Mathematical modelling of bacterial resistance to multiple antibiotics and immune system response

Abstract

Resistance of developed bacteria to antibiotic treatment is a very important issue, because introduction of any new antibiotic is after a little while followed by the formation of resistant bacterial isolates in the clinic. The significant increase in clinical resistance to antibiotics is a troubling situation especially in nosocomial infections, where already defenseless patients can be unsuccessful to respond to treatment, causing even greater health issue. Nosocomial infections can be identified as those happening within 2 days of hospital acceptance, 3 days of discharge or 1 month of an operation. They influence 1 out of 10 patients admitted to hospital. Annually, this outcomes in 5000 deaths only in UK with a cost to the National Health Service of a billion pounds. Despite these problems, antibiotic therapy is still the most common method used to treat bacterial infections. On the other hand, it is often mentioned that immune system plays a major role in the progress of infections. In this context, we proposed a mathematical model defining population dynamics of both the specific immune cells produced according to the properties of bacteria by host and the bacteria exposed to multiple antibiotics synchronically, presuming that resistance is gained through mutations due to exposure to antibiotic. Qualitative analysis found out infection-free equilibrium point and other equilibrium points where resistant bacteria and immune system cells exist, only resistant bacteria exists and sensitive bacteria, resistant bacteria and immune system cells exist. As a result of this analysis, our model highlights the fact that when an individual’s immune system weakens, he/she suffers more from the bacterial infections which are believed to have been confined or terminated. Also, these results was supported by numerical simulations.

Switching Logistic Maps to Design Cycling Approaches Against Antimicrobial Resistance

“…For a complete picture of a within-host infection and the corresponding selective pressure that could derive into a new phenotype, the immune responses would need to be modelled. However, this would result in a complex model with many parameters to fit and still difficult to represent the reality [22,12]. As we focus to chronic infections that could not been cleared by the immune system, the main pressure and clearance of pathogenic variants would be directed by the drug.…”

Lokal Bakteriyel enfeksiyon durumunda çoklu antibiyotik tedavisine karşı bakteriyel direncin kesirsel mertebeden matematiksel modellemesi

“…When both the conditions (5) and the polynomial (6) are considered together, the conditions for locally asymptotically stability of the equilibrium point ( 1 , 2 ) are either Routh-Hurwitz conditions ( 1 , 2 > 0) [2,26] or:…”

“…where matrix ( 2 ) is the block matrix of (21). Characteristic equation of (22) Because the biological existence condition of 2 is 0 > , it is 1 , 2 > 0.…”

“…The most common procedure to combat bacterial infection is through antibiotic therapy. Howeover, the most important problem derived from this therapy is the development of the bacteria resistance ability against the used antibiotic [2]. The expression of resistance to antimicrobial agents is both the logical and inevitable consequence of using these agents to treat human infections [3,4].…”

A Simple Mathematical Model Through Fractional-Order Differential Equation for Pathogenic Infection

“…Immune system is called as the system of biological structures and processes in an organism protecting host against the possible harmful organisms by recognizing and responding to the antigens of pathogens [12]. In this context, dynamics between immune system cells of host and pathogen that causes disease are important to understand the nature of disease and are tried to be explained in [13][14][15][16][17][18][19] in different ways. The proposed mathematical model in form, nonlinear autonomous two-dimensional fractional-order differential equation system considered the main mechanisms of pathogen and immune system cells in host, was presented in this study.…”