Dynamics of prey–predator model with strong and weak Allee effect in the prey with gestation delay

This study proposes two prey–predator models with strong and weak Allee effects in prey population with Crowley–Martin functional response. Further, gestation delay of the predator population is introduced in both the models. We discussed the boundedness, local stability and Hopf-bifurcation of both nondelayed and delayed systems. The stability and direction of Hopfbifurcation is also analyzed by using Normal form theory and Center manifold theory. It is shown that species in the model with strong Allee effect become extinct beyond a threshold value of Allee parameter at low density of prey population, whereas species never become extinct in weak Allee effect if they are initially present. It is also shown that gestation delay is unable to avoiding the status of extinction. Lastly, numerical simulation is conducted to verify the theoretical findings.&nbsp

Dynamics of Bacterial white spot disease spreads in Litopenaeus Vannamei with time-varying delay

In this paper, we mainly consider a eco-epidemiological predator-prey system where delay is time-varying to study the transmission dynamics of Bacterial white spot disease in Litopenaeus Vannamei, which will contribute to the sustainable development of shrimp. First, the permanence and the positiveness of solutions are given. Then, the conditions for the local asymptotic stability of the equilibriums are established. Next, the global asymptotic stability for the system around the positive equilibrium is gained by applying the functional differential equation theory and constructing a proper Lyapunov function. Last, some numerical examples verify the validity and feasibility of previous theoretical results

The dynamics of a delayed generalized fractional-order biological networks with predation behavior and material cycle

In this paper, a delayed generalized fractional-order biological networks with predation behavior and material cycle is comprehensively discussed. Some criteria of stability and bifurcation for the present system is presented. Moreover some results of two delays are obtained. Finally, some numerical simulations are presented to support the analytical results

Stability and bifurcation of a delayed prey-predator eco-epidemiological model with the impact of media

In this paper, a delayed prey-predator eco-epidemiological model with the nonlinear media is considered. First, the positivity and boundedness of solutions are given. Then, the basic reproductive number is showed, and the local stability of the trivial equilibrium and the disease-free equilibrium are discussed. Next, by taking the infection delay as a parameter, the conditions of the stability switches are given due to stability switching criteria, which concludes that the delay can generate instability and oscillation of the population through Hopf bifurcation. Further, by using normal form theory and center manifold theory, some explicit expressions determining direction of Hopf bifurcation and stability of periodic solutions are obtained. What's more, the correctness of the theoretical analysis is verified by numerical simulation, and the biological explanations are also given. Last, the main conclusions are included in the end

Dynamics of nonautonomous eco-pidemiological models

We consider a general eco-epidemiological model which includes a large variety of eco-epidemiological models available in the literature. We assume that the parameters are time dependent and we consider general functions for the predation on infected and uninfected prey and also for the vital dynamics of uninfected prey and predator populations. We studied this model in four scenarios: non-autonomous, periodic, discrete and random. In the non-autonomous and discrete case we discussed the uniform strong persistence and extinction of the disease, in the periodic case, we studied the existence of an endemic periodic orbit, and nally, in the random case we studied the existence of random global attractors.Nesta tese consideramos um modelo eco-epidemiológico geral que inclui uma grande variedade de modelos eco-epidemiológicos presentes na literatura. Assumimos que os parâmetros dependem do tempo e consideramos funções gerais para a predação de presas infectadas e não infectadas e também para a dinâmica vital de presas não infectadas e da população de predadores. Estudamos estes modelos em quatro cenários: não-autónomo geral, periódico, discreto e aleatório. Nos casos não-autónomo geral e discreto analisamos a persistência forte e extinção da doença, no caso periódico estudamos as condições para a existência de uma órbita periódica endémica e, finalmente, no caso aleatório estudamos a existência de atratores globais aleatórios

A Stage-structure Leslie-Gower Model with Linear Harvesting and Disease in Predator

The growth dynamics of various species are affected by various aspects. Harvesting interventions and the spread of disease in species are two important aspects that affect population dynamics and it can be studied. In this work, we consider a stage-structure Leslie–Gower model with linear harvesting on the both prey and predator. Additionally, we also consider the infection aspect in the predator population. The population is divided into four subpopulations: immature prey, mature prey, susceptible predator, and infected predator. We analyze the existences and stabilities of feasible equilibrium points. Our results shown that the harvesting in prey and the disease in predator impacts the behavioral of system. The situation in the system is more complex due to disease in the predator population. Some numerical simulations are given to confirm our results

