1
|
Li M, Zhang H, Georgescu P, Li T. The stochastic evolution of a rumor spreading model with two distinct spread inhibiting and attitude adjusting mechanisms in a homogeneous social network. Physica A 2021; 562:125321. [PMID: 33012966 PMCID: PMC7524510 DOI: 10.1016/j.physa.2020.125321] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2019] [Revised: 08/19/2020] [Indexed: 05/02/2023]
Abstract
In this paper, we propose and analyze from a stability viewpoint a deterministic, ODE-based class of rumor spreading models with two distinct inhibiting and adjusting mechanisms, together with its corresponding stochastic counterpart. For the deterministic model, a threshold parameter R 0 defined ad hoc, called the basic influence number, is used to ascertain whether the rumors are prevailing or not. If R 0 < 1 , the rumor-free equilibrium is found to be locally asymptotically stable, while if R 0 > 1 it is shown that there is at least one additional rumor-prevailing equilibrium, which is necessarily locally asymptotically stable. For the stochastic model, we first show that there exists a unique global solution. Subsequently, we investigate the asymptotic behavior of the stochastic system around the equilibria of the deterministic system by constructing suitable Lyapunov functionals. Furthermore, numerical simulations are given to illustrate, support and enhance our theoretical analysis.
Collapse
Affiliation(s)
- Ming Li
- School of Economics and Management, Changzhou Institute of Technology, Changzhou, Jiangsu 213032, PR China
| | - Hong Zhang
- School of Economics and Management, Changzhou Institute of Technology, Changzhou, Jiangsu 213032, PR China
| | - Paul Georgescu
- Department of Mathematics, Technical University of Iaşi, Bd. Copou 11A, 700506 Iaşi, Romania
| | - Tan Li
- School of Innovation and Entrepreneurship, Changzhou Institute of Technology, Changzhou, Jiangsu 213032, PR China
| |
Collapse
|
2
|
Harvim P, Zhang H, Georgescu P, Zhang L. Transmission Dynamics and Control Mechanisms of Vector-Borne Diseases with Active and Passive Movements Between Urban and Satellite Cities. Bull Math Biol 2019; 81:4518-4563. [PMID: 31641984 DOI: 10.1007/s11538-019-00671-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2019] [Accepted: 10/10/2019] [Indexed: 11/26/2022]
Abstract
A metapopulation model which explicitly integrates vector-borne and sexual transmission of an epidemic disease with passive and active movements between an urban city and a satellite city is formulated and analysed. The basic reproduction number of the disease is explicitly determined as a combination of sexual and vector-borne transmission parameters. The sensitivity analysis reveals that the disease is primarily transmitted via the vector-borne mode, rather than via sexual transmission, and that sexual transmission by itself may not initiate or sustain an outbreak. Also, increasing the population movements from one city to the other leads to an increase in the basic reproduction number of the later city but a decrease in the basic reproduction number of the former city. The influence of other significant parameters is also investigated via the analysis of suitable partial rank correlation coefficients. After gauging the effects of mobility, we explore the potential effects of optimal control strategies relying upon several distinct restrictions on population movement.
Collapse
Affiliation(s)
- Prince Harvim
- Faculty of Science, Jiangsu University, Zhenjiang, 212013, Jiangsu, People's Republic of China
| | - Hong Zhang
- School of Economics and Management, Changzhou Institute of Technology, Changzhou, 213032, Jiangsu, People's Republic of China
| | - Paul Georgescu
- Department of Mathematics, Technical University of Iaşi, Bd. Copou 11A, 700506, Iasi, Romania
| | - Lai Zhang
- School of Mathematical Science, Yangzhou University, Yangzhou, 225002, Jiangsu, People's Republic of China.
| |
Collapse
|
3
|
Abstract
Many models of mutualism have been proposed and studied individually. In this paper, we develop a general class of models of facultative mutualism that covers many of such published models. Using mild assumptions on the growth and self-limiting functions, we establish necessary and sufficient conditions on the boundedness of model solutions and prove the global stability of a unique coexistence equilibrium whenever it exists. These results allow for a greater flexibility in the way each mutualist species can be modelled and avoid the need to analyse any single model of mutualism in isolation. Our generalization also allows each of the mutualists to be subject to a weak Allee effect. Moreover, we find that if one of the interacting species is subject to a strong Allee effect, then the mutualism can overcome it and cause a unique coexistence equilibrium to be globally stable.
Collapse
Affiliation(s)
- D Maxin
- a Department of Mathematics and Statistics , Valparaiso University , Valparaiso , IN , USA
| | - P Georgescu
- b Department of Mathematics , Technical University of Iaşi , Iaşi , Romania
| | - L Sega
- c Department of Mathematics , Augusta University , Augusta , GA , USA
| | - L Berec
- d Department of Ecology, Institute of Entomology , Biology Centre CAS , České Budějovice , Czech Republic
- e Faculty of Science , Institute of Mathematics and Biomathematics, University of South Bohemia , České Budějovice , Czech Republic
| |
Collapse
|
4
|
Abstract
We analyze the global stability of the coexisting equilibria for several models of commensalism, first by devising a procedure to modify several Lyapunov functionals which were introduced earlier for corresponding models of mutualism, further confirming their usefulness. It is seen that commensalism promotes global stability, in connection with higher-order self-limiting terms which prevent unboundedness. We then use the theory of asymptotically autonomous systems to prove global stability results for models of commensalism which are subject to Allee effects, finding that commensalisms of appropriate strength can overcome the influence of strong Allee effects.
