based on this clause instead of random choice. We prove the existence and uniqueness of the solution to the model. Theoretically, we state that, when species coexist, one may drive the other to die out, so both species become extinct, considering all possible rational values of parameters. These results highlight a worthy-of attention study between two populations based on harvesting coefficients. Finally, we solve the model for two spatial dimensions by using a backward Euler, decoupled and linearized time-stepping fully discrete algorithm in a series of examples and observe a match between the theoretical and numerical findings.

Vaccine efficacy and SARS-CoV-2 control in California and U.S. during the session 2020-2026: A modeling study.

BACKGROUND: Besides maintaining health precautions, vaccination has been the only prevention from SARS-CoV-2, though no clinically proved 100% effective vaccine has been developed till date. At this stage, to withhold the debris of this pandemic-experts need to know the impact of the vaccine efficacy rates, the threshold level of vaccine effectiveness and how long this pandemic may extent with vaccines that have different efficacy rates. In this article, a mathematical model study has been done on the importance of vaccination and vaccine efficiency rate during an ongoing pandemic. METHODS: We simulated a five compartment mathematical model to analyze the pandemic scenario in both California, and whole U.S. We considered four vaccines, Pfizer (95%), Moderna (94%), AstraZeneca (79%), and Johnson & Johnson (72%), which are being used rigorously to control the SARS-CoV-2 pandemic, in addition with two special cases: a vaccine with 100% efficacy rate and no vaccine under use. SARS-CoV-2 related data of California, and U.S. were used in this study. FINDINGS: Both the infection and death rates are very high in California. Our model suggests that the pandemic situation in California will be under control in the last quartile of the year 2023 if vaccination program is continued with the Pfizer vaccine. During this time, six waves may happen from the beginning of the immunization where the case fatality and recovery rates will be 1.697% and 98.30%, respectively. However, according to the considered model, this period might be extended to the mid of 2024 when vaccines with lower efficacy rates are used. On the other hand, the daily cases and deaths in the U.S. will be under control at the end of 2026 with multiple waves. Although the number of susceptible people will fall down to none in the beginning of 2027, there is less chance to stop the vaccination program if vaccinated with a vaccine other than a 100% effective vaccine or Pfizer, and at that case vaccination program must run till the mid of 2028. According to this study, the unconfirmed-infectious and infected cases will be under control at the end of 2027 and at the mid of 2028, respectively. INTERPRETATION: The more effective a vaccine is, the less people suffer from this malign infection. Vaccines which are less than 90% effective do not have notable contribution to control the pandemic besides hard immunity. Furthermore, specific groups of people are getting prioritized initially, mass vaccination and quick responses are required to control the spread of this disease.

Optimal treatment strategies to control acute HIV infection.

Various antiretroviral therapies (ART) are administered to symptomatic human immunodeficiency virus (HIV) infected individuals to improve their health. The treatment effectiveness may depend on suppressing development of drug resistance, reduce evolution of new viral strains, minimize serious side effects and the costs of drugs. This paper deals with some results concerning optimal drug administration scheme successful in improving patients' health especially in poorly resourced settings. The model under consideration describes the interaction between the uninfected cells, the latently infected cells, the productively infected cells, and the free viruses. Generally, in viral infection, the drug strategy aspects either the virus infectivity or reduce the virion production. The mathematical model proposed here, deals with both situations with the objective function based on a combination of maximizing benefit relied on T cells count (the white cells that coordinate activities of the immune system) and minimizing the systemic cost. The existence of the optimal control pair is established and the Pontryagin's minimum principle is used to characterize these two optimal controls. The optimality system is derived and solved numerically using the forward and backward sweep method (FBSM). Our results indicate that early initiation of treatment makes a profound impact in both improving the quality of life and reducing the economic costs of therapy.

Dynamics of a diffusive vaccination model with therapeutic impact and non-linear incidence in epidemiology.

In this paper, we study a more general diffusive spatially dependent vaccination model for infectious disease. In our diffusive vaccination model, we consider both therapeutic impact and nonlinear incidence rate. Also, in this model, the number of compartments of susceptible, vaccinated and infectious individuals are considered to be functions of both time and location, where the set of locations (equivalently, spatial habitats) is a subset of Rn with a smooth boundary. Both local and global stability of the model are studied. Our study shows that if the threshold level R0≤1, the disease-free equilibrium E0 is globally asymptotically stable. On the other hand, if R0>1 then there exists a unique stable disease equilibrium E∗. The existence of solutions of the model and uniform persistence results are studied. Finally, using finite difference scheme, we present a number of numerical examples to verify our analytical results. Our results indicate that the global dynamics of the model are completely determined by the threshold value R0.

Mathematical Modeling and COVID-19 Forecast in Texas, USA: A Prediction Model Analysis and the Probability of Disease Outbreak.

BACKGROUND: Response to the unprecedented coronavirus disease 2019 (COVID-19) outbreak needs to be augmented in Texas, United States, where the first 5 cases were reported on March 6, 2020, and were rapidly followed by an exponential rise within the next few weeks. This study aimed to determine the ongoing trend and upcoming infection status of COVID-19 in county levels of Texas. METHODS: Data were extracted from the following sources: published literature, surveillance, unpublished reports, and websites of Texas Department of State Health Services (DSHS), Natality report of Texas, and WHO Coronavirus Disease (COVID-19) Dashboard. The 4-compartment Susceptible-Exposed-Infectious-Removal (SEIR) mathematical model was used to estimate the current trend and future prediction of basic reproduction number and infection cases in Texas. Because the basic reproduction number is not sufficient to predict the outbreak, we applied the Continuous-Time Markov Chain (CTMC) model to calculate the probability of the COVID-19 outbreak. RESULTS: The estimated mean basic reproduction number of COVID-19 in Texas is predicted to be 2.65 by January 31, 2021. Our model indicated that the third wave might occur at the beginning of May 2021, which will peak at the end of June 2021. This prediction may come true if the current spreading situation/level persists, i.e., no clinically effective vaccine is available, or this vaccination program fails for some reason in this area. CONCLUSION: Our analysis indicates an alarming ongoing and upcoming infection rate of COVID-19 at county levels in Texas, thereby emphasizing the promotion of more coordinated and disciplined actions by policy-makers and the population to contain its devastating impact.