Hydrological, Anthropogenic and Ecological Processes in Cholera Dynamics

The present Thesis deals with understanding, measuring and modelling epidemic cholera. The relevance of the endeavour stems from the fact that mathematical epidemiology, properly guided by model-guided field validation, is a reliable and powerful tool to monitor and predict ongoing epidemics in time for action, and to save lives through evaluation of the effectiveness of mitigation policies or the deployment of medical staff and supplies. In recent years, waterborne diseases – and cholera in particular – have consolidated their role as a major threat for developing countries, where sanitation conditions are poor and the vulnerability to extreme events is highest. Several important features controlling the dynamics of occurrence and spreading of the disease in a region are studied in the present Thesis, from both theoretical and experimental perspective. Understanding the basic processes that regulate cholera infection is key to build reliable prediction tools. In this Thesis several driving mechanisms of cholera are investigated, with the objective of connecting together hydro-climatology, ecology and epidemiology in a comprehensive framework. First, the role of water volume fluctuations is analyzed partly through a bifurcation study in a mostly theoretical assessment. Such work is then particularized in a field campaign carried out in rural Bangladesh, where hydro-climatological variables and Vibrio cholerae concentrations have been monitored for more than a year in one of the ponds constituting the local water reservoir. Concomitantly, a procedure for the detection of Vibrio cholerae, based on flow cytometry, is tested in the field. Further emphasis is also given to the role of human mobility in disseminating the disease among different communities. In particular, the contribution of human mobility in the dispersal of vibrios along the hydrologic network is specifically analyzed. All the knowledge collected in these studies is then used to add essential details to a modeling framework that is applied to the dramatic case of the Haiti epidemic. A spatially explicit model, taking into account both hydrological transport and human mobility, is developed to simulate the spreading of the disease since its onset. It is also shown that the resurgence of the disease, coinciding with the rainy season of June-July 2011, can only be reproduced if hydrological forcings are considered. The framework is tested by forcing it with synthetic rainfall scenarios and projecting epidemiological outputs. It is shown that the model can quantify correctly the number of cases in a given time span, even when calibrated with limited information. This result allows then to use it as a tool to assess a priori the effectiveness of intervention policies, such as vaccination and sanitation. The effect of these two is tested both in the short- and in the long-term, with different results. Such endeavour represents the ultimate goal of the work presented in this Thesis – albeit further effort is needed to link together public health management and mathematical epidemiology in this field

Mathematical modelling to study infectious diseases: from understanding to prediction

