Modelling the Dynamics of Campylobacteriosis Using Nonstandard Finite Difference Approach with Optimal Control

Abstract

Campylobacter genus is the bacteria responsible for campylobacteriosis infections, and it is the commonest cause of gastroenteritis in adults and infants. The disease is hyperendemic in children in most parts of developing countries. It is a zoonotic disease that can be contracted via direct contact, food, and water. In this paper, we formulated a deterministic model for Campylobacteriosis as a zoonotic disease with optimal control and to determine the best control measure. The nonstandard finite difference scheme was used for the model analysis. The disease-free equilibrium of the scheme in its explicit form was determined, and it was shown to be both locally and globally asymptotically stable. The campylobacteriosis model was extended to optimal control using prevention of susceptible humans contracting the disease and treatment of infected humans and animals. The objective function was optimised, and it was established that combining prevention of susceptible humans and treatment of infected animals was the effective control measure in combating campylobacteriosis infections. An analysis of the effects of contact between susceptible and infected animals as well susceptible and infected humans was conducted. It showed an increase in infected animals and humans whenever the contact rate increases and decreases otherwise. Biologically, it implies that campylobacteriosis infections can be controlled by ensuring that interactions among susceptible humans, infected animals, and infected humans is reduced to the barest minimum.

Using Microbial Responses Viewer and a Regression Approach to Assess the Effect of pH, Activity of Water and Temperature on the Survival of Campylobacter spp.

“…A model for predictive purposes could be a useful tool to increase safety and to prevent foodborne illnesses; however, to the best of our knowledge, few attempts have been made for Campylobacter spp. mainly to model thermal inactivation [ 24 , 25 ] or for a qualitative risk assessment for Campylobacter prevalence and diffusion in the food chain [ 19 , 26 , 27 , 28 ].…”

Dynamics of Tuberculosis (TB) with Drug Resistance to First-Line Treatment and Leaky Vaccination: A Deterministic Modelling Perspective

“…Theorem 4. Let R o be defined as in equation (11). Then, the threshold property holds for system (1).…”

“…The basic reproductive number can be computed utilizing the cutting edge matrix approach. The basic reproduction number determines the state of a disease with time in a dynamical system [ 11 , 12 ]. It is utilized to predict the stability of the disease equilibrium.…”

Modeling the Transmission Routes of Hepatitis E Virus as a Zoonotic Disease Using Fractional-Order Derivative

“…According to the Routh-Hurwitz stability criterion [41][42][43][44], all the eigenvalues of the characteristic Equation (30) have negative real part if and only if R 0 < 1 such that the following conditions hold: q j > 0, j = 1, ⋯, 5 q 1 q 2 − q 3 > 0 q 3 q 1 q 2 − q 3 + q 1 q 5 − q 1 q 4 > 0 q 1 q 2 − q 3 q 4 q 3 − q 2 q 5 − q 5 − q 1 q 4 2 > 0 Theorem 5. The DFE of the system ((1)) is locally asymptotically stable if R 0 < 1 and the conditions ((1))-((4)) above are satisfied.…”