Collapse
Affiliation(s)
- Paul Georgescu
- Department of Mathematics, Technical University of Iaşi, Bld. Copou 11A, 700506 Iaşi, Romania
| | - Daniel Maxin
- Department of Mathematics and Computer Science, Valparaiso University, 1900 Chapel Drive, Valparaiso, IN 46383, USA
| | - Hong Zhang
- Department of Financial Mathematics, Jiangsu University, Zhenjiang, Jiangsu 212013, P. R. China
| |
Collapse
|
5
|
Zhang H, Tian F, Harvim P, Georgescu P. Effects of size refuge specificity on a predator-prey model. Biosystems 2016; 152:11-23. [PMID: 28034644 DOI: 10.1016/j.biosystems.2016.12.001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2016] [Revised: 11/01/2016] [Accepted: 12/06/2016] [Indexed: 11/27/2022]
Abstract
Predation is a major cause of early-stage mortality for prey individuals, which are often forced to use refuges in order to reduce the risk of being consumed. The ability of certain genotypes in a prey population to reach a size refuge from predation may contribute significantly to the preservation of community diversity. We investigate how the specificity of this behavior affects the evolution of a given population by using a modified Lotka-Volterra model, in which the proportion of each genotype available for predation consists of two components: an intrinsic part and a combination from all genotypes present in the population. The trade-off of these components is characterized by a specificity parameter. From the viewpoint of population dynamics, we observe that the ability of the mutant to invade the resident population strongly depends on the values of this parameter. Finally, we describe the possible evolutionary outcomes, analytically and numerically.
Collapse
Affiliation(s)
- Hong Zhang
- Department of Financial Mathematics, Jiangsu University, ZhenJiang, JiangSu 212013, PR China.
| | - Feng Tian
- Faculty of Science, Jiangsu University, ZhenJiang, JiangSu 212013, PR China.
| | - Prince Harvim
- Faculty of Science, Jiangsu University, ZhenJiang, JiangSu 212013, PR China.
| | - Paul Georgescu
- Department of Mathematics, Technical University of Iaşi, Bd. Copou 11A, 700506 Iaşi, Romania.
| |
Collapse
|
6
|
Abstract
We analyze the dynamics of three models of mutualism, establishing the global stability of coexisting equilibria by means of Lyapunov's second method. This further establishes the usefulness of certain Lyapunov functionals of an abstract nature introduced in an earlier paper. As a consequence, it is seen that the use of higher order self-limiting terms cures the shortcomings of Lotka-Volterra mutualisms, preventing unbounded growth and promoting global stability.
Collapse
Affiliation(s)
- Paul Georgescu
- Department of Mathematics, Technical University of Iasi, Bd. Copou 11, 700506 Iasi, Romania.
| | | | | |
Collapse
|
7
|
Georgescu P, Zhang H. An impulsively controlled pest management model with n predator species and a common prey. Biosystems 2012; 110:162-70. [PMID: 23123675 DOI: 10.1016/j.biosystems.2012.10.001] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2012] [Revised: 10/04/2012] [Accepted: 10/05/2012] [Indexed: 10/27/2022]
Abstract
This paper investigates the dynamics of a competitive single-prey n-predators model of integrated pest management, which is subject to periodic and impulsive controls, from the viewpoint of finding sufficient conditions for the extinction of prey and for prey and predator permanence. The per capita death rates of prey due to predation are given in abstract, unspecified forms, which encompass large classes of death rates arising from usual predator functional responses, both prey-dependent and predator-dependent. The stability and permanence conditions are then expressed as balance conditions between the cumulative death rate of prey in a period, due to predation from all predator species and to the use of control, and to the cumulative birth rate of prey in the same amount of time. These results are then specialized for the case of prey-dependent functional responses, their biological significance being also discussed.
Collapse
Affiliation(s)
- Paul Georgescu
- Department of Mathematics, Technical University of Iaşi, Bd. Copou 11, 700506 Iaşi, Romania.
| | | |
Collapse
|
8
|
|
9
|
Zhang H, Georgescu P, Chen L. On the impulsive controllability and bifurcation of a predator-pest model of IPM. Biosystems 2008; 93:151-71. [PMID: 18467020 DOI: 10.1016/j.biosystems.2008.03.008] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2007] [Revised: 03/09/2008] [Accepted: 03/19/2008] [Indexed: 11/16/2022]
Abstract
From a practical point of view, the most efficient strategy for pest control is to combine an array of techniques to control the wide variety of potential pests that may threaten crops in an approach known as integrated pest management (IPM). In this paper, we propose a predator-prey (pest) model of IPM in which pests are impulsively controlled by means of spraying pesticides (the chemical control) and releasing natural predators (the biological control). It is assumed that the biological and chemical control are used with the same periodicity, but not simultaneously. The functional response of the predator is allowed to be predator-dependent, in the form of a Beddington-DeAngelis functional response, rather than to have a perhaps more classical prey-only dependence. The local and global stability of the pest-eradication periodic solution, as well as the permanence of the system, are obtained under integral conditions which are shown to have biological significance. In a certain limiting case, it is shown that a nontrivial periodic solution emerges via a supercritical bifurcation. Finally, our findings are confirmed by means of numerical simulations.