Tesi de modalitat de compendi de publicacionsEach year 10 million people die from communicable diseases. They are infectious diseases caused by agents transmitted between individuals. Nowadays, the two infectious diseases that have the greatest impact are tuberculosis (TB) and coronavirus disease 2019 (COVID-19). According to the World Health Organization, TB killed 40 million individuals in the last 20 years. The COVID-19 pandemic has had an overwhelming effect on human life. It has caused millions of deaths and conditioned people’s life since January 2020. Mathematical and computational models are powerful tools in science to better understand, predict, and condition the dynamics of a desired system. In this thesis, we present a compendium of five publications where mathematical modelling is used to better understand and predict the dynamics of TB and COVID-19 at different spatio-temporal scales. Although TB is a disease identified many years ago, its natural history is not fully understood yet. The main objectives of this thesis in this area are related with the understanding of the factors and processes that facilitate the triggering of an active disease from a latent tuberculosis infection. We also aim at improving understanding of the human-TB coexistence for more than 70,000 years and some of the particularities that have facilitated this coexistence. We have built several models of the pulmonary TB infection at different spatial scales. At the alveolus level, we have seen that the correct balance of the immune response determines the outcome of the infection. At the secondary lobe level, we identified the distance to pulmonary membranes as an important factor to determine final lesion size. At the lung level, we have reproduced a dynamic hypothesis that explains the generation of secondary granulomas after the bronchial dissemination of the infectious bacilli from a preceding lesion. We have assessed the importance of lesion merging as a driving force for the triggering of the active disease. In addition, we have modelled human-TB coexistence in the Paleolithic and Neolithic ages, and determined that female protection against TB was crucial for the survival of the human species. In the Neolithic age, new "modern" lineages emerged, displacing "ancient" ones. Mathematical modelling yields results that explain why this emergence was not possible in the Paleolithic age. When the COVID-19 pandemic started, there was a lack of monitoring systems to help control and manage the pandemic. In this thesis, we focus on several aims related to the assessment of the real incidence during the first wave, as well as on the building and testing of a short-term prediction model. We developed a methodology to estimate the real incidence of COVID-19 based on the estimated lethality and the reported death series. We applied this to several European countries, after analyzing possible bias due to differing age structures. As well, we proposed and calibrated an empirical model based on the Gompertz growth that allows for reliable short-term forecasting at the country level. This thesis demonstrates how mathematical and computational models can be used to predict and better understand important characteristics of infectious diseases such as TB and COVID-19.Cada any 10 milions de persones es moren a causa de malalties transmissibles. Són malalties infeccioses causades per agents que es transmeten entre els diferents individus. Actualment, la tuberculosi (TB) i la COVID-19 són les dues malalties infeccioses que tenen un gran impacte. Segons les estimacions de l’Organització Mundial de la Salut, la TB ha causat la mort de gairebé 40 milions d’individus en els últims 20 anys. La pandèmia de la covid-19 ha afectat enormement la manera de viure de la població mundial. Des del gener del 2020 ha causat milions de morts i ha condicionat les vides i el comportament de les persones. Els models matemàtics i computacionals són una eina fonamental que, en ciència, es poden usar per entendre, predir i/o condicionar la dinàmica d’un sistema en concret. En aquesta tesi presentem un compendi de cinc articles on s’usen els models matemàtics per entendre i predir les dinàmiques de la tuberculosi i la COVID-19 en diferents escales espai-temporals. Tot i que la TB és una malaltia que es va identificar fa molts anys, alguns detalls de la seva història natural encara són desconeguts. L’objectiu principal d’aquesta tesi en relació a la TB és entendre els factors i processos que faciliten el pas de la infecció latent cap a malaltia activa. També hem intentat millorar el coneixement i identificar les particularitats dels 70000 anys de coexistència entre els humans i la TB. S’han creat diferents models de la infecció tuberculosa pulmonar a diferents escales espacials. Al nivell alveolar, hem identificat que el correcte balanç entre la resposta immune i la resposta inflamatòria condiciona el resultat de la infecció. A escala de lòbul secundari, hem vist que la distància entre la lesió i la membrana pulmonar és un factor important que determinarà la seva mida final. A escala del pulmó, s’ha reproduït la hipòtesi dinàmica que ens permet explicar la generació de noves lesions a partir de disseminació bronquial de les lesions inicials. S’ha identificat el procés de fusió de lesions com un dels processos més importants que fa aparèixer lesions més grans i acaba originant la malaltia activa. A més, hem modelitzat la coexistència entre els humans i la TB en el Paleolític i el Neolític. S’ha identificat que la protecció femenina envers la TB va ser crucial per la supervivència de l’espècie humana. En el neolític, van aparèixer soques "modernes" que van desplaçar les “antigues”. Amb models matemàtics s’ha pogut observar perquè aquesta aparició no va ser possible en el paleolític. Quan la pandèmia de la COVID-19 va començar, els sistemes de vigilància que havien de servir per controlar i monitoritzar la pandèmia eren inexistents o deficients. En aquesta tesi hem treballat principalment en dos aspectes per ajudar a la monitorització de la pandèmia: determinar la incidència real de la primera onada i crear un model de prediccions a curt termini. Hem desenvolupat una metodologia per determinar la incidència real que va tenir la COVID-19 basada en la letalitat de la malaltia i les sèries temporals de defuncions. Aquesta metodologia s’ha pogut aplicar a diversos països europeus, tenint en compte els possibles biaixos, per exemple, les diferents piràmides de població. S’ha proposat i calibrat un model empíric bastant en l’equació de Gompertz que ens permet fer una predicció dels casos a curt termini a nivell de país. Aquesta tesi demostra com els models computacionals i matemàtics poden ajudar a predir i entendre millor les característiques de les malalties infeccioses usant com a exemple la tuberculosi i la COVID-19.Cada año 10 millones de personas mueren a causa de enfermedades contagiosas. Son enfermedades infecciosas causadas por agentes que se transmiten entre los diferentes individuos. Hoy en día, la tuberculosis (TB) y el COVID-19 son las dos enfermedades infecciosas que tienen un mayor impacto mundial. Según las estimaciones de la Organización Mundial de la Salud, la TB ha causado la muerte de casi 40 millones de individuos en los últimos 20 años. La pandemia del COVID-19 ha cambiado por completo la forma de vivir de la población mundial. Desde enero de 2020 ha causado millones de muertos y ha condicionado las vidas y el comportamiento de las personas. Los modelos matemáticos y computacionales son una herramienta muy potente que, en ciencia, pueden ayudar a entender, predecir y/o condicionar la dinámica de un sistema en concreto. En esta tesis presentamos un compendio de cinco artículos donde se usan los modelos matemáticos para entender y predecir las dinámicas de la tuberculosis y el COVID-19 en diferentes escalas espacio-temporales. Aunque la TB es una enfermedad que se identificó hace muchos años, algunos detalles de su historia natural aún son desconocidos. El objetivo principal de esta tesis en relación a la TB es entender los factores y procesos que facilitan el paso desde una infección latente a enfermedad activa. También hemos intentado mejorar el conocimiento e identificar las particularidades de los 70000 años de coexistencia entre los humanos y la TB. Hemos creado diferentes modelos sobre la infección tuberculosa pulmonar a diferentes escalas espaciales. A nivel alveolar, hemos identificado que el correcto balance entre la respuesta inmune y la respuesta inflamatoria es determinante para el resultado de la infección. A escala del lóbulo secundario hemos visto que la distancia entre la lesión y la membrana pulmonar es un factor importante que determinará el tamaño final de la lesión. A escala del pulmón, se ha reproducido la hipótesis dinámica que nos permite explicar la generación de nuevas lesiones a partir de diseminación bronquial de las lesiones iniciales. Se ha identificado el proceso de fusión de lesiones como uno de los procesos más importantes que hace aparecer lesiones más grandes y acaba originando la enfermedad activa. Además, hemos modelizado la coexistencia entre los humanos y la TB en el Paleolítico y el Neolítico. Se ha identificado que la protección femenina ante la TB fue crucial para la supervivencia de la especie humana. En el Neolítico, aparecieron cepas ”modernas”que desplazaron las ”antiguas”. Con modelos matemáticos se ha podido observar que esta aparición no era posible en el Paleolítico. Al iniciarse la pandemia del COVID-19, los sistemas de vigilancia que debían servir para controlar y monitorizar la pandemia eran inexistentes o deficientes. En esta tesis hemos trabajado principalmente en dos aspectos para ayudar a la monitorización de la pandemia: determinar la incidencia real de la primera ola y crear un modelo de predicciones a corto plazo. Hemos desarrollado una metodología para determinar la incidencia real que tuvo el COVID-19 basada en la letalidad de la enfermedad y las series temporales de defunciones. Esta metodología se ha podido aplicar en varios países europeos, teniendo en cuenta los posibles sesgos, por ejemplo, las diferentes pirámides de población. También se ha usado y calibrado un modelo empírico basado en la ecuación de Gompertz que nos permite hacer una predicción de los casos a corto plazo a nivel de país. Esta tesis demuestra cómo los modelos computacionales y matemáticos pueden ayudar a predecir y entender mejor las características de las enfermedades infecciosas usando como ejemplo la tuberculosis y el COVID-19.Postprint (published version

