Covid-19 is a highly prevalent contagious disease, with high fatalities. With the absence of a one bullet drug or vaccine, infected individual is highly likely to die within a short time. The transmission and progression of Covid-19 can be described using distinct stages, namely exposure and latency, infectiousness, and recovery with waning immunity or death. This implies that, mathematical model will place individuals into four compartments, that is, Susceptible (S), Exposed (E), Infective (I) and Recovered (R), representing a SEIR model. Due to its fast fatal capacity, changes in population due to births do not affect the disease dynamics, but for the purpose of monitoring deaths, a compartment for deaths (D) is incorporated. The analysis of intervention strategies necessitates modification of SEIR model to include Quarantine (Q), Isolation (I), and Homebased care (H) compartments. In this paper, Public health Education Campaign, Quarantine and testing, Isolation, Treatment, use of facemask and Social distance intervention strategies were analyzed. Numerical results indicated that the most responsive mitigation strategy is use of quality facemask and observance of social distance. At 90% adherence to this plan reduces the force of infection from β=0.0197 to β=0.0033. This will consequently reduce the basic reproductive ratio from R 0 =14.0362 to R 0 =2.3388, which prevents 99.37% of population from contracting the disease. However, it is shown that a combination of other intervention strategies have synergetic effect of bringing down reproductive ratio to less than one. Sensitivity analysis indicated that isolation and treatment of infected individuals in government facilities is the most effective method with elasticity of v=-6.4, but due to financial implications, the alternative homebased care need to be fortified. This means, for Covid-19 pandemic to die off, we require early identification of infected individuals through mass testing and immediate isolation. In order to optimize financial constraints associated with isolation, currently at α=11%, the threshold efficacy of other intervention strategies should be enhanced to; public health campaign є > 50%, complacency ξ < 30%, facemask quality c > 89%, social distance r > 2m, and mass testing τ > 0.27. With these interventions, it is estimated that the reproductive ratio, reduces to less than one after 225 days from the first occurrence of Covid-19, and the epidemic will then begin to decline gradually to insignificant levels.

Abstract:The spread of the Human Immunodeficiency Virus (HIV) and the resulting Acquired Immune Deficiency syndrome (AIDS) is a major health concern. Mathematical models are therefore commonly applied to understand the spread of the HIV epidemic. In this study, HIV dynamics is analyzed using a Stochastic Discrete-Time Markov Chain Mathematical Model. Demographic and epidemiological parameters that affect the model population dynamics were investigated. Well posedness of the model determined and the conditions for the existence and stability of disease-free and endemic equilibrium points proved, using the next generation matrix technique. The effect of various intervention strategies, were simulated by varying the parameters representing the possible strategies and comparing the respective values of the reproductive ratio . The numerical simulation results using intervention transition matrix showed that vertical transmission is the most sensitive parameter standing at 0.6 followed by the use of HAART at 0.4. This indicates the strategy which requires much effort to avert progression of infected individual to AIDS.

The current use of Highly Active Anti-Retroviral Therapy (HAART) strategy to control Human Immunodeficiency Virus (HIV) and Acquired Immune Deficiency Syndrome (AIDS) is inefficient in eradicating HIV/AIDS due to inadequate understanding of the dynamics relating to interaction between the immune system components and HIV. As a result, a pool of potential transmitters is continuously created and thus HIV has remained a pandemic. In this paper, we formulate a mathematical model using differential equations to study the effects of time lag τ>0 due to cellular latency and pharmacological delays and chemotherapy on the control strategy of AIDS epidemic. Equilibrium points of the model are computed and used to determine the reproductive ratio〖 R〗_0. This important threshold parameter is then used to determine the critical bounds of time lag τ∈[τ_min,τ_min] and therapeutic window C_p∈[MEC,MTC] that is, the bounds; above Minimum Effect Concentration (MEC) and below Minimum Toxic Concentration (MTC), where drug plasma concentration C_p should lie for effective maintenance of low levels of viral load and reduction of drug toxicity. The mathematical model gives qualitative understanding of HIV prognostic information which is a means of rejuvenating the existing Antiretroviral drugs (ARV’s). Numerical simulations show that a stable and persistent endemic equilibrium state of low viral load is achieved when these thresholds τ∈[0,25] and C_p∈[0.79,0.91] are satisfied. This persistent equilibrium state will lead to eventual eradication of HIV/AIDS.