##### Modeling Co-infection of Bovine Brucellosis and Tuberculosis

Paride O. Lolika, Mohamed Y. A. Bakhet, Ben Saliba Lagure

Asian Research Journal of Mathematics, Page 1-13
DOI: 10.9734/arjom/2021/v17i830319

Bovine tuberculosis and bovine brucellosis continue to cause serious economic and public health burden in low-income countries, especially in many regions of sub-Saharan Africa where the diseases are co-endemic. The economic burden of the two infections in low-income countries trigger important questions about the optimal intervention strategies in co-endemic regions. Hence, the need for comprehensive modelling studies to address such questions is therefore essential, yet only a limited of such studies exist to date despite the power of models to predict the future and, most importantly, to quantify the uncertainty in these predictions. Here, we develop a brucellosistuberculosis co-infection modelling framework that incorporates all relevant biological factors and culling of infectious animals-as the sole intervention strategy. We performed an optimal control study to assess the impact of culling infectious animals on controlling the prevalence of the two infections. Two objective functions have been considered, a linear and a quadratic. Existence and the characterization of the optimal control has been determined. Numerical results are carried out to illustrate the main findings. Our findings highlight the importance of optimal culling on controlling the spread of two infections.

##### Existence of Positive Solution For a Fourth-order Differential System

B. Kov´acs

Asian Research Journal of Mathematics, Page 14-29
DOI: 10.9734/arjom/2021/v17i830320

Existence of Positive Solution For a Fourth-order Differential System

where µ > 0 is a constant, and the nonlinear terms f, g may be singular with respect to the time and space variables. By fixed point theorem in cones, the existence is established for singular differential system. The results obtained herein generalize and improve some known results including singular and non-singular cases.

##### Picard and Adomian Solutions of a Nonlocal Cauchy Problem of a Delay Dierential Equation

Asian Research Journal of Mathematics, Page 30-43
DOI: 10.9734/arjom/2021/v17i830321

In this paper, two methods are used to solve a nonlocal Cauchy problem of a delay differential equation; Adomian decomposition method (ADM) and Picard method. The existence and uniqueness of the solution are proved. The convergence of the series solution and the error analysis are studied.

##### Admissible Inversion on Γ1 Non-Deranged Permutations

M. S. Magami, M. Ibrahim

Asian Research Journal of Mathematics, Page 44-53
DOI: 10.9734/arjom/2021/v17i830322

Some further theoretic properties of scheme called Γ1 non deranged permutations, the permutation which fixes the first element in the permutations were identified and studied in relation to admissible inversion in this paper. This was done first through some computation on this scheme using prime number p ≥ 5, the admissible inversion descent aid (ωp-1) is equi-distributed with descent number des (ωp-1) and also showed that the admissible inversion set Ai (ω) and admissible inversion set Ai (ωp-i ) are disjoint.

##### Mathematical Modeling of Transmission Dynamics with Periodic Contact Rate and Control by Different Vaccination Rates of Hepatitis B Infection in Ghana

Ali Abubakar, Reindorf Nartey Borkor, Anas Musah, Frank Kofi Owusu

Asian Research Journal of Mathematics, Page 54-75
DOI: 10.9734/arjom/2021/v17i830323

The paper evidenced that Hepatitis B infection is the world's deadliest liver infection and Vaccination is among the principal clinical strategies in fighting it. These have encouraged a lot of researchers to formulate mathematical models to accurately predict the mode of transmission and make deductions for better health decision-making processes. In this paper, an SEIR model is used to model the transmission of the Hepatitis B infection with periodic contact rate and examine the impact of vaccination. The model was validated using estimated data in Ghana and simulated in a MATLAB environment. The results showed that the vaccination rate has a great impact on the transmission mode of the Hepatitis B infection and the periodic contact rate may lead to a chaotic solution which could result in an uncontrolled spreading of the infection. It is concluded that even if the vaccination rate is 70%, the infection rate would reduce to the minimum barest so more newborns must be vaccinated.

##### Modeling the Transmission Dynamics of Measles in the Presence of Treatment as Control Strategy

Rose Veronica Paul, William Atokolo, Salawu Ademu Saka, Achonu Omale Joseph

Asian Research Journal of Mathematics, Page 76-86
DOI: 10.9734/arjom/2021/v17i830324

We present in this research work, mathematical modeling of the transmission dynamics of measles using treatment as a control measure. We determined the Disease Free Equilibrium (DFE) point of the model after which we obtained the Basic Reproduction Number ( R0 ) of the model using the next generation approach. The model Endemic Equilibrium (EE) point was also determined after which we performed Local Stability Analysis(LAS) of the Disease Free Equilibrium point and result shows that the Disease Free Equilibrium point of the model would be stable if ( R0 <1). Global Stability Analysis (GAS) result shows that, ( R0 ≤ 1) remains the necessary and sufficient condition for the infection to go into extinction from a population. We carried out Sensitivity Analysis of the model using the Basic Reproduction Number and we discovered that ( δ , μ, ν , θ ) are sensitive parameters that should be targeted towards control intervention strategy as an increase in these values can reduce the value of ( R0 ) to a value less than unity and such can reduce the spread of measles in a population. Model simulation was carried out using mat lab software to support our analytical results.