SARS-CoV-2 and Rohingya Refugee Camp, Bangladesh: Uncertainty and How the Government Took Over the Situation.

Background: Bangladesh hosts more than 800,000 Rohingya refugees from Myanmar. The low health immunity, lifestyle, access to good healthcare services, and social-security cause this population to be at risk of far more direct effects of COVID-19 than the host population. Therefore, evidence-based forecasting of the COVID-19 burden is vital in this regard. In this study, we aimed to forecast the COVID-19 obligation among the Rohingya refugees of Bangladesh to keep up with the disease outbreak's pace, health needs, and disaster preparedness. Methodology and Findings: To estimate the possible consequences of COVID-19 in the Rohingya camps of Bangladesh, we used a modified Susceptible-Exposed-Infectious-Recovered (SEIR) transmission model. All of the values of different parameters used in this model were from the Bangladesh Government's database and the relevant emerging literature. We addressed two different scenarios, i.e., the best-fitting model and the good-fitting model with unique consequences of COVID-19. Our best fitting model suggests that there will be reasonable control over the transmission of the COVID-19 disease. At the end of December 2020, there will be only 169 confirmed COVID-19 cases in the Rohingya refugee camps. The average basic reproduction number (R0) has been estimated to be 0.7563. Conclusions: Our analysis suggests that, due to the extensive precautions from the Bangladesh government and other humanitarian organizations, the coronavirus disease will be under control if the maintenance continues like this. However, detailed and pragmatic preparedness should be adopted for the worst scenario.

Disease-specific out-of-pocket healthcare expenditure in urban Bangladesh: A Bayesian analysis.

BACKGROUND: Because of the rapid increase of non-communicable diseases (NCDs) and high burden of healthcare-related financial issues in Bangladesh, there is a concern that out-of-pocket (OOP) payments related to illnesses may become a major burden on household. It is crucial to understand what are the major illnesses responsible for high OPP at the household level to help policymakers prioritize key areas of actions to protect the household from 100% financial hardship for seeking health care as part of universal health coverage. OBJECTIVES: We first estimated the costs of illnesses among a population in urban Bangladesh, and then assessed the household financial burden associated with these illnesses. METHOD: A cross-sectional survey of 1593 randomly selected households was carried out in Bangladesh (urban area of Rajshahi city), in 2011. Catastrophic expenditure was estimated at 40% threshold of household capacity to pay. We employed the Bayesian two-stage hurdle model and Bayesian logistic regression model to estimate age-adjusted average cost and the incidence of household financial catastrophe for each illness, respectively. RESULTS: Overall, approximately 45% of the population of Bangladesh had at least one episode of illness. The age-sex-adjusted average medical expenses and catastrophic health care expenditure among the households were TK 621 and 8%, respectively. Households spent the highest amount of money 7676.9 on paralysis followed by liver disease (TK 2695.4), injury (TK 2440.0), mental disease (TK 2258.0), and tumor (TK 2231.2). These diseases were also responsible for higher incidence of financial catastrophe. Our study showed that 24% of individuals who suffered typhoid incurred catastrophic expenditure followed by liver disease (12.3%), tumor (12.1%), heart disease (8.4%), injury (7.9%), mental disease (7.9%), cataract (7.1%), and paralysis (6.5%). CONCLUSION: The study findings suggest that chronic illnesses were responsible for high costs and high catastrophic expenditures in Bangladesh. Effective risk pooling mechanism might reduce household financial burden related to illnesses. Chronic illness related to NCDs is the major cause of OOP. It is also important to consider prioritizing vulnerable population by subsidizing the high health care cost for some of the chronic illnesses.

Lotka systems with directed dispersal dynamics: Competition and influence of diffusion strategies.

We study a Lotka system describing two competing populations, and each of them chooses its diffusion strategy as the tendency to have a distribution proportional to a certain positive prescribed function. For instance, the standard diffusion corresponds to the choice of a uniform distribution. The paper is focused on the interplay of species competition and diffusion strategies. In the case when one of the diffusion strategies is proportional to the carrying capacity, while the other is not, and the competition does not discriminate the former species, we prove the competitive exclusion of the latter one. If the competition favors the latter species, there is still a range of parameters for which there is a coexistence, thanks to the better dispersal strategy chosen by the former species. The dependency on the interaction type, diffusion coefficients and intrinsic growth rates is explored. We prove that in the limit case, higher diffusion coefficients are detrimental while higher growth rates, as well as lower resources sharing, are beneficial for population survival.

Competitive spatially distributed population dynamics models: Does diversity in diffusion strategies promote coexistence?

We study the interaction between different types of dispersal, intrinsic growth rates and carrying capacities of two competing species in a heterogeneous environment: one of them is subject to a regular diffusion while the other moves in the direction of most per capita available resources. If spatially heterogeneous carrying capacities coincide, and intrinsic growth rates are proportional then competitive exclusion of a regularly diffusing population is inevitable. However, the situation may change if intrinsic growth rates for the two populations have different spatial forms. We also consider the case when carrying capacities are different. If the carrying capacity of a regularly diffusing population is higher than for the other species, the two populations may coexist; as the difference between the two carrying capacities grows, competitive exclusion of the species with a lower carrying capacity occurs.