Collapse
Affiliation(s)
- Hong Zhang
- Department of Mathematics, Jiangsu University, Zhenjiang, Jiangsu 212013, PR China.
| | | | | |
Collapse
|
10
|
Georgescu P, Manta D, Traşcă E, Burdescu C, Sabetay C. [A simple procedure for the repair of the abdominal wall in the prevention and treatment of postoperative evisceration]. Rev Chir Oncol Radiol O R L Oftalmol Stomatol Chir 1988; 37:1-4. [PMID: 2969121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
|
11
|
Georgescu P, Pătru V, Bănică D, Serbescu A. [Study of the diagnostic significance of the serum IgE level in patients with bronchial asthma]. Rev Ig Bacteriol Virusol Parazitol Epidemiol Pneumoftiziol Pneumoftiziol 1980; 29:107-13. [PMID: 6252592] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
The serum level of IgE was determined in 59 patients (of whom 36 had atopic asthma, 15 had non-atopic asthma, and 8 had various other pneumopathies with a bronchospastic component). A radioimmunological method was used. The data obtained show that the average values for IgE are high in atopic asthma (796 +/- 161 I.U. per ml). The highest values were of 4.000 I.U. per ml. The average value is clearly different from that found in non-atopic asthmatic patients (185 +/- 30 I.U. per ml), as well as from that recorded in the other patients (260 +/- 76 I.U. per ml), an indication that an assay of the serum level of the type of bronchial asthma. With regard to the di-sodium cromoglycate treatment it was demonstrated that this does not produce signficant changes in the concentration of serum IgE, and it is not possible to foresee, on the basis of the initial level of reagins, what the results of the application of this drug will ultimately be.
Collapse
|
12
|
Georgescu P, Serbescu A, Pătru V, Filip A. [Radioisotope study of the action of rifampicin on immunity conferred by BCG]. Ftiziologia 1973; 22:185-94. [PMID: 4701136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
|
13
|
Proca E, Pop T, Georgescu P, Nicolescu D. Value of sodium-hippuran I-131 clearance for the diagnosis of acute rejection in experimental renal allotransplantation. Int Urol Nephrol 1972; 4:277-84. [PMID: 4592132 DOI: 10.1007/bf02081881] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
|
14
|
Neagu V, Ioanid CP, Georgescu P, Duvan S. [Lithotripsy with hydraulic shock waves]. Chirurgia (Bucur) 1971; 20:781-6. [PMID: 5153910] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
|
15
|
Simici P, Georgescu P, Noica N. [Contribution to the use of an ileal graft in the treatment of complex vesico-vaginal fistulas]. J Urol Nephrol (Paris) 1971; 77:491-8. [PMID: 5115291] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
|
16
|
Georgescu P, Muşeţeanu R, Zaharescu C. [Method for determination of rifampicin in urine]. Ftiziologia 1971; 20:93-6. [PMID: 5162269] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
|
17
|
Cornea P, Georgescu P, Rădulescu R, Ellenbogen S, Marcovici G, Lupescu R, Popesu M. [Pulmonary tuberculosis in psychiatric patients]. Med Interna (Bucur) 1969; 21:831-6. [PMID: 5345127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
|
18
|
Cornea P, Stăncescu I, Georgescu P, Popescu M, Lupescu R, Nicolau G, Volosceanu D, Marcovici G. [Tuberculosis-syphilis correlations. (Clinical and experimental study)]. Med Interna (Bucur) 1968; 20:1387-98. [PMID: 5731993] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
|
19
|
Dimitriu D, Georgescu P, Mares V, Alexandrescu M. [Total ossification of the kdiney or ossified nephrogenic cyst?]. J Urol Nephrol (Paris) 1968; 74:805-12. [PMID: 4973507] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
|
20
|
Păunescu E, Algeorge G, Georgescu P, Berger L. [Alpha-2 globulin and gamma globulin electrophoretic fractions in tuberculosis. Their diagnostic and prognostic value]. Rev Med Chir Soc Med Nat Iasi 1968; 72:311-6. [PMID: 4175780] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
|
21
|
Papadopol S, Georgescu P, Nicolescu D. [Angiotensin resistance test in arterial hypertension of renal origin. Limitations and indications]. Med Interna (Bucur) 1967; 19:933-40. [PMID: 4294761] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
|
22
|
Suciu T, Mogoş I, Iosub A, Georgescu P. Intermittent intraarterial infusions with cytostatics in the treatment of neoplasms of the head and limbs. Rom Med Rev 1966; 20:52-7. [PMID: 5212560] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
|