scholarly journals Immune dynamics in a time of covid

2021 ◽  
Author(s):  
Troy Shinbrot
Keyword(s):  
Mathematical Model ◽  
Immune System ◽  
Disease Progression ◽  
Adaptive Immunity ◽  
Recurrent Infections ◽  
Immunomodulatory Agents ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
The Mathematical Model

Motivated by curiosities of disease progression seen in the coronavirus pandemic, we analyze a minimalist predator-prey model for the immune system (predator) competing against a pathogen (prey). We find that the mathematical model alone accounts for numerous paradoxical behaviors observed in this and other infections. These include why an exponentially growing pathogen requires an exposure threshold to take hold, how chronic and recurrent infections can arise, and what can allow very sick patients to recover, while healthier patients succumb. We also examine the distinct dynamical roles that specific, innate, and nonspecific, adaptive, immunity play, and we describe mathematical effects of infection history on prognosis. Finally, we briefly discuss predictions for some of the effects of timing and strengths of antibiotics or immunomodulatory agents.

scholarly journals Economic and Mathematical Model for Size and Structure Optimisation of Predator and Prey Populations

2019 ◽  
Vol 8 (4) ◽  
pp. 9081-9090
Keyword(s):  
Mathematical Model ◽  
Animal Species ◽  
Volterra Model ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Vito Volterra ◽  
Size And Structure ◽  
Prey Populations

The paper proposes an original economic and mathematical model for size and structure optimisation of Predator and Prey populations. The most well-known mathematical model in biology for periodical dynamics of antagonistic animal species was developed independently by Alfred Lotka and Vito Volterra. This classical mathematical Predator-Prey model is known as the Lotka-Volterra model.

scholarly journals Model matematis predator-prey tanaman padi, hama penggerek batang, tikus, dan wereng batang coklat di Karawang

2018 ◽  
Vol 13 (1) ◽  
pp. 52-62
Author(s):  
Tesa Nur Padilah ◽  
Betha Nurina Sari ◽  
Hannie Hannie
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
Brown Planthopper ◽  
Stem Borer ◽  
Behavioral Analysis ◽  
Predator Prey ◽  
Rice Plants ◽  
Predator Prey Model ◽  
Prey Model ◽  
Plant Pest

Karawang merupakan salah satu pusat penanaman padi di Pulau Jawa. Keberhasilan panen dapat terganggu oleh adanya organisme pengganggu tumbuhan (OPT) sehingga dapat mengancam target swasembada beras. Hubungan antara tanaman padi dengan OPT dapat dibentuk menjadi suatu model matematis yaitu model predator-prey. Untuk itu, penelitian ini bertujuan untuk menganalisis model matematis predator-prey tanaman padi dan OPT. Predator (pemangsa) adalah makhluk hidup yang memakan mangsa (prey). Model predator-prey antara tanaman padi dengan OPT yang dibahas adalah model tiga predator yaitu hama penggerek batang, tikus, dan wereng batang coklat dengan prey yaitu padi. Pertumbuhan padi mengikuti model pertumbuhan logistik. Model yang diturunkan berbentuk sistem persamaan diferensial nonlinier. Pada model diperoleh lima titik ekuilibrium. Analisis perilaku model dilakukan pada tiga titik ekuilibrium dan ketiganya bersifat stabil asimtotik. Simulasi model dengan menggunakan software Maple 13 sejalan dengan analisis perilaku model. Faktor-faktor yang berpengaruh agar populasi hama penggerek batang, tikus, dan wereng batang coklat dapat menurun bahkan hilang dari populasi yaitu tingkat kematian alami serta tingkat interaksi padi terhadap hama-hama tersebut. Predator-prey mathematical model of rice plants, stem borer, rat, and brown planthopper in Karawang AbstractKarawang was one of the center of rice planting in Java Island. The success of the harvest may be disrupted by the presence of plant pest organisms that may threaten the rice self-sufficiency target. The relationship between rice plants and pests can be formed into a mathematical model, that was a predator-prey model. Therefore, this research aimed to analyze the mathematical model of predator-prey between rice plants and plant pest organisme. Predators were living things that eat prey. The predator-prey model between rice plants and pests discussed was a three predator model of stem borer, rat, and brown stem rhizome with the prey, that was rice. Rice growth follows the logistic growth model. The derived model was an nonlinear differential equation system. In this model obtained five equilibrium points. Model behavioral analysis was performed on three equilibrium points and they were stable asymptotically. Simulations of the model using Maple 13 software were in good agreement with behavioral analysis model. Factors that influence the stem borer, rat, and brown planthopper population could decrease even disapear from the population were the natural death rate and the interaction rate of rice to the pests.

scholarly journals Dynamics of an Eco-Epidemic Predator–Prey Model Involving Fractional Derivatives with Power-Law and Mittag–Leffler Kernel

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 785
Author(s):  
Hasan S. Panigoro ◽  
Agus Suryanto ◽  
Wuryansari Muharini Kusumawinahyu ◽  
Isnani Darti
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Derivative ◽  
Equilibrium Point ◽  
Power Law ◽  
Equilibrium Points ◽  
Essential Difference ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Infected Prey

In this paper, we consider a fractional-order eco-epidemic model based on the Rosenzweig–MacArthur predator–prey model. The model is derived by assuming that the prey may be infected by a disease. In order to take the memory effect into account, we apply two fractional differential operators, namely the Caputo fractional derivative (operator with power-law kernel) and the Atangana–Baleanu fractional derivative in the Caputo (ABC) sense (operator with Mittag–Leffler kernel). We take the same order of the fractional derivative in all equations for both senses to maintain the symmetry aspect. The existence and uniqueness of solutions of both eco-epidemic models (i.e., in the Caputo sense and in ABC sense) are established. Both models have the same equilibrium points, namely the trivial (origin) equilibrium point, the extinction of infected prey and predator point, the infected prey free point, the predator-free point and the co-existence point. For a model in the Caputo sense, we also show the non-negativity and boundedness of solution, perform the local and global stability analysis and establish the conditions for the existence of Hopf bifurcation. It is found that the trivial equilibrium point is a saddle point while other equilibrium points are conditionally asymptotically stable. The numerical simulations show that the solutions of the model in the Caputo sense strongly agree with analytical results. Furthermore, it is indicated numerically that the model in the ABC sense has quite similar dynamics as the model in the Caputo sense. The essential difference between the two models is the convergence rate to reach the stable equilibrium point. When a Hopf bifurcation occurs, the bifurcation points and the diameter of the limit cycles of both models are different. Moreover, we also observe a bistability phenomenon which disappears via Hopf bifurcation.

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