Dynamical Analysis on a Malaria Model with Relapse Preventive Treatment and Saturated Fumigation

Abstract

Malaria has produced health issues in many parts of the world. One of the reason is due to the recurrence phenomenon, which can happen years after the main infection has appeared in the human body. Furthermore, the fumigation intervention, which has become a major worry in several regions of the world, has yielded unsatisfactory results, as seen by the high number of cases reported each year in several African countries. We present a novel mathematical model that integrates tafenoquine treatments to prevent relapse in the human population and saturation fumigation to control mosquito populations in this study. The endemic threshold, also known as the basic reproduction number, is calculated analytically, as is the existence and local stability of the equilibrium points. Through careful investigation, we discovered that the malaria-free equilibrium is locally asymptotically stable if the basic reproduction number is less than one and unstable if it is greater than one. According to the sensitivity analysis, the utilization of tafenoquine treatment is inversely proportional to the basic reproduction number. Although our model never exhibits a backward bifurcation at the basic reproduction number equal to one, we have demonstrated that it is possible; when the basic reproduction number is greater than one, two stable malaria-endemic equilibrium can exist. As a result, when the basic reproduction number is more than one, the final state will be determined by the initial condition of the population. As a result, enormous temporal fumigation can shift the stability of our malaria model from a big endemic size to a smaller endemic size, which is more advantageous in terms of the malaria prevention strategy. Despite the fact that this is not a case study, the numerical results presented in this article are intended to support any theoretical analysis of current malaria eradication tactics in the field.

Collateral Effects of Insecticide-Treated Nets on Human and Environmental Safety in an Epidemiological Model for Malaria with Human Risk Perception

“…As mentioned before, one of the leading mitigation measures over time has been the use of ITNs, which has had a significant impact in the reduction of malaria cases, in combination with other mitigation strategies [ 1 , 7 , 12 , 14 , 41 ]. This result has been supported and analyzed by mathematical models [ 35 , 42 , 43 , 44 , 45 , 46 ].…”

Enhancing Malaria Control Strategy: Optimal Control and Cost‐Effectiveness Analysis on the Impact of Vector Bias on the Efficacy of Mosquito Repellent and Hospitalization

“…As mentioned by [31], vector bias phenomena cannot be ignored in the malaria transmission process since it gives a higher preference to mosquitoes to bite infected humans. Unlike the proposed vector bias model by the author in [15,29,30,53], here, we consider optimal control and asymptomatic cases in our analysis. With this model, infected humans are divided into two compartments, namely, asymptomatic and symptomatic individuals.…”

“…Mathematical models have been employed by many researchers to comprehend how diseases may spread among populations, as demonstrated in references [15][16][17][18]. In the context of malaria transmission models, numerous approaches have been explored to assess how malaria spreads, considering factors such as vector bias [19,20], repellent [21,22], and treatment [23].…”

Modelling the co-infection of malaria and zika virus disease

“…Common symptoms of malaria include headache, profuse sweating, nausea, severe anaemia, high or moderate fever, severe or moderate shaking chills, morbidity, infant mortality, abdominal pain, muscle pain, etc. [5]. Recent studies have shown there is in-1 Duru et al / J. Nig.…”