Numerical Optimization Identification of a Keller-Segel Model for Thermoregulation in Honey Bee Colonies in Winter

Reconstruction coefficient analysis of honeybee collapse due to pesticide contamination

“…In the recent decades, many real phenomena and processes were studied by inverse problems due to their strong mathematical formulation and theoretical study as well as efficient numerical treatment [11,13,14,15,16,21,24]. In the present paper we continue our research on inverse problems modelling the honeybee population dynamics [5,6,7].…”

“…On the second day, we substitute the initial values u(0, x, y) = u 0 (x, y) and c(0, x, y) = c 0 (x, y) with u(1, x, y) = u 1 (x, y) and c(1, x, y) = c 1 (x, y), and then proceed to solve ( 5), ( 6) using this revised initial condition on the time interval t ∈ [1,2]. The identical procedure, employing equations such as (7) for the second day, extends to time intervals [2,3], [3,4].…”

“…Identification of µ(x, y) and α(x, y) in the model with contamination As before, the direct problem is the system ( 5), (6) with known coefficient d, µ, α and siutable initial and boundary conditions. Then, using the theory of PDEs, developed in [24,31], we can obtain existence and uniqueness of classical suficiently smooth solution of the initial boundary value problem for the system (5), (6). Now we consider the case of finding µ(x, y) , α(x, y) and u(t, x, y) , c(t, x, y) that satisfy the system (5), (6) at observation (9) and (10).…”

“…Theorem 3 Suppose (u, c) is the solution of the system (5), (6). Then, there exists a minimizer ( µ(x, y), α(x, y)) ∈ A, such that…”

“…The reasons behind colony losses are attributed to several potential factors, including emerging pathogens and pests, diminished genetic diversity, pesticide usage, scarcity of highquality food, and alterations in the environment [3,6,9,12]. Notable pathogens and pests known to contribute to colony losses encompass Paenibacillus larvae and Melissococcus plutonius (causing American and European foulbrood, respectively), the parasitic mite Varroa destructor, parasitic microsporidia Nosema species, and various honeybee viruses [4,12,19,20].…”