A Deterministic Model for Q Fever Transmission Dynamics within Dairy Cattle Herds: Using Sensitivity Analysis and Optimal Controls

Abstract

This paper presents a differential equation model which describes a possible transmission route for Q fever dynamics in cattle herds. The model seeks to ascertain epidemiological and theoretical inferences in understanding how to avert an outbreak of Q fever in dairy cattle herds (livestock). To prove the stability of the model’s equilibria, we use a matrix-theoretic method and a Lyapunov function which establishes the local and global asymptotic behaviour of the model. We introduce time-dependent vaccination, environmental hygiene, and culling and then solve for optimal strategies. The optimal control strategies are necessary management practices that may increase animal health in a Coxiella burnetii-induced environment and may also reduce the transmission of the disease from livestock into the human population. The sensitivity analysis presents the relative importance of the various generic parameters in the model. We hope that the description of the results and the optimality trajectories provides some guidelines for animal owners and veterinary officers on how to effectively minimize the bacteria and control cost before/during an outbreak.

Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana

“…Grounded on this, we can say that matrix M has all its off diagonal entries to be non-negative and that matrix M 1 ≥ 0, which proves the properties of Metzler matrix [33] , [36] . Therefore it implies that model (1) is positively invariant in [33] . For alternative proof to the above assertion see Atangana et al.…”

“…The solution set { S ( t ), E ( t ), A ( t ), I ( t ), R ( t ), V ( t )} is positive whenever the parameters are non-negative such that the initial conditions are also given as The proof of Theorem 1 can be obtained using the procedures presented in [33] , as shown below.…”

“…We let and where is transposition, then our differential Eq. (1) can be rewritten in a matrix form as where Now, using the third equation in model (1) , thus and deploying the method of integration factor and change of variables [33] , yields Next, we consider the fourth, fifth, sixth equation of model (1) and using the same above process, we have Hence, from [34] and [35] , we see that and provided with same ideas being valid for S ( t ), this guarantees that the state variable remain positive during the entire scope of the study [33] . Grounded on this, we can say that matrix M has all its off diagonal entries to be non-negative and that matrix M 1 ≥ 0, which proves the properties of Metzler matrix [33] , [36] .…”

Evaluation of the Diagnostic Potential of Recombinant Coxiella burnetii Com1 in an ELISA for the Diagnosis of Q Fever in Sheep, Goats and Cattle

“…An infection in ruminants is often symptomless and serologically negative shedders have been reported [ 7 ]. Symptoms may vary from reproductive disorders, abortion, weak offspring to loss of performance finally causing economic losses [ 8 ]. As reproductive disorders can have different etiologies, Q fever is often not considered and the spread of C. burnetii via aerosols proceeds [ 9 ].…”

Caputo SIR model for COVID-19 under optimized fractional order

“…It is popularly known that the cause of raping transmission is associated directly with the basic reproduction number . The elasticity indices of to the associated parameters in the model are defined as follows [ 39 ]: where denotes the basic reproduction ratio and is as stated above. for model ( 5 ) under consideration is defined by the following expression: Thus, after some computation we reach …”