Numerical treatment for mathematical model of farming awareness in crop pest management

The most important factor for increasing crop production is pest and pathogen resistance, which has a major impact on global food security. Pest management also emphasizes the need for farming awareness. A high crop yield is ultimately achieved by protecting crops from pests and raising public awareness of the devastation caused by pests. In this research, we aim to investigate the intricate impacts of nonlinear delayed systems for managing crop pest management (CPM) supervised by Ordinary Differential Equations (ODEs). Our focus will be on highlighting the intricate and often unpredictable relationships that occur over time among crops, pests, strategies for rehabilitation, and environmental factors. The nonlinear delayed CPM model incorporated the four compartments: crop biomass density [B(t)], susceptible pest density [S(t)], infected pest density [I(t)], and population awareness level [A(t)]. The approximate solutions for the four compartments B(t), S(t), I(t), and A(t) are determined by the implementation of sundry scenarios generated with the variation in crop biomass growth rate, rate of pest attacks, pest natural death rate, disease associated death rate and memory loss of aware people, by means of exploiting the strength of the Adams (ADS) and explicit Runge-Kutta (ERK) numerical solvers. Comparative analysis of the designed approach is carried out for the dynamic impacts of the nonlinear delayed CPM model in terms of numerical outcomes and simulations based on sundry